LMFDB - Embedded newform 105.4.d.a.64.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("105.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.84052224.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 6x^{3} + 36x^{2} - 36x + 18 $ x^6 - 2x^5 + 2x^4 + 6x^3 + 36x^2 - 36*x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.3
Root			$0.461746 + 0.461746i$ of defining polynomial
Character	$\chi$	$=$	105.64
Dual form			105.4.d.a.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0765073i q^{2} -3.00000i q^{3} +7.99415 q^{4} +(10.6442 + 3.42057i) q^{5} -0.229522 q^{6} +7.00000i q^{7} -1.22367i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-0.0765073i q^{2} -3.00000i q^{3} +7.99415 q^{4} +(10.6442 + 3.42057i) q^{5} -0.229522 q^{6} +7.00000i q^{7} -1.22367i q^{8} -9.00000 q^{9} +(0.261698 - 0.814361i) q^{10} +10.8947 q^{11} -23.9824i q^{12} +26.5468i q^{13} +0.535551 q^{14} +(10.2617 - 31.9327i) q^{15} +63.8596 q^{16} -95.1237i q^{17} +0.688565i q^{18} +35.4649 q^{19} +(85.0916 + 27.3445i) q^{20} +21.0000 q^{21} -0.833522i q^{22} -62.8303i q^{23} -3.67101 q^{24} +(101.599 + 72.8186i) q^{25} +2.03102 q^{26} +27.0000i q^{27} +55.9590i q^{28} -117.823 q^{29} +(-2.44308 - 0.785094i) q^{30} -171.090 q^{31} -14.6751i q^{32} -32.6840i q^{33} -7.27766 q^{34} +(-23.9440 + 74.5096i) q^{35} -71.9473 q^{36} +203.813i q^{37} -2.71332i q^{38} +79.6404 q^{39} +(4.18564 - 13.0250i) q^{40} -428.705 q^{41} -1.60665i q^{42} +96.5851i q^{43} +87.0936 q^{44} +(-95.7981 - 30.7851i) q^{45} -4.80698 q^{46} -407.806i q^{47} -191.579i q^{48} -49.0000 q^{49} +(5.57115 - 7.77310i) q^{50} -285.371 q^{51} +212.219i q^{52} +380.874i q^{53} +2.06570 q^{54} +(115.965 + 37.2660i) q^{55} +8.56568 q^{56} -106.395i q^{57} +9.01429i q^{58} +287.149 q^{59} +(82.0335 - 255.275i) q^{60} -823.988 q^{61} +13.0897i q^{62} -63.0000i q^{63} +509.754 q^{64} +(-90.8051 + 282.570i) q^{65} -2.50057 q^{66} +585.549i q^{67} -760.433i q^{68} -188.491 q^{69} +(5.70053 + 1.83189i) q^{70} -653.856 q^{71} +11.0130i q^{72} +1051.77i q^{73} +15.5932 q^{74} +(218.456 - 304.798i) q^{75} +283.512 q^{76} +76.2627i q^{77} -6.09307i q^{78} +751.268 q^{79} +(679.736 + 218.436i) q^{80} +81.0000 q^{81} +32.7991i q^{82} -844.677i q^{83} +167.877 q^{84} +(325.377 - 1012.52i) q^{85} +7.38946 q^{86} +353.468i q^{87} -13.3315i q^{88} +262.334 q^{89} +(-2.35528 + 7.32925i) q^{90} -185.828 q^{91} -502.275i q^{92} +513.271i q^{93} -31.2001 q^{94} +(377.497 + 121.310i) q^{95} -44.0252 q^{96} -814.908i q^{97} +3.74886i q^{98} -98.0521 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 14 q^{5} - 6 q^{6} - 54 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 14 * q^5 - 6 * q^6 - 54 * q^9	$ 6 q - 6 q^{4} - 14 q^{5} - 6 q^{6} - 54 q^{9} - 84 q^{10} - 132 q^{11} + 14 q^{14} - 24 q^{15} - 138 q^{16} + 276 q^{19} + 334 q^{20} + 126 q^{21} + 126 q^{24} + 366 q^{25} - 196 q^{26} - 340 q^{29} - 54 q^{30} - 732 q^{31} + 72 q^{34} + 56 q^{35} + 54 q^{36} + 612 q^{39} + 12 q^{40} - 412 q^{41} + 612 q^{44} + 126 q^{45} - 1344 q^{46} - 294 q^{49} + 1216 q^{50} - 912 q^{51} + 54 q^{54} + 1860 q^{55} - 294 q^{56} + 1760 q^{59} + 624 q^{60} - 1740 q^{61} + 1626 q^{64} - 16 q^{65} - 1116 q^{66} - 1080 q^{69} + 126 q^{70} - 2036 q^{71} - 1960 q^{74} + 936 q^{75} - 900 q^{76} + 3240 q^{79} + 3794 q^{80} + 486 q^{81} - 126 q^{84} + 432 q^{85} - 5864 q^{86} + 3876 q^{89} + 756 q^{90} - 1428 q^{91} - 4224 q^{94} - 828 q^{95} + 906 q^{96} + 1188 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 14 * q^5 - 6 * q^6 - 54 * q^9 - 84 * q^10 - 132 * q^11 + 14 * q^14 - 24 * q^15 - 138 * q^16 + 276 * q^19 + 334 * q^20 + 126 * q^21 + 126 * q^24 + 366 * q^25 - 196 * q^26 - 340 * q^29 - 54 * q^30 - 732 * q^31 + 72 * q^34 + 56 * q^35 + 54 * q^36 + 612 * q^39 + 12 * q^40 - 412 * q^41 + 612 * q^44 + 126 * q^45 - 1344 * q^46 - 294 * q^49 + 1216 * q^50 - 912 * q^51 + 54 * q^54 + 1860 * q^55 - 294 * q^56 + 1760 * q^59 + 624 * q^60 - 1740 * q^61 + 1626 * q^64 - 16 * q^65 - 1116 * q^66 - 1080 * q^69 + 126 * q^70 - 2036 * q^71 - 1960 * q^74 + 936 * q^75 - 900 * q^76 + 3240 * q^79 + 3794 * q^80 + 486 * q^81 - 126 * q^84 + 432 * q^85 - 5864 * q^86 + 3876 * q^89 + 756 * q^90 - 1428 * q^91 - 4224 * q^94 - 828 * q^95 + 906 * q^96 + 1188 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	0.0765073i		−	0.0270494i	−0.999909	−	0.0135247i	$-0.995695\pi$
$2$		−	0.0765073i		−	0.0270494i	0.999909	−	0.0135247i	$-0.00430518\pi$
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	7.99415			0.999268
$5$	10.6442	+	3.42057i	0.952049	+	0.305945i
$5$	10.6442	+	3.42057i	0.952049	+	0.305945i
$6$	−0.229522			−0.0156170
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$		−	1.22367i		−	0.0540790i
$9$	−9.00000			−0.333333
$10$	0.261698	−	0.814361i	0.00827562	−	0.0257524i
$11$	10.8947			0.298624			0.149312	−	0.988790i	$-0.452294\pi$
$11$	10.8947			0.298624			0.149312	+	0.988790i	$0.452294\pi$
$12$		−	23.9824i		−	0.576928i
$13$			26.5468i			0.566366i	0.959066	+	0.283183i	$0.0913904\pi$
$13$			26.5468i			0.566366i	−0.959066	+	0.283183i	$0.908610\pi$
$14$	0.535551			0.0102237
$15$	10.2617	−	31.9327i	0.176637	−	0.549666i
$16$	63.8596			0.997806
$17$		−	95.1237i		−	1.35711i	−0.734549	−	0.678556i	$-0.762606\pi$
$17$		−	95.1237i		−	1.35711i	0.734549	−	0.678556i	$-0.237394\pi$
$18$			0.688565i			0.00901647i
$19$	35.4649			0.428221			0.214111	−	0.976809i	$-0.431315\pi$
$19$	35.4649			0.428221			0.214111	+	0.976809i	$0.431315\pi$
$20$	85.0916	+	27.3445i	0.951353	+	0.305721i
$21$	21.0000			0.218218
$22$		−	0.833522i		−	0.00807761i
$23$		−	62.8303i		−	0.569610i	−0.958585	−	0.284805i	$-0.908071\pi$
$23$		−	62.8303i		−	0.569610i	0.958585	−	0.284805i	$-0.0919288\pi$
$24$	−3.67101			−0.0312225
$25$	101.599	+	72.8186i	0.812796	+	0.582549i
$26$	2.03102			0.0153199
$27$			27.0000i			0.192450i
$28$			55.9590i			0.377688i
$29$	−117.823			−0.754452			−0.377226	−	0.926121i	$-0.623122\pi$
$29$	−117.823			−0.754452			−0.377226	+	0.926121i	$0.623122\pi$
$30$	−2.44308	−	0.785094i	−0.0148681	−	0.00477793i
$31$	−171.090			−0.991250			−0.495625	−	0.868537i	$-0.665061\pi$
$31$	−171.090			−0.991250			−0.495625	+	0.868537i	$0.665061\pi$
$32$		−	14.6751i		−	0.0810691i
$33$		−	32.6840i		−	0.172411i
$34$	−7.27766			−0.0367091
$35$	−23.9440	+	74.5096i	−0.115636	+	0.359841i
$36$	−71.9473			−0.333089
$37$			203.813i			0.905584i	0.891616	+	0.452792i	$0.149572\pi$
$37$			203.813i			0.905584i	−0.891616	+	0.452792i	$0.850428\pi$
$38$		−	2.71332i		−	0.0115831i
$39$	79.6404			0.326992
$40$	4.18564	−	13.0250i	0.0165452	−	0.0514859i
$41$	−428.705			−1.63299			−0.816494	−	0.577354i	$-0.804085\pi$
$41$	−428.705			−1.63299			−0.816494	+	0.577354i	$0.804085\pi$
$42$		−	1.60665i		−	0.00590266i
$43$			96.5851i			0.342537i	0.985224	+	0.171268i	$0.0547865\pi$
$43$			96.5851i			0.342537i	−0.985224	+	0.171268i	$0.945213\pi$
$44$	87.0936			0.298406
$45$	−95.7981	−	30.7851i	−0.317350	−	0.101982i
$46$	−4.80698			−0.0154076
$47$		−	407.806i		−	1.26563i	−0.774303	−	0.632816i	$-0.781899\pi$
$47$		−	407.806i		−	1.26563i	0.774303	−	0.632816i	$-0.218101\pi$
$48$		−	191.579i		−	0.576083i
$49$	−49.0000			−0.142857
$50$	5.57115	−	7.77310i	0.0157576	−	0.0219856i
$51$	−285.371			−0.783529
$52$			212.219i			0.565952i
$53$			380.874i			0.987115i	0.869713	+	0.493558i	$0.164304\pi$
$53$			380.874i			0.987115i	−0.869713	+	0.493558i	$0.835696\pi$
$54$	2.06570			0.00520566
$55$	115.965	+	37.2660i	0.284305	+	0.0913625i
$56$	8.56568			0.0204399
$57$		−	106.395i		−	0.247234i
$58$			9.01429i			0.0204075i
$59$	287.149			0.633620			0.316810	−	0.948489i	$-0.397388\pi$
$59$	287.149			0.633620			0.316810	+	0.948489i	$0.397388\pi$
$60$	82.0335	−	255.275i	0.176508	−	0.549264i
$61$	−823.988			−1.72952			−0.864761	−	0.502183i	$-0.832530\pi$
$61$	−823.988			−1.72952			−0.864761	+	0.502183i	$0.832530\pi$
$62$			13.0897i			0.0268127i
$63$		−	63.0000i		−	0.125988i
$64$	509.754			0.995613
$65$	−90.8051	+	282.570i	−0.173277	+	0.539209i
$66$	−2.50057			−0.00466361
$67$			585.549i			1.06770i	0.845578	+	0.533852i	$0.179256\pi$
$67$			585.549i			1.06770i	−0.845578	+	0.533852i	$0.820744\pi$
$68$		−	760.433i		−	1.35612i
$69$	−188.491			−0.328864
$70$	5.70053	+	1.83189i	0.00973348	+	0.00312789i
$71$	−653.856			−1.09294			−0.546468	−	0.837480i	$-0.684028\pi$
$71$	−653.856			−1.09294			−0.546468	+	0.837480i	$0.684028\pi$
$72$			11.0130i			0.0180263i
$73$			1051.77i			1.68630i	0.537676	+	0.843152i	$0.319302\pi$
$73$			1051.77i			1.68630i	−0.537676	+	0.843152i	$0.680698\pi$
$74$	15.5932			0.0244955
$75$	218.456	−	304.798i	0.336335	−	0.469268i
$76$	283.512			0.427908
$77$			76.2627i			0.112869i
$78$		−	6.09307i		−	0.00884493i
$79$	751.268			1.06993			0.534964	−	0.844875i	$-0.320325\pi$
$79$	751.268			1.06993			0.534964	+	0.844875i	$0.320325\pi$
$80$	679.736	+	218.436i	0.949960	+	0.305273i
$81$	81.0000			0.111111
$82$			32.7991i			0.0441713i
$83$		−	844.677i		−	1.11705i	−0.829487	−	0.558526i	$-0.811367\pi$
$83$		−	844.677i		−	1.11705i	0.829487	−	0.558526i	$-0.188633\pi$
$84$	167.877			0.218058
$85$	325.377	−	1012.52i	0.415201	−	1.29204i
$86$	7.38946			0.00926542
$87$			353.468i			0.435583i
$88$		−	13.3315i		−	0.0161493i
$89$	262.334			0.312442			0.156221	−	0.987722i	$-0.450069\pi$
$89$	262.334			0.312442			0.156221	+	0.987722i	$0.450069\pi$
$90$	−2.35528	+	7.32925i	−0.00275854	+	0.00858412i
$91$	−185.828			−0.214066
$92$		−	502.275i		−	0.569193i
$93$			513.271i			0.572298i
$94$	−31.2001			−0.0342346
$95$	377.497	+	121.310i	0.407688	+	0.131012i
$96$	−44.0252			−0.0468052
$97$		−	814.908i		−	0.853004i	−0.904487	−	0.426502i	$-0.859746\pi$
$97$		−	814.908i		−	0.853004i	0.904487	−	0.426502i	$-0.140254\pi$
$98$			3.74886i			0.00386420i
$99$	−98.0521			−0.0995414
$100$	812.201	+	582.123i	0.812201	+	0.582123i
$101$	315.660			0.310984			0.155492	−	0.987837i	$-0.450304\pi$
$101$	315.660			0.310984			0.155492	+	0.987837i	$0.450304\pi$
$102$			21.8330i			0.0211940i
$103$		−	1858.26i		−	1.77767i	−0.458228	−	0.888835i	$-0.651516\pi$
$103$		−	1858.26i		−	1.77767i	0.458228	−	0.888835i	$-0.348484\pi$
$104$	32.4845			0.0306285
$105$	223.529	+	71.8319i	0.207754	+	0.0667626i
$106$	29.1397			0.0267009
$107$			1202.75i			1.08668i	0.839514	+	0.543338i	$0.182840\pi$
$107$			1202.75i			1.08668i	−0.839514	+	0.543338i	$0.817160\pi$
$108$			215.842i			0.192309i
$109$	−262.450			−0.230625			−0.115313	−	0.993329i	$-0.536787\pi$
$109$	−262.450			−0.230625			−0.115313	+	0.993329i	$0.536787\pi$
$110$	2.85112	−	8.87220i	0.00247130	−	0.00769028i
$111$	611.438			0.522839
$112$			447.017i			0.377135i
$113$			138.803i			0.115553i	0.998330	+	0.0577765i	$0.0184011\pi$
$113$			138.803i			0.115553i	−0.998330	+	0.0577765i	$0.981599\pi$
$114$	−8.13997			−0.00668752
$115$	214.915	−	668.781i	0.174269	−	0.542297i
$116$	−941.892			−0.753900
$117$		−	238.921i		−	0.188789i
$118$		−	21.9690i		−	0.0171390i
$119$	665.866			0.512940
$120$	−39.0750	−	12.5569i	−0.0297254	−	0.00955237i
$121$	−1212.31			−0.910824
$122$			63.0411i			0.0467826i
$123$			1286.12i			0.942806i
$124$	−1367.72			−0.990525
$125$	832.368	+	1122.63i	0.595594	+	0.803286i
$126$	−4.81996			−0.00340790
$127$		−	2632.46i		−	1.83931i	−0.392722	−	0.919657i	$-0.628466\pi$
$127$		−	2632.46i		−	1.83931i	0.392722	−	0.919657i	$-0.371534\pi$
$128$		−	156.400i		−	0.108000i
$129$	289.755			0.197764
$130$	21.6187	+	6.94725i	0.0145853	+	0.00468703i
$131$	−301.676			−0.201203			−0.100601	−	0.994927i	$-0.532077\pi$
$131$	−301.676			−0.201203			−0.100601	+	0.994927i	$0.532077\pi$
$132$		−	261.281i		−	0.172285i
$133$			248.254i			0.161852i
$134$	44.7987			0.0288808
$135$	−92.3553	+	287.394i	−0.0588791	+	0.183222i
$136$	−116.400			−0.0733913
$137$			2131.17i			1.32904i	0.747271	+	0.664520i	$0.231364\pi$
$137$			2131.17i			1.32904i	−0.747271	+	0.664520i	$0.768636\pi$
$138$			14.4209i			0.00889559i
$139$	−1691.63			−1.03225			−0.516123	−	0.856515i	$-0.672625\pi$
$139$	−1691.63			−1.03225			−0.516123	+	0.856515i	$0.672625\pi$
$140$	−191.412	+	595.641i	−0.115552	+	0.359578i
$141$	−1223.42			−0.730712
$142$			50.0247i			0.0295633i
$143$			289.219i			0.169131i
$144$	−574.736			−0.332602
$145$	−1254.13	−	403.020i	−0.718276	−	0.230821i
$146$	80.4679			0.0456135
$147$			147.000i			0.0824786i
$148$			1629.31i			0.904921i
$149$	80.4827			0.0442510			0.0221255	−	0.999755i	$-0.492957\pi$
$149$	80.4827			0.0442510			0.0221255	+	0.999755i	$0.492957\pi$
$150$	−23.3193	−	16.7135i	−0.0126934	−	0.00909765i
$151$	833.698			0.449307			0.224654	−	0.974439i	$-0.427875\pi$
$151$	833.698			0.449307			0.224654	+	0.974439i	$0.427875\pi$
$152$		−	43.3973i		−	0.0231578i
$153$			856.114i			0.452371i
$154$	5.83465			0.00305305
$155$	−1821.13	−	585.226i	−0.943719	−	0.303268i
$156$	636.657			0.326752
$157$		−	2108.68i		−	1.07192i	−0.844244	−	0.535960i	$-0.819950\pi$
$157$		−	2108.68i		−	1.07192i	0.844244	−	0.535960i	$-0.180050\pi$
$158$		−	57.4775i		−	0.0289409i
$159$	1142.62			0.569911
$160$	50.1970	−	156.205i	0.0248027	−	0.0771817i
$161$	439.812			0.215292
$162$		−	6.19709i		−	0.00300549i
$163$			174.223i			0.0837189i	0.999124	+	0.0418594i	$0.0133282\pi$
$163$			174.223i			0.0837189i	−0.999124	+	0.0418594i	$0.986672\pi$
$164$	−3427.13			−1.63179
$165$	111.798	−	347.896i	0.0527482	−	0.164144i
$166$	−64.6239			−0.0302156
$167$			1009.94i			0.467972i	0.972240	+	0.233986i	$0.0751771\pi$
$167$			1009.94i			0.467972i	−0.972240	+	0.233986i	$0.924823\pi$
$168$		−	25.6970i		−	0.0118010i
$169$	1492.27			0.679229
$170$	−77.4651	−	24.8937i	−0.0349488	−	0.0112309i
$171$	−319.184			−0.142740
$172$			772.115i			0.342286i
$173$		−	3404.03i		−	1.49598i	−0.663712	−	0.747988i	$-0.731020\pi$
$173$		−	3404.03i		−	1.49598i	0.663712	−	0.747988i	$-0.268980\pi$
$174$	27.0429			0.0117823
$175$	−509.730	+	711.196i	−0.220183	+	0.307208i
$176$	695.729			0.297969
$177$		−	861.446i		−	0.365820i
$178$		−	20.0704i		−	0.00845136i
$179$	1493.22			0.623509			0.311755	−	0.950163i	$-0.399083\pi$
$179$	1493.22			0.623509			0.311755	+	0.950163i	$0.399083\pi$
$180$	−765.824	−	246.101i	−0.317118	−	0.101907i
$181$	−1293.52			−0.531196			−0.265598	−	0.964084i	$-0.585569\pi$
$181$	−1293.52			−0.531196			−0.265598	+	0.964084i	$0.585569\pi$
$182$			14.2172i			0.00579037i
$183$			2471.96i			0.998540i
$184$	−76.8835			−0.0308039
$185$	−697.155	+	2169.43i	−0.277059	+	0.862160i
$186$	39.2690			0.0154803
$187$		−	1036.34i		−	0.405267i
$188$		−	3260.06i		−	1.26471i
$189$	−189.000			−0.0727393
$190$	9.28110	−	28.8812i	0.00354380	−	0.0110277i
$191$	2004.86			0.759510			0.379755	−	0.925087i	$-0.376008\pi$
$191$	2004.86			0.759510			0.379755	+	0.925087i	$0.376008\pi$
$192$		−	1529.26i		−	0.574817i
$193$			446.924i			0.166686i	0.996521	+	0.0833428i	$0.0265596\pi$
$193$			446.924i			0.166686i	−0.996521	+	0.0833428i	$0.973440\pi$
$194$	−62.3464			−0.0230733
$195$	847.711	+	272.415i	0.311312	+	0.100041i
$196$	−391.713			−0.142753
$197$			713.335i			0.257985i	0.991646	+	0.128992i	$0.0411743\pi$
$197$			713.335i			0.257985i	−0.991646	+	0.128992i	$0.958826\pi$
$198$			7.50170i			0.00269254i
$199$	4073.28			1.45099			0.725496	−	0.688227i	$-0.241611\pi$
$199$	4073.28			1.45099			0.725496	+	0.688227i	$0.241611\pi$
$200$	89.1058	−	124.324i	0.0315037	−	0.0439552i
$201$	1756.65			0.616439
$202$		−	24.1503i		−	0.00841192i
$203$		−	824.759i		−	0.285156i
$204$	−2281.30			−0.782955
$205$	−4563.24	−	1466.41i	−1.55468	−	0.499604i
$206$	−142.170			−0.0480849
$207$			565.473i			0.189870i
$208$			1695.27i			0.565123i
$209$	386.378			0.127877
$210$	5.49566	−	17.1016i	0.00180589	−	0.00561963i
$211$	4996.44			1.63018			0.815092	−	0.579331i	$-0.196686\pi$
$211$	4996.44			1.63018			0.815092	+	0.579331i	$0.196686\pi$
$212$			3044.77i			0.986393i
$213$			1961.57i			0.631007i
$214$	92.0192			0.0293939
$215$	−330.376	+	1028.07i	−0.104797	+	0.326112i
$216$	33.0390			0.0104075
$217$		−	1197.63i		−	0.374657i
$218$			20.0793i			0.00623827i
$219$	3155.30			0.973588
$220$	927.045	+	297.909i	0.284097	+	0.0912957i
$221$	2525.23			0.768622
$222$		−	46.7795i		−	0.0141425i
$223$			2326.57i			0.698650i	0.937002	+	0.349325i	$0.113589\pi$
$223$			2326.57i			0.698650i	−0.937002	+	0.349325i	$0.886411\pi$
$224$	102.725			0.0306412
$225$	−914.395	−	655.368i	−0.270932	−	0.194183i
$226$	10.6194			0.00312564
$227$			731.574i			0.213904i	0.994264	+	0.106952i	$0.0341092\pi$
$227$			731.574i			0.213904i	−0.994264	+	0.106952i	$0.965891\pi$
$228$		−	850.535i		−	0.247053i
$229$	913.230			0.263528			0.131764	−	0.991281i	$-0.457936\pi$
$229$	913.230			0.263528			0.131764	+	0.991281i	$0.457936\pi$
$230$	−51.1666	−	16.4426i	−0.0146688	−	0.00471388i
$231$	228.788			0.0651652
$232$			144.176i			0.0408000i
$233$		−	5301.18i		−	1.49052i	−0.666772	−	0.745262i	$-0.732325\pi$
$233$		−	5301.18i		−	1.49052i	0.666772	−	0.745262i	$-0.267675\pi$
$234$	−18.2792			−0.00510662
$235$	1394.93	−	4340.79i	0.387213	−	1.20494i
$236$	2295.51			0.633156
$237$		−	2253.80i		−	0.617723i
$238$		−	50.9436i		−	0.0138747i
$239$	2696.95			0.729920			0.364960	−	0.931023i	$-0.381083\pi$
$239$	2696.95			0.729920			0.364960	+	0.931023i	$0.381083\pi$
$240$	655.307	−	2039.21i	0.176250	−	0.548460i
$241$	4299.38			1.14916			0.574579	−	0.818449i	$-0.305166\pi$
$241$	4299.38			1.14916			0.574579	+	0.818449i	$0.305166\pi$
$242$			92.7502i			0.0246372i
$243$		−	243.000i		−	0.0641500i
$244$	−6587.08			−1.72826
$245$	−521.567	−	167.608i	−0.136007	−	0.0437064i
$246$	98.3972			0.0255023
$247$			941.480i			0.242530i
$248$			209.358i			0.0536058i
$249$	−2534.03			−0.644930
$250$	85.8891	−	63.6822i	0.0217284	−	0.0161105i
$251$	4712.81			1.18514			0.592570	−	0.805519i	$-0.298113\pi$
$251$	4712.81			1.18514			0.592570	+	0.805519i	$0.298113\pi$
$252$		−	503.631i		−	0.125896i
$253$		−	684.516i		−	0.170099i
$254$	−201.402			−0.0497524
$255$	−3037.56	−	976.131i	−0.745958	−	0.239716i
$256$	4066.06			0.992691
$257$			6833.53i			1.65861i	0.558793	+	0.829307i	$0.311265\pi$
$257$			6833.53i			1.65861i	−0.558793	+	0.829307i	$0.688735\pi$
$258$		−	22.1684i		−	0.00534939i
$259$	−1426.69			−0.342278
$260$	−725.909	+	2258.91i	−0.173150	+	0.538814i
$261$	1060.40			0.251484
$262$			23.0804i			0.00544242i
$263$		−	8221.38i		−	1.92757i	−0.266674	−	0.963787i	$-0.585925\pi$
$263$		−	8221.38i		−	1.92757i	0.266674	−	0.963787i	$-0.414075\pi$
$264$	−39.9944			−0.00932381
$265$	−1302.81	+	4054.12i	−0.302003	+	0.939783i
$266$	18.9933			0.00437801
$267$		−	787.001i		−	0.180388i
$268$			4680.96i			1.06692i
$269$	−6319.20			−1.43230			−0.716149	−	0.697947i	$-0.754097\pi$
$269$	−6319.20			−1.43230			−0.716149	+	0.697947i	$0.754097\pi$
$270$	21.9878	+	7.06585i	0.00495604	+	0.00159264i
$271$	−1127.67			−0.252771			−0.126386	−	0.991981i	$-0.540338\pi$
$271$	−1127.67			−0.252771			−0.126386	+	0.991981i	$0.540338\pi$
$272$		−	6074.56i		−	1.35413i
$273$			557.483i			0.123591i
$274$	163.050			0.0359497
$275$	1106.89	+	793.335i	0.242721	+	0.173963i
$276$	−1506.82			−0.328624
$277$			2522.90i			0.547243i	0.961837	+	0.273622i	$0.0882216\pi$
$277$			2522.90i			0.547243i	−0.961837	+	0.273622i	$0.911778\pi$
$278$			129.422i			0.0279216i
$279$	1539.81			0.330417
$280$	91.1751	+	29.2995i	0.0194598	+	0.00625349i
$281$	−9070.33			−1.92559			−0.962794	−	0.270235i	$-0.912898\pi$
$281$	−9070.33			−1.92559			−0.962794	+	0.270235i	$0.912898\pi$
$282$			93.6004i			0.0197653i
$283$		−	145.080i		−	0.0304739i	−0.999884	−	0.0152369i	$-0.995150\pi$
$283$		−	145.080i		−	0.0304739i	0.999884	−	0.0152369i	$-0.00485025\pi$
$284$	−5227.02			−1.09214
$285$	363.930	−	1132.49i	0.0756398	−	0.235379i
$286$	22.1273			0.00457489
$287$		−	3000.94i		−	0.617211i
$288$			132.076i			0.0270230i
$289$	−4135.53			−0.841752
$290$	−30.8340	+	95.9502i	−0.00624356	+	0.0194289i
$291$	−2444.73			−0.492482
$292$			8407.99i			1.68507i
$293$			5876.23i			1.17165i	0.810438	+	0.585824i	$0.199229\pi$
$293$			5876.23i			1.17165i	−0.810438	+	0.585824i	$0.800771\pi$
$294$	11.2466			0.00223100
$295$	3056.48	+	982.211i	0.603237	+	0.193853i
$296$	249.399			0.0489731
$297$			294.156i			0.0574703i
$298$		−	6.15751i		−	0.00119696i
$299$	1667.94			0.322608
$300$	1746.37	−	2436.60i	0.336089	−	0.468924i
$301$	−676.095			−0.129467
$302$		−	63.7839i		−	0.0121535i
$303$		−	946.980i		−	0.179547i
$304$	2264.77			0.427282
$305$	−8770.72	−	2818.51i	−1.64659	−	0.529138i
$306$	65.4989			0.0122364
$307$			2894.45i			0.538094i	0.963127	+	0.269047i	$0.0867087\pi$
$307$			2894.45i			0.538094i	−0.963127	+	0.269047i	$0.913291\pi$
$308$			609.655i			0.112787i
$309$	−5574.78			−1.02634
$310$	−44.7740	+	139.329i	−0.00820321	+	0.0255270i
$311$	3009.61			0.548744			0.274372	−	0.961624i	$-0.411530\pi$
$311$	3009.61			0.548744			0.274372	+	0.961624i	$0.411530\pi$
$312$		−	97.4535i		−	0.0176834i
$313$			10064.0i			1.81741i	0.417436	+	0.908706i	$0.362929\pi$
$313$			10064.0i			1.81741i	−0.417436	+	0.908706i	$0.637071\pi$
$314$	−161.330			−0.0289948
$315$	215.496	−	670.587i	0.0385454	−	0.119947i
$316$	6005.75			1.06914
$317$		−	8304.18i		−	1.47132i	−0.677349	−	0.735661i	$-0.736871\pi$
$317$		−	8304.18i		−	1.47132i	0.677349	−	0.735661i	$-0.263129\pi$
$318$		−	87.4190i		−	0.0154158i
$319$	−1283.64			−0.225298
$320$	5425.94	+	1743.65i	0.947872	+	0.304602i
$321$	3608.25			0.627393
$322$		−	33.6488i		−	0.00582353i
$323$		−	3373.55i		−	0.581144i
$324$	647.526			0.111030
$325$	−1933.10	+	2697.14i	−0.329936	+	0.460340i
$326$	13.3293			0.00226455
$327$			787.349i			0.133151i
$328$			524.593i			0.0883103i
$329$	2854.64			0.478364
$330$	−26.6166	−	8.55335i	−0.00443999	−	0.00142681i
$331$	−7066.25			−1.17340			−0.586702	−	0.809803i	$-0.699574\pi$
$331$	−7066.25			−1.17340			−0.586702	+	0.809803i	$0.699574\pi$
$332$		−	6752.47i		−	1.11623i
$333$		−	1834.31i		−	0.301861i
$334$	77.2677			0.0126584
$335$	−2002.91	+	6232.72i	−0.326658	+	1.01651i
$336$	1341.05			0.217739
$337$		−	1510.59i		−	0.244175i	−0.992519	−	0.122087i	$-0.961041\pi$
$337$		−	1510.59i		−	0.244175i	0.992519	−	0.122087i	$-0.0389588\pi$
$338$		−	114.169i		−	0.0183727i
$339$	416.409			0.0667145
$340$	2601.11	−	8094.23i	0.414897	−	1.29109i
$341$	−1863.97			−0.296011
$342$			24.4199i			0.00386104i
$343$		−	343.000i		−	0.0539949i
$344$	118.188			0.0185241
$345$	−2006.34	−	644.746i	−0.313095	−	0.100614i
$346$	−260.433			−0.0404653
$347$			11921.4i			1.84431i	0.386822	+	0.922154i	$0.373573\pi$
$347$			11921.4i			1.84431i	−0.386822	+	0.922154i	$0.626427\pi$
$348$			2825.68i			0.435265i
$349$	3329.00			0.510594			0.255297	−	0.966863i	$-0.417827\pi$
$349$	3329.00			0.510594			0.255297	+	0.966863i	$0.417827\pi$
$350$	54.4117	+	38.9981i	0.00830979	+	0.00595581i
$351$	−716.764			−0.108997
$352$		−	159.880i		−	0.0242092i
$353$		−	5883.87i		−	0.887158i	−0.896235	−	0.443579i	$-0.853709\pi$
$353$		−	5883.87i		−	0.887158i	0.896235	−	0.443579i	$-0.146291\pi$
$354$	−65.9069			−0.00989523
$355$	−6959.80	−	2236.56i	−1.04053	−	0.334378i
$356$	2097.13			0.312213
$357$		−	1997.60i		−	0.296146i
$358$		−	114.242i		−	0.0168656i
$359$	−822.114			−0.120862			−0.0604311	−	0.998172i	$-0.519248\pi$
$359$	−822.114			−0.120862			−0.0604311	+	0.998172i	$0.519248\pi$
$360$	−37.6707	+	117.225i	−0.00551506	+	0.0171620i
$361$	−5601.24			−0.816626
$362$			98.9636i			0.0143685i
$363$			3636.92i			0.525864i
$364$	−1485.53			−0.213910
$365$	−3597.64	+	11195.3i	−0.515916	+	1.60544i
$366$	189.123			0.0270099
$367$		−	9873.06i		−	1.40428i	−0.712040	−	0.702139i	$-0.752229\pi$
$367$		−	9873.06i		−	1.40428i	0.712040	−	0.702139i	$-0.247771\pi$
$368$		−	4012.32i		−	0.568360i
$369$	3858.35			0.544329
$370$	165.977	+	53.3374i	0.0233209	+	0.00749427i
$371$	−2666.12			−0.373095
$372$			4103.17i			0.571880i
$373$		−	7152.24i		−	0.992840i	−0.868083	−	0.496420i	$-0.834648\pi$
$373$		−	7152.24i		−	0.992840i	0.868083	−	0.496420i	$-0.165352\pi$
$374$	−79.2877			−0.0109622
$375$	3367.88	−	2497.10i	0.463777	−	0.343866i
$376$	−499.020			−0.0684441
$377$		−	3127.82i		−	0.427296i
$378$			14.4599i			0.00196755i
$379$	14117.4			1.91336			0.956680	−	0.291140i	$-0.0940346\pi$
$379$	14117.4			1.91336			0.956680	+	0.291140i	$0.0940346\pi$
$380$	3017.76	+	969.770i	0.407390	+	0.130916i
$381$	−7897.38			−1.06193
$382$		−	153.386i		−	0.0205443i
$383$			5293.18i			0.706185i	0.935588	+	0.353093i	$0.114870\pi$
$383$			5293.18i			0.706185i	−0.935588	+	0.353093i	$0.885130\pi$
$384$	−469.201			−0.0623537
$385$	−260.862	+	811.758i	−0.0345318	+	0.107457i
$386$	34.1930			0.00450875
$387$		−	869.266i		−	0.114179i
$388$		−	6514.50i		−	0.852380i
$389$	8910.01			1.16132			0.580662	−	0.814144i	$-0.302794\pi$
$389$	8910.01			1.16132			0.580662	+	0.814144i	$0.302794\pi$
$390$	20.8418	−	64.8561i	0.00270606	−	0.00842081i
$391$	−5976.66			−0.773024
$392$			59.9598i			0.00772557i
$393$			905.029i			0.116165i
$394$	54.5753			0.00697834
$395$	7996.67	+	2569.76i	1.01862	+	0.327339i
$396$	−783.843			−0.0994686
$397$			3986.11i			0.503922i	0.967737	+	0.251961i	$0.0810755\pi$
$397$			3986.11i			0.503922i	−0.967737	+	0.251961i	$0.918925\pi$
$398$		−	311.636i		−	0.0392485i
$399$	744.763			0.0934456
$400$	6488.10	+	4650.16i	0.811012	+	0.581271i
$401$	3119.10			0.388429			0.194215	−	0.980959i	$-0.437784\pi$
$401$	3119.10			0.388429			0.194215	+	0.980959i	$0.437784\pi$
$402$		−	134.396i		−	0.0166743i
$403$		−	4541.90i		−	0.561410i
$404$	2523.43			0.310756
$405$	862.183	+	277.066i	0.105783	+	0.0339939i
$406$	−63.1000			−0.00771331
$407$			2220.47i			0.270429i
$408$			349.200i			0.0423725i
$409$	4125.99			0.498819			0.249410	−	0.968398i	$-0.419763\pi$
$409$	4125.99			0.498819			0.249410	+	0.968398i	$0.419763\pi$
$410$	−112.191	+	349.121i	−0.0135140	+	0.0420533i
$411$	6393.52			0.767321
$412$		−	14855.2i		−	1.77637i
$413$			2010.04i			0.239486i
$414$	43.2628			0.00513587
$415$	2889.27	−	8990.94i	0.341756	−	1.06349i
$416$	389.576			0.0459148
$417$			5074.89i			0.595967i
$418$		−	29.5608i		−	0.00345901i
$419$	13550.2			1.57988			0.789939	−	0.613185i	$-0.210112\pi$
$419$	13550.2			1.57988			0.789939	+	0.613185i	$0.210112\pi$
$420$	1786.92	+	574.235i	0.207602	+	0.0667138i
$421$	6464.49			0.748361			0.374180	−	0.927356i	$-0.377924\pi$
$421$	6464.49			0.748361			0.374180	+	0.927356i	$0.377924\pi$
$422$		−	382.264i		−	0.0440955i
$423$			3670.26i			0.421877i
$424$	466.064			0.0533822
$425$	6926.78	−	9664.52i	0.790584	−	1.10305i
$426$	150.074			0.0170684
$427$		−	5767.92i		−	0.653698i
$428$			9614.97i			1.08588i
$429$	867.656			0.0976477
$430$	78.6551	+	25.2761i	0.00882113	+	0.00283471i
$431$	−8652.70			−0.967020			−0.483510	−	0.875339i	$-0.660638\pi$
$431$	−8652.70			−0.967020			−0.483510	+	0.875339i	$0.660638\pi$
$432$			1724.21i			0.192028i
$433$			10201.3i			1.13221i	0.824334	+	0.566103i	$0.191550\pi$
$433$			10201.3i			1.13221i	−0.824334	+	0.566103i	$0.808450\pi$
$434$	−91.6276			−0.0101343
$435$	−1209.06	+	3762.40i	−0.133264	+	0.414697i
$436$	−2098.06			−0.230456
$437$		−	2228.27i		−	0.243919i
$438$		−	241.404i		−	0.0263350i
$439$	−13063.9			−1.42029			−0.710143	−	0.704057i	$-0.751370\pi$
$439$	−13063.9			−1.42029			−0.710143	+	0.704057i	$0.751370\pi$
$440$	45.6012	−	141.903i	0.00494080	−	0.0153749i
$441$	441.000			0.0476190
$442$		−	193.199i		−	0.0207908i
$443$		−	2032.27i		−	0.217959i	−0.994044	−	0.108980i	$-0.965242\pi$
$443$		−	2032.27i		−	0.217959i	0.994044	−	0.108980i	$-0.0347583\pi$
$444$	4887.93			0.522456
$445$	2792.34	+	897.329i	0.297460	+	0.0955899i
$446$	178.000			0.0188981
$447$		−	241.448i		−	0.0255483i
$448$			3568.28i			0.376306i
$449$	−1640.75			−0.172454			−0.0862271	−	0.996276i	$-0.527481\pi$
$449$	−1640.75			−0.172454			−0.0862271	+	0.996276i	$0.527481\pi$
$450$	−50.1404	+	69.9579i	−0.00525253	+	0.00732855i
$451$	−4670.60			−0.487650
$452$			1109.61i			0.115468i
$453$		−	2501.09i		−	0.259408i
$454$	55.9707			0.00578598
$455$	−1977.99	−	635.636i	−0.203802	−	0.0654925i
$456$	−130.192			−0.0133702
$457$			5578.74i			0.571033i	0.958374	+	0.285517i	$0.0921652\pi$
$457$			5578.74i			0.571033i	−0.958374	+	0.285517i	$0.907835\pi$
$458$		−	69.8687i		−	0.00712828i
$459$	2568.34			0.261176
$460$	1718.06	−	5346.33i	0.174142	−	0.541900i
$461$	−15124.5			−1.52803			−0.764013	−	0.645201i	$-0.776773\pi$
$461$	−15124.5			−1.52803			−0.764013	+	0.645201i	$0.776773\pi$
$462$		−	17.5040i		−	0.00176268i
$463$		−	14882.8i		−	1.49387i	−0.664898	−	0.746934i	$-0.731525\pi$
$463$		−	14882.8i		−	1.49387i	0.664898	−	0.746934i	$-0.268475\pi$
$464$	−7524.10			−0.752797
$465$	−1755.68	+	5463.38i	−0.175092	+	0.544856i
$466$	−405.579			−0.0403178
$467$			5926.96i			0.587296i	0.955914	+	0.293648i	$0.0948693\pi$
$467$			5926.96i			0.587296i	−0.955914	+	0.293648i	$0.905131\pi$
$468$		−	1909.97i		−	0.188651i
$469$	−4098.84			−0.403554
$470$	−332.102	−	106.722i	−0.0325930	−	0.0104739i
$471$	−6326.05			−0.618873
$472$		−	351.375i		−	0.0342655i
$473$			1052.26i			0.102290i
$474$	−172.432			−0.0167090
$475$	3603.21	+	2582.50i	0.348056	+	0.249460i
$476$	5323.03			0.512565
$477$		−	3427.87i		−	0.329038i
$478$		−	206.336i		−	0.0197439i
$479$	−13214.0			−1.26046			−0.630231	−	0.776407i	$-0.717040\pi$
$479$	−13214.0			−1.26046			−0.630231	+	0.776407i	$0.717040\pi$
$480$	−468.615	−	150.591i	−0.0445609	−	0.0143198i
$481$	−5410.58			−0.512892
$482$		−	328.933i		−	0.0310840i
$483$		−	1319.44i		−	0.124299i
$484$	−9691.35			−0.910157
$485$	2787.45	−	8674.08i	0.260972	−	0.812102i
$486$	−18.5913			−0.00173522
$487$			17646.0i			1.64192i	0.570984	+	0.820961i	$0.306562\pi$
$487$			17646.0i			1.64192i	−0.570984	+	0.820961i	$0.693438\pi$
$488$			1008.29i			0.0935309i
$489$	522.668			0.0483351
$490$	−12.8232	+	39.9037i	−0.00118223	+	0.00367891i
$491$	−11540.7			−1.06074			−0.530371	−	0.847766i	$-0.677947\pi$
$491$	−11540.7			−1.06074			−0.530371	+	0.847766i	$0.677947\pi$
$492$			10281.4i			0.942116i
$493$			11207.7i			1.02388i
$494$	72.0301			0.00656029
$495$	−1043.69	−	335.394i	−0.0947684	−	0.0304542i
$496$	−10925.8			−0.989075
$497$		−	4576.99i		−	0.413091i
$498$			193.872i			0.0174450i
$499$	6820.43			0.611873			0.305936	−	0.952052i	$-0.401031\pi$
$499$	6820.43			0.611873			0.305936	+	0.952052i	$0.401031\pi$
$500$	6654.07	+	8974.44i	0.595158	+	0.802698i
$501$	3029.82			0.270184
$502$		−	360.564i		−	0.0320573i
$503$			7174.71i			0.635993i	0.948092	+	0.317996i	$0.103010\pi$
$503$			7174.71i			0.635993i	−0.948092	+	0.317996i	$0.896990\pi$
$504$	−77.0911			−0.00681332
$505$	3359.96	+	1079.74i	0.296072	+	0.0951438i
$506$	−52.3704			−0.00460109
$507$		−	4476.80i		−	0.392153i
$508$		−	21044.3i		−	1.83797i
$509$	3889.82			0.338729			0.169365	−	0.985553i	$-0.445828\pi$
$509$	3889.82			0.338729			0.169365	+	0.985553i	$0.445828\pi$
$510$	−74.6811	+	232.395i	−0.00648419	+	0.0201777i
$511$	−7362.38			−0.637363
$512$		−	1562.29i		−	0.134851i
$513$			957.552i			0.0824112i
$514$	522.815			0.0448645
$515$	6356.30	−	19779.8i	0.543868	−	1.69243i
$516$	2316.35			0.197619
$517$		−	4442.92i		−	0.377948i
$518$			109.152i			0.00925843i
$519$	−10212.1			−0.863702
$520$	345.773	+	111.115i	0.0291599	+	0.00937064i
$521$	3687.49			0.310080			0.155040	−	0.987908i	$-0.450449\pi$
$521$	3687.49			0.310080			0.155040	+	0.987908i	$0.450449\pi$
$522$		−	81.1286i		−	0.00680250i
$523$		−	8280.56i		−	0.692320i	−0.938175	−	0.346160i	$-0.887485\pi$
$523$		−	8280.56i		−	0.692320i	0.938175	−	0.346160i	$-0.112515\pi$
$524$	−2411.65			−0.201056
$525$	2133.59	+	1529.19i	0.177367	+	0.127123i
$526$	−628.995			−0.0521397
$527$			16274.8i			1.34524i
$528$		−	2087.19i		−	0.172032i
$529$	8219.35			0.675545
$530$	310.169	+	99.6741i	0.0254206	+	0.00816900i
$531$	−2584.34			−0.211207
$532$			1984.58i			0.161734i
$533$		−	11380.8i		−	0.924869i
$534$	−60.2113			−0.00487940
$535$	−4114.09	+	12802.4i	−0.332463	+	1.03457i
$536$	716.518			0.0577404
$537$		−	4479.65i		−	0.359983i
$538$			483.465i			0.0387428i
$539$	−533.839			−0.0426606
$540$	−738.302	+	2297.47i	−0.0588360	+	0.183088i
$541$	9002.84			0.715457			0.357728	−	0.933826i	$-0.383551\pi$
$541$	9002.84			0.715457			0.357728	+	0.933826i	$0.383551\pi$
$542$			86.2748i			0.00683731i
$543$			3880.56i			0.306686i
$544$	−1395.95			−0.110020
$545$	−2793.58	−	897.727i	−0.219566	−	0.0705585i
$546$	42.6515			0.00334307
$547$		−	17066.3i		−	1.33401i	−0.745053	−	0.667005i	$-0.767576\pi$
$547$		−	17066.3i		−	1.33401i	0.745053	−	0.667005i	$-0.232424\pi$
$548$			17036.9i			1.32807i
$549$	7415.89			0.576508
$550$	60.6959	−	84.6854i	0.00470560	−	0.00656545i
$551$	−4178.57			−0.323073
$552$			230.650i			0.0177847i
$553$			5258.88i			0.404395i
$554$	193.020			0.0148026
$555$	6508.29	+	2091.46i	0.497769	+	0.159960i
$556$	−13523.1			−1.03149
$557$			23487.4i			1.78670i	0.449360	+	0.893351i	$0.351652\pi$
$557$			23487.4i			1.78670i	−0.449360	+	0.893351i	$0.648348\pi$
$558$		−	117.807i		−	0.00893757i
$559$	−2564.03			−0.194001
$560$	−1529.05	+	4758.15i	−0.115382	+	0.359051i
$561$	−3109.03			−0.233981
$562$			693.946i			0.0520860i
$563$			15357.7i			1.14964i	0.818279	+	0.574821i	$0.194928\pi$
$563$			15357.7i			1.14964i	−0.818279	+	0.574821i	$0.805072\pi$
$564$	−9780.19			−0.730178
$565$	−474.785	+	1477.45i	−0.0353528	+	0.110012i
$566$	−11.0997			−0.000824300
$567$			567.000i			0.0419961i
$568$			800.103i			0.0591049i
$569$	−8871.22			−0.653604			−0.326802	−	0.945093i	$-0.605971\pi$
$569$	−8871.22			−0.653604			−0.326802	+	0.945093i	$0.605971\pi$
$570$	−86.6437	−	27.8433i	−0.00636685	−	0.00204601i
$571$	−6428.16			−0.471121			−0.235561	−	0.971860i	$-0.575693\pi$
$571$	−6428.16			−0.471121			−0.235561	+	0.971860i	$0.575693\pi$
$572$			2312.06i			0.169007i
$573$		−	6014.57i		−	0.438503i
$574$	−229.593			−0.0166952
$575$	4575.22	−	6383.53i	0.331826	−	0.462976i
$576$	−4587.78			−0.331871
$577$		−	8519.56i		−	0.614686i	−0.951599	−	0.307343i	$-0.900560\pi$
$577$		−	8519.56i		−	0.614686i	0.951599	−	0.307343i	$-0.0994399\pi$
$578$			316.398i			0.0227689i
$579$	1340.77			0.0962360
$580$	−10025.7	−	3221.80i	−0.717750	−	0.230652i
$581$	5912.74			0.422206
$582$			187.039i			0.0133214i
$583$			4149.50i			0.294777i
$584$	1287.02			0.0911936
$585$	817.246	−	2543.13i	0.0577589	−	0.179736i
$586$	449.574			0.0316924
$587$		−	13458.2i		−	0.946300i	−0.880982	−	0.473150i	$-0.843117\pi$
$587$		−	13458.2i		−	0.946300i	0.880982	−	0.473150i	$-0.156883\pi$
$588$			1175.14i			0.0824183i
$589$	−6067.70			−0.424474
$590$	75.1463	−	233.843i	0.00524360	−	0.0163172i
$591$	2140.01			0.148948
$592$			13015.4i			0.903597i
$593$		−	15744.8i		−	1.09032i	−0.838331	−	0.545162i	$-0.816468\pi$
$593$		−	15744.8i		−	1.09032i	0.838331	−	0.545162i	$-0.183532\pi$
$594$	22.5051			0.00155454
$595$	7087.64	+	2277.64i	0.488344	+	0.156931i
$596$	643.390			0.0442186
$597$		−	12219.8i		−	0.837730i
$598$		−	127.610i		−	0.00872635i
$599$	9108.67			0.621319			0.310660	−	0.950521i	$-0.399450\pi$
$599$	9108.67			0.621319			0.310660	+	0.950521i	$0.399450\pi$
$600$	−372.972	−	267.318i	−0.0253775	−	0.0181887i
$601$	25596.1			1.73725			0.868625	−	0.495470i	$-0.165004\pi$
$601$	25596.1			1.73725			0.868625	+	0.495470i	$0.165004\pi$
$602$			51.7262i			0.00350200i
$603$		−	5269.94i		−	0.355901i
$604$	6664.70			0.448978
$605$	−12904.1	−	4146.77i	−0.867149	−	0.278662i
$606$	−72.4509			−0.00485663
$607$			4719.62i			0.315590i	0.987472	+	0.157795i	$0.0504386\pi$
$607$			4719.62i			0.315590i	−0.987472	+	0.157795i	$0.949561\pi$
$608$		−	520.450i		−	0.0347155i
$609$	−2474.28			−0.164635
$610$	−215.636	+	671.024i	−0.0143129	+	0.0445393i
$611$	10826.0			0.716811
$612$			6843.90i			0.452040i
$613$			8663.56i			0.570829i	0.958404	+	0.285414i	$0.0921312\pi$
$613$			8663.56i			0.570829i	−0.958404	+	0.285414i	$0.907869\pi$
$614$	221.446			0.0145551
$615$	−4399.24	+	13689.7i	−0.288446	+	0.897597i
$616$	93.3203			0.00610387
$617$		−	22393.6i		−	1.46115i	−0.682830	−	0.730577i	$-0.739251\pi$
$617$		−	22393.6i		−	1.46115i	0.682830	−	0.730577i	$-0.260749\pi$
$618$			426.511i			0.0277618i
$619$	22053.3			1.43198			0.715991	−	0.698109i	$-0.245975\pi$
$619$	22053.3			1.43198			0.715991	+	0.698109i	$0.245975\pi$
$620$	−14558.4	−	4678.38i	−0.943028	−	0.303046i
$621$	1696.42			0.109621
$622$		−	230.257i		−	0.0148432i
$623$			1836.34i			0.118092i
$624$	5085.80			0.326274
$625$	5019.90	+	14796.7i	0.321274	+	0.946986i
$626$	769.968			0.0491599
$627$		−	1159.14i		−	0.0738300i
$628$		−	16857.1i		−	1.07114i
$629$	19387.4			1.22898
$630$	−51.3048	−	16.4870i	−0.00324449	−	0.00104263i
$631$	−1637.02			−0.103278			−0.0516392	−	0.998666i	$-0.516445\pi$
$631$	−1637.02			−0.103278			−0.0516392	+	0.998666i	$0.516445\pi$
$632$		−	919.303i		−	0.0578606i
$633$		−	14989.3i		−	0.941187i
$634$	−635.330			−0.0397984
$635$	9004.50	−	28020.5i	0.562729	−	1.75112i
$636$	9134.30			0.569494
$637$		−	1300.79i		−	0.0809095i
$638$			98.2078i			0.00609417i
$639$	5884.70			0.364312
$640$	534.978	−	1664.76i	0.0330420	−	0.102821i
$641$	25331.3			1.56089			0.780443	−	0.625227i	$-0.214994\pi$
$641$	25331.3			1.56089			0.780443	+	0.625227i	$0.214994\pi$
$642$		−	276.058i		−	0.0169706i
$643$		−	2162.69i		−	0.132641i	−0.997798	−	0.0663205i	$-0.978874\pi$
$643$		−	2162.69i		−	0.132641i	0.997798	−	0.0663205i	$-0.0211260\pi$
$644$	3515.92			0.215135
$645$	3084.22	+	991.127i	0.188281	+	0.0605048i
$646$	−258.101			−0.0157196
$647$			247.980i			0.0150682i	0.999972	+	0.00753408i	$0.00239820\pi$
$647$			247.980i			0.0150682i	−0.999972	+	0.00753408i	$0.997602\pi$
$648$		−	99.1171i		−	0.00600878i
$649$	3128.39			0.189214
$650$	206.351	+	147.896i	0.0124519	+	0.00892457i
$651$	−3592.90			−0.216308
$652$			1392.76i			0.0836576i
$653$		−	1225.37i		−	0.0734339i	−0.999326	−	0.0367169i	$-0.988310\pi$
$653$		−	1225.37i		−	0.0734339i	0.999326	−	0.0367169i	$-0.0116900\pi$
$654$	60.2380			0.00360167
$655$	−3211.11	−	1031.90i	−0.191555	−	0.0615570i
$656$	−27376.9			−1.62940
$657$		−	9465.91i		−	0.562101i
$658$		−	218.401i		−	0.0129394i
$659$	2284.95			0.135067			0.0675335	−	0.997717i	$-0.478487\pi$
$659$	2284.95			0.135067			0.0675335	+	0.997717i	$0.478487\pi$
$660$	893.728	−	2781.13i	0.0527096	−	0.164024i
$661$	24079.0			1.41689			0.708445	−	0.705766i	$-0.249397\pi$
$661$	24079.0			1.41689			0.708445	+	0.705766i	$0.249397\pi$
$662$			540.620i			0.0317399i
$663$		−	7575.70i		−	0.443764i
$664$	−1033.60			−0.0604091
$665$	−849.170	+	2642.48i	−0.0495179	+	0.154092i
$666$	−140.338			−0.00816517
$667$			7402.84i			0.429744i
$668$			8073.60i			0.467630i
$669$	6979.72			0.403366
$670$	476.848	+	153.237i	0.0274959	+	0.00883592i
$671$	−8977.08			−0.516478
$672$		−	308.176i		−	0.0176907i
$673$			31756.3i			1.81889i	0.415819	+	0.909447i	$0.363495\pi$
$673$			31756.3i			1.81889i	−0.415819	+	0.909447i	$0.636505\pi$
$674$	−115.571			−0.00660479
$675$	−1966.10	+	2743.19i	−0.112112	+	0.156423i
$676$	11929.4			0.678732
$677$		−	19214.7i		−	1.09081i	−0.838172	−	0.545406i	$-0.816375\pi$
$677$		−	19214.7i		−	1.09081i	0.838172	−	0.545406i	$-0.183625\pi$
$678$		−	31.8583i		−	0.00180459i
$679$	5704.36			0.322405
$680$	−1238.99	−	398.154i	−0.0698721	−	0.0224537i
$681$	2194.72			0.123498
$682$			142.608i			0.00800693i
$683$			16969.5i			0.950688i	0.879800	+	0.475344i	$0.157676\pi$
$683$			16969.5i			0.950688i	−0.879800	+	0.475344i	$0.842324\pi$
$684$	−2551.60			−0.142636
$685$	−7289.82	+	22684.7i	−0.406613	+	1.26531i
$686$	−26.2420			−0.00146053
$687$		−	2739.69i		−	0.152148i
$688$			6167.88i			0.341785i
$689$	−10111.0			−0.559069
$690$	−49.3277	+	153.500i	−0.00272156	+	0.00846904i
$691$	9412.73			0.518202			0.259101	−	0.965850i	$-0.416574\pi$
$691$	9412.73			0.518202			0.259101	+	0.965850i	$0.416574\pi$
$692$		−	27212.3i		−	1.49488i
$693$		−	686.364i		−	0.0376231i
$694$	912.075			0.0498875
$695$	−18006.1	−	5786.33i	−0.982749	−	0.315810i
$696$	432.528			0.0235559
$697$			40780.0i			2.21615i
$698$		−	254.693i		−	0.0138113i
$699$	−15903.5			−0.860554
$700$	−4074.86	+	5685.41i	−0.220022	+	0.306983i
$701$	14947.9			0.805384			0.402692	−	0.915335i	$-0.368075\pi$
$701$	14947.9			0.805384			0.402692	+	0.915335i	$0.368075\pi$
$702$			54.8376i			0.00294831i
$703$			7228.20i			0.387790i
$704$	5553.60			0.297314
$705$	−13022.4	−	4184.79i	−0.695674	−	0.223558i
$706$	−450.159			−0.0239971
$707$			2209.62i			0.117541i
$708$		−	6886.52i		−	0.365553i
$709$	−14067.4			−0.745152			−0.372576	−	0.928002i	$-0.621525\pi$
$709$	−14067.4			−0.745152			−0.372576	+	0.928002i	$0.621525\pi$
$710$	−171.113	+	532.475i	−0.00904472	+	0.0281457i
$711$	−6761.41			−0.356642
$712$		−	321.009i		−	0.0168965i
$713$			10749.7i			0.564626i
$714$	−152.831			−0.00801057
$715$	−989.292	+	3078.51i	−0.0517447	+	0.161021i
$716$	11937.0			0.623053
$717$		−	8090.84i		−	0.421420i
$718$			62.8977i			0.00326925i
$719$	−20536.2			−1.06519			−0.532595	−	0.846370i	$-0.678783\pi$
$719$	−20536.2			−1.06519			−0.532595	+	0.846370i	$0.678783\pi$
$720$	−6117.62	−	1965.92i	−0.316653	−	0.101758i
$721$	13007.8			0.671896
$722$			428.536i			0.0220893i
$723$		−	12898.1i		−	0.663467i
$724$	−10340.6			−0.530807
$725$	−11970.7	−	8579.68i	−0.613216	−	0.439505i
$726$	278.251			0.0142243
$727$		−	15008.2i		−	0.765643i	−0.923822	−	0.382821i	$-0.874953\pi$
$727$		−	15008.2i		−	0.765643i	0.923822	−	0.382821i	$-0.125047\pi$
$728$			227.391i			0.0115765i
$729$	−729.000			−0.0370370
$730$	856.519	+	275.246i	0.0434263	+	0.0139552i
$731$	9187.53			0.464861
$732$			19761.2i			0.997810i
$733$		−	26461.7i		−	1.33340i	−0.745325	−	0.666701i	$-0.767706\pi$
$733$		−	26461.7i		−	1.33340i	0.745325	−	0.666701i	$-0.232294\pi$
$734$	−755.361			−0.0379849
$735$	−502.823	+	1564.70i	−0.0252339	+	0.0785237i
$736$	−922.039			−0.0461777
$737$			6379.36i			0.318842i
$738$		−	295.191i		−	0.0147238i
$739$	−21868.2			−1.08854			−0.544272	−	0.838909i	$-0.683194\pi$
$739$	−21868.2			−1.08854			−0.544272	+	0.838909i	$0.683194\pi$
$740$	−5573.16	+	17342.7i	−0.276856	+	0.861530i
$741$	2824.44			0.140025
$742$			203.978i			0.0100920i
$743$			23832.7i			1.17677i	0.808582	+	0.588383i	$0.200235\pi$
$743$			23832.7i			1.17677i	−0.808582	+	0.588383i	$0.799765\pi$
$744$	628.074			0.0309493
$745$	856.676	+	275.296i	0.0421291	+	0.0135384i
$746$	−547.199			−0.0268557
$747$			7602.09i			0.372351i
$748$		−	8284.67i		−	0.404970i
$749$	−8419.26			−0.410725
$750$	−191.046	−	257.667i	−0.00930138	−	0.0125449i
$751$	−17221.2			−0.836763			−0.418381	−	0.908271i	$-0.637402\pi$
$751$	−17221.2			−0.836763			−0.418381	+	0.908271i	$0.637402\pi$
$752$		−	26042.3i		−	1.26285i
$753$		−	14138.4i		−	0.684241i
$754$	−239.301			−0.0115581
$755$	8874.07	+	2851.72i	0.427762	+	0.137463i
$756$	−1510.89			−0.0726861
$757$		−	1461.19i		−	0.0701557i	−0.999385	−	0.0350779i	$-0.988832\pi$
$757$		−	1461.19i		−	0.0701557i	0.999385	−	0.0350779i	$-0.0111679\pi$
$758$		−	1080.09i		−	0.0517553i
$759$	−2053.55			−0.0982069
$760$	148.443	−	461.931i	0.00708500	−	0.0220474i
$761$	−6949.62			−0.331043			−0.165521	−	0.986206i	$-0.552931\pi$
$761$	−6949.62			−0.331043			−0.165521	+	0.986206i	$0.552931\pi$
$762$			604.207i			0.0287245i
$763$		−	1837.15i		−	0.0871681i
$764$	16027.1			0.758954
$765$	−2928.39	+	9112.68i	−0.138400	+	0.430679i
$766$	404.967			0.0191019
$767$			7622.88i			0.358861i
$768$		−	12198.2i		−	0.573131i
$769$	12778.2			0.599209			0.299605	−	0.954063i	$-0.403145\pi$
$769$	12778.2			0.599209			0.299605	+	0.954063i	$0.403145\pi$
$770$	62.1054	+	19.9578i	0.00290665	+	0.000934064i
$771$	20500.6			0.957602
$772$			3572.78i			0.166564i
$773$			20178.8i			0.938915i	0.882955	+	0.469458i	$0.155551\pi$
$773$			20178.8i			0.938915i	−0.882955	+	0.469458i	$0.844449\pi$
$774$	−66.5051			−0.00308847
$775$	−17382.7	−	12458.6i	−0.805684	−	0.577452i
$776$	−997.178			−0.0461296
$777$			4280.07i			0.197615i
$778$		−	681.680i		−	0.0314131i
$779$	−15204.0			−0.699280
$780$	6776.73	+	2177.73i	0.311084	+	0.0999682i
$781$	−7123.55			−0.326377
$782$			457.258i			0.0209098i
$783$		−	3181.21i		−	0.145194i
$784$	−3129.12			−0.142544
$785$	7212.90	−	22445.3i	0.327948	−	1.02052i
$786$	69.2413			0.00314218
$787$			782.952i			0.0354628i	0.999843	+	0.0177314i	$0.00564438\pi$
$787$			782.952i			0.0354628i	−0.999843	+	0.0177314i	$0.994356\pi$
$788$			5702.51i			0.257796i
$789$	−24664.1			−1.11289
$790$	196.605	−	611.804i	0.00885431	−	0.0275532i
$791$	−971.620			−0.0436749
$792$			119.983i			0.00538310i
$793$		−	21874.3i		−	0.979543i
$794$	304.966			0.0136308
$795$	12162.3	+	3908.42i	0.542584	+	0.174361i
$796$	32562.4			1.44993
$797$			18184.7i			0.808200i	0.914715	+	0.404100i	$0.132415\pi$
$797$			18184.7i			0.808200i	−0.914715	+	0.404100i	$0.867585\pi$
$798$		−	56.9798i		−	0.00252765i
$799$	−38792.1			−1.71760
$800$	1068.62	−	1490.98i	0.0472267	−	0.0658926i
$801$	−2361.00			−0.104147
$802$		−	238.634i		−	0.0105068i
$803$			11458.7i			0.503571i
$804$	14042.9			0.615988
$805$	4681.46	+	1504.41i	0.204969	+	0.0658675i
$806$	−347.489			−0.0151858
$807$			18957.6i			0.826938i
$808$		−	386.263i		−	0.0168177i
$809$	−33601.8			−1.46029			−0.730146	−	0.683291i	$-0.760548\pi$
$809$	−33601.8			−1.46029			−0.730146	+	0.683291i	$0.760548\pi$
$810$	21.1976	−	65.9633i	0.000919514	−	0.00286137i
$811$	−4640.05			−0.200905			−0.100453	−	0.994942i	$-0.532029\pi$
$811$	−4640.05			−0.200905			−0.100453	+	0.994942i	$0.532029\pi$
$812$		−	6593.24i		−	0.284948i
$813$			3383.01i			0.145937i
$814$	169.882			0.00731495
$815$	−595.940	+	1854.47i	−0.0256133	+	0.0797045i
$816$	−18223.7			−0.781809
$817$			3425.38i			0.146682i
$818$		−	315.668i		−	0.0134928i
$819$	1672.45			0.0713554
$820$	−36479.2	−	11722.7i	−1.55355	−	0.499238i
$821$	34248.4			1.45588			0.727939	−	0.685641i	$-0.240478\pi$
$821$	34248.4			1.45588			0.727939	+	0.685641i	$0.240478\pi$
$822$		−	489.151i		−	0.0207556i
$823$		−	5076.24i		−	0.215002i	−0.994205	−	0.107501i	$-0.965715\pi$
$823$		−	5076.24i		−	0.215002i	0.994205	−	0.107501i	$-0.0342849\pi$
$824$	−2273.90			−0.0961346
$825$	2380.01	−	3320.68i	0.100438	−	0.140135i
$826$	153.783			0.00647795
$827$		−	10769.6i		−	0.452835i	−0.974030	−	0.226418i	$-0.927299\pi$
$827$		−	10769.6i		−	0.452835i	0.974030	−	0.226418i	$-0.0727014\pi$
$828$			4520.47i			0.189731i
$829$	−25104.1			−1.05175			−0.525876	−	0.850561i	$-0.676262\pi$
$829$	−25104.1			−1.05175			−0.525876	+	0.850561i	$0.676262\pi$
$830$	−687.872	−	221.050i	−0.0287667	−	0.00924430i
$831$	7568.70			0.315951
$832$			13532.3i			0.563881i
$833$			4661.06i			0.193873i
$834$	388.266			0.0161206
$835$	−3454.56	+	10750.0i	−0.143174	+	0.445533i
$836$	3088.77			0.127784
$837$		−	4619.44i		−	0.190766i
$838$		−	1036.69i		−	0.0427348i
$839$	−37028.0			−1.52366			−0.761829	−	0.647778i	$-0.775699\pi$
$839$	−37028.0			−1.52366			−0.761829	+	0.647778i	$0.775699\pi$
$840$	87.8984	−	273.525i	0.00361046	−	0.0112351i
$841$	−10506.8			−0.430801
$842$		−	494.580i		−	0.0202427i
$843$			27211.0i			1.11174i
$844$	39942.3			1.62899
$845$	15884.0	+	5104.40i	0.646660	+	0.207807i
$846$	280.801			0.0114115
$847$		−	8486.14i		−	0.344259i
$848$			24322.5i			0.984949i
$849$	−435.240			−0.0175941
$850$	−739.406	−	529.949i	−0.0298370	−	0.0213848i
$851$	12805.6			0.515829
$852$			15681.1i			0.630545i
$853$		−	22334.8i		−	0.896518i	−0.893904	−	0.448259i	$-0.852044\pi$
$853$		−	22334.8i		−	0.896518i	0.893904	−	0.448259i	$-0.147956\pi$
$854$	−441.288			−0.0176821
$855$	−3397.47	−	1091.79i	−0.135896	−	0.0436707i
$856$	1471.77			0.0587664
$857$		−	18241.5i		−	0.727090i	−0.931577	−	0.363545i	$-0.881566\pi$
$857$		−	18241.5i		−	0.727090i	0.931577	−	0.363545i	$-0.118434\pi$
$858$		−	66.3820i		−	0.00264131i
$859$	12413.0			0.493045			0.246523	−	0.969137i	$-0.420712\pi$
$859$	12413.0			0.493045			0.246523	+	0.969137i	$0.420712\pi$
$860$	−2641.07	+	8218.57i	−0.104721	+	0.325873i
$861$	−9002.81			−0.356347
$862$			661.994i			0.0261573i
$863$		−	4676.16i		−	0.184448i	−0.995738	−	0.0922238i	$-0.970602\pi$
$863$		−	4676.16i		−	0.184448i	0.995738	−	0.0922238i	$-0.0293975\pi$
$864$	396.227			0.0156017
$865$	11643.7	−	36233.3i	0.457686	−	1.42424i
$866$	780.477			0.0306255
$867$			12406.6i			0.485986i
$868$		−	9574.05i		−	0.374383i
$869$	8184.82			0.319506
$870$	287.851	+	92.5019i	0.0112173	+	0.00360472i
$871$	−15544.5			−0.604711
$872$			321.152i			0.0124720i
$873$			7334.18i			0.284335i
$874$	−170.479			−0.00659787
$875$	−7858.38	+	5826.57i	−0.303613	+	0.225113i
$876$	25224.0			0.972875
$877$			7649.96i			0.294551i	0.989096	+	0.147275i	$0.0470503\pi$
$877$			7649.96i			0.294551i	−0.989096	+	0.147275i	$0.952950\pi$
$878$			999.483i			0.0384179i
$879$	17628.7			0.676451
$880$	7405.50	+	2379.79i	0.283681	+	0.0911620i
$881$	6816.13			0.260660			0.130330	−	0.991471i	$-0.458396\pi$
$881$	6816.13			0.260660			0.130330	+	0.991471i	$0.458396\pi$
$882$		−	33.7397i		−	0.00128807i
$883$		−	22141.7i		−	0.843860i	−0.906628	−	0.421930i	$-0.861353\pi$
$883$		−	22141.7i		−	0.843860i	0.906628	−	0.421930i	$-0.138647\pi$
$884$	20187.1			0.768060
$885$	2946.63	−	9169.43i	0.111921	−	0.348279i
$886$	−155.483			−0.00589566
$887$			28729.2i			1.08752i	0.839240	+	0.543762i	$0.183001\pi$
$887$			28729.2i			1.08752i	−0.839240	+	0.543762i	$0.816999\pi$
$888$		−	748.197i		−	0.0282746i
$889$	18427.2			0.695196
$890$	68.6522	−	213.634i	0.00258565	−	0.00804611i
$891$	882.469			0.0331805
$892$			18599.0i			0.698139i
$893$		−	14462.8i		−	0.541970i
$894$	−18.4725			−0.000691067
$895$	15894.1	+	5107.64i	0.593612	+	0.190759i
$896$	1094.80			0.0408201
$897$		−	5003.83i		−	0.186258i
$898$			125.530i			0.00466478i
$899$	20158.3			0.747851
$900$	−7309.81	−	5239.10i	−0.270734	−	0.194041i
$901$	36230.2			1.33963
$902$			357.335i			0.0131906i
$903$			2028.29i			0.0747477i
$904$	169.849			0.00624899
$905$	−13768.5	−	4424.57i	−0.505725	−	0.162517i
$906$	−191.352			−0.00701682
$907$		−	47268.0i		−	1.73044i	−0.501395	−	0.865219i	$-0.667180\pi$
$907$		−	47268.0i		−	1.73044i	0.501395	−	0.865219i	$-0.332820\pi$
$908$			5848.31i			0.213748i
$909$	−2840.94			−0.103661
$910$	−48.6308	+	151.331i	−0.00177153	+	0.00551271i
$911$	−32904.1			−1.19666			−0.598332	−	0.801248i	$-0.704170\pi$
$911$	−32904.1			−1.19666			−0.598332	+	0.801248i	$0.704170\pi$
$912$		−	6794.32i		−	0.246691i
$913$		−	9202.48i		−	0.333579i
$914$	426.814			0.0154461
$915$	−8455.52	+	26312.2i	−0.305498	+	0.950660i
$916$	7300.49			0.263335
$917$		−	2111.73i		−	0.0760476i
$918$		−	196.497i		−	0.00706466i
$919$	2561.48			0.0919426			0.0459713	−	0.998943i	$-0.485362\pi$
$919$	2561.48			0.0919426			0.0459713	+	0.998943i	$0.485362\pi$
$920$	−818.366	−	262.985i	−0.0293269	−	0.00942430i
$921$	8683.34			0.310669
$922$			1157.14i			0.0413322i
$923$		−	17357.8i		−	0.619002i
$924$	1828.97			0.0651175
$925$	−14841.4	+	20707.3i	−0.527547	+	0.736055i
$926$	−1138.64			−0.0404082
$927$			16724.4i			0.592556i
$928$			1729.06i			0.0611628i
$929$	44532.6			1.57273			0.786365	−	0.617762i	$-0.211960\pi$
$929$	44532.6			1.57273			0.786365	+	0.617762i	$0.211960\pi$
$930$	417.988	+	134.322i	0.0147380	+	0.00473613i
$931$	−1737.78			−0.0611745
$932$		−	42378.4i		−	1.48943i
$933$		−	9028.83i		−	0.316817i
$934$	453.456			0.0158860
$935$	3544.88	−	11031.1i	0.123989	−	0.385834i
$936$	−292.360			−0.0102095
$937$		−	6891.28i		−	0.240265i	−0.992758	−	0.120133i	$-0.961668\pi$
$937$		−	6891.28i		−	0.240265i	0.992758	−	0.120133i	$-0.0383319\pi$
$938$			313.591i			0.0109159i
$939$	30192.0			1.04928
$940$	11151.3	−	34700.9i	0.386930	−	1.20406i
$941$	36509.6			1.26480			0.632401	−	0.774641i	$-0.282069\pi$
$941$	36509.6			1.26480			0.632401	+	0.774641i	$0.282069\pi$
$942$			483.989i			0.0167401i
$943$			26935.7i			0.930166i
$944$	18337.2			0.632229
$945$	−2011.76	−	646.487i	−0.0692514	−	0.0222542i
$946$	80.5057			0.00276688
$947$			23454.7i			0.804830i	0.915457	+	0.402415i	$0.131829\pi$
$947$			23454.7i			0.804830i	−0.915457	+	0.402415i	$0.868171\pi$
$948$		−	18017.2i		−	0.617271i
$949$	−27921.1			−0.955065
$950$	197.580	−	275.672i	0.00674774	−	0.00941472i
$951$	−24912.5			−0.849469
$952$		−	814.799i		−	0.0277393i
$953$			8009.19i			0.272238i	0.990692	+	0.136119i	$0.0434630\pi$
$953$			8009.19i			0.272238i	−0.990692	+	0.136119i	$0.956537\pi$
$954$	−262.257			−0.00890030
$955$	21340.2	+	6857.75i	0.723091	+	0.232368i
$956$	21559.8			0.729386
$957$			3850.92i			0.130076i
$958$			1010.96i			0.0340948i
$959$	−14918.2			−0.502330
$960$	5230.94	−	16277.8i	0.175862	−	0.547254i
$961$	−519.069			−0.0174237
$962$			413.948i			0.0138734i
$963$		−	10824.8i		−	0.362225i
$964$	34369.8			1.14832
$965$	−1528.73	+	4757.17i	−0.0509966	+	0.158693i
$966$	−100.946			−0.00336222
$967$			1962.54i			0.0652648i	0.999467	+	0.0326324i	$0.0103891\pi$
$967$			1962.54i			0.0652648i	−0.999467	+	0.0326324i	$0.989611\pi$
$968$			1483.46i			0.0492564i
$969$	−10120.7			−0.335524
$970$	−663.630	−	213.260i	−0.0219669	−	0.00705914i
$971$	−52109.6			−1.72222			−0.861110	−	0.508419i	$-0.830230\pi$
$971$	−52109.6			−1.72222			−0.861110	+	0.508419i	$0.830230\pi$
$972$		−	1942.58i		−	0.0641031i
$973$		−	11841.4i		−	0.390152i
$974$	1350.05			0.0444130
$975$	8091.42	+	5799.31i	0.265777	+	0.190489i
$976$	−52619.5			−1.72573
$977$		−	10104.1i		−	0.330868i	−0.986221	−	0.165434i	$-0.947097\pi$
$977$		−	10104.1i		−	0.330868i	0.986221	−	0.165434i	$-0.0529025\pi$
$978$		−	39.9879i		−	0.00130744i
$979$	2858.04			0.0933027
$980$	−4169.49	−	1339.88i	−0.135908	−	0.0436744i
$981$	2362.05			0.0768750
$982$			882.947i			0.0286924i
$983$			18109.7i			0.587599i	0.955867	+	0.293799i	$0.0949197\pi$
$983$			18109.7i			0.587599i	−0.955867	+	0.293799i	$0.905080\pi$
$984$	1573.78			0.0509860
$985$	−2440.01	+	7592.91i	−0.0789291	+	0.245614i
$986$	857.473			0.0276952
$987$		−	8563.93i		−	0.276183i
$988$			7526.33i			0.242353i
$989$	6068.47			0.195112
$990$	−25.6600	+	79.8498i	−0.000823767	+	0.00256343i
$991$	−48982.5			−1.57011			−0.785055	−	0.619426i	$-0.787366\pi$
$991$	−48982.5			−1.57011			−0.785055	+	0.619426i	$0.787366\pi$
$992$			2510.76i			0.0803597i
$993$			21198.8i			0.677465i
$994$	−350.173			−0.0111739
$995$	43357.0	+	13932.9i	1.38142	+	0.443923i
$996$	−20257.4			−0.644458
$997$		−	41760.0i		−	1.32653i	−0.748384	−	0.663265i	$-0.769170\pi$
$997$		−	41760.0i		−	1.32653i	0.748384	−	0.663265i	$-0.230830\pi$
$998$		−	521.813i		−	0.0165508i
$999$	−5502.94			−0.174280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.d.a.64.3	✓	6
3.2	odd	2		315.4.d.a.64.4		6
5.2	odd	4		525.4.a.r.1.2		3
5.3	odd	4		525.4.a.q.1.2		3
5.4	even	2	inner	105.4.d.a.64.4	yes	6
15.2	even	4		1575.4.a.bc.1.2		3
15.8	even	4		1575.4.a.bd.1.2		3
15.14	odd	2		315.4.d.a.64.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.a.64.3	✓	6	1.1	even	1	trivial
105.4.d.a.64.4	yes	6	5.4	even	2	inner
315.4.d.a.64.3		6	15.14	odd	2
315.4.d.a.64.4		6	3.2	odd	2
525.4.a.q.1.2		3	5.3	odd	4
525.4.a.r.1.2		3	5.2	odd	4
1575.4.a.bc.1.2		3	15.2	even	4
1575.4.a.bd.1.2		3	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.0765073i q^{2} -3.00000i q^{3} +7.99415 q^{4} +(10.6442 + 3.42057i) q^{5} -0.229522 q^{6} +7.00000i q^{7} -1.22367i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-0.0765073i q^{2} -3.00000i q^{3} +7.99415 q^{4} +(10.6442 + 3.42057i) q^{5} -0.229522 q^{6} +7.00000i q^{7} -1.22367i q^{8} -9.00000 q^{9} +(0.261698 - 0.814361i) q^{10} +10.8947 q^{11} -23.9824i q^{12} +26.5468i q^{13} +0.535551 q^{14} +(10.2617 - 31.9327i) q^{15} +63.8596 q^{16} -95.1237i q^{17} +0.688565i q^{18} +35.4649 q^{19} +(85.0916 + 27.3445i) q^{20} +21.0000 q^{21} -0.833522i q^{22} -62.8303i q^{23} -3.67101 q^{24} +(101.599 + 72.8186i) q^{25} +2.03102 q^{26} +27.0000i q^{27} +55.9590i q^{28} -117.823 q^{29} +(-2.44308 - 0.785094i) q^{30} -171.090 q^{31} -14.6751i q^{32} -32.6840i q^{33} -7.27766 q^{34} +(-23.9440 + 74.5096i) q^{35} -71.9473 q^{36} +203.813i q^{37} -2.71332i q^{38} +79.6404 q^{39} +(4.18564 - 13.0250i) q^{40} -428.705 q^{41} -1.60665i q^{42} +96.5851i q^{43} +87.0936 q^{44} +(-95.7981 - 30.7851i) q^{45} -4.80698 q^{46} -407.806i q^{47} -191.579i q^{48} -49.0000 q^{49} +(5.57115 - 7.77310i) q^{50} -285.371 q^{51} +212.219i q^{52} +380.874i q^{53} +2.06570 q^{54} +(115.965 + 37.2660i) q^{55} +8.56568 q^{56} -106.395i q^{57} +9.01429i q^{58} +287.149 q^{59} +(82.0335 - 255.275i) q^{60} -823.988 q^{61} +13.0897i q^{62} -63.0000i q^{63} +509.754 q^{64} +(-90.8051 + 282.570i) q^{65} -2.50057 q^{66} +585.549i q^{67} -760.433i q^{68} -188.491 q^{69} +(5.70053 + 1.83189i) q^{70} -653.856 q^{71} +11.0130i q^{72} +1051.77i q^{73} +15.5932 q^{74} +(218.456 - 304.798i) q^{75} +283.512 q^{76} +76.2627i q^{77} -6.09307i q^{78} +751.268 q^{79} +(679.736 + 218.436i) q^{80} +81.0000 q^{81} +32.7991i q^{82} -844.677i q^{83} +167.877 q^{84} +(325.377 - 1012.52i) q^{85} +7.38946 q^{86} +353.468i q^{87} -13.3315i q^{88} +262.334 q^{89} +(-2.35528 + 7.32925i) q^{90} -185.828 q^{91} -502.275i q^{92} +513.271i q^{93} -31.2001 q^{94} +(377.497 + 121.310i) q^{95} -44.0252 q^{96} -814.908i q^{97} +3.74886i q^{98} -98.0521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 14 q^{5} - 6 q^{6} - 54 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 14 * q^5 - 6 * q^6 - 54 * q^9	\( 6 q - 6 q^{4} - 14 q^{5} - 6 q^{6} - 54 q^{9} - 84 q^{10} - 132 q^{11} + 14 q^{14} - 24 q^{15} - 138 q^{16} + 276 q^{19} + 334 q^{20} + 126 q^{21} + 126 q^{24} + 366 q^{25} - 196 q^{26} - 340 q^{29} - 54 q^{30} - 732 q^{31} + 72 q^{34} + 56 q^{35} + 54 q^{36} + 612 q^{39} + 12 q^{40} - 412 q^{41} + 612 q^{44} + 126 q^{45} - 1344 q^{46} - 294 q^{49} + 1216 q^{50} - 912 q^{51} + 54 q^{54} + 1860 q^{55} - 294 q^{56} + 1760 q^{59} + 624 q^{60} - 1740 q^{61} + 1626 q^{64} - 16 q^{65} - 1116 q^{66} - 1080 q^{69} + 126 q^{70} - 2036 q^{71} - 1960 q^{74} + 936 q^{75} - 900 q^{76} + 3240 q^{79} + 3794 q^{80} + 486 q^{81} - 126 q^{84} + 432 q^{85} - 5864 q^{86} + 3876 q^{89} + 756 q^{90} - 1428 q^{91} - 4224 q^{94} - 828 q^{95} + 906 q^{96} + 1188 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 14 * q^5 - 6 * q^6 - 54 * q^9 - 84 * q^10 - 132 * q^11 + 14 * q^14 - 24 * q^15 - 138 * q^16 + 276 * q^19 + 334 * q^20 + 126 * q^21 + 126 * q^24 + 366 * q^25 - 196 * q^26 - 340 * q^29 - 54 * q^30 - 732 * q^31 + 72 * q^34 + 56 * q^35 + 54 * q^36 + 612 * q^39 + 12 * q^40 - 412 * q^41 + 612 * q^44 + 126 * q^45 - 1344 * q^46 - 294 * q^49 + 1216 * q^50 - 912 * q^51 + 54 * q^54 + 1860 * q^55 - 294 * q^56 + 1760 * q^59 + 624 * q^60 - 1740 * q^61 + 1626 * q^64 - 16 * q^65 - 1116 * q^66 - 1080 * q^69 + 126 * q^70 - 2036 * q^71 - 1960 * q^74 + 936 * q^75 - 900 * q^76 + 3240 * q^79 + 3794 * q^80 + 486 * q^81 - 126 * q^84 + 432 * q^85 - 5864 * q^86 + 3876 * q^89 + 756 * q^90 - 1428 * q^91 - 4224 * q^94 - 828 * q^95 + 906 * q^96 + 1188 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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