LMFDB - Embedded newform 27.4.e.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,4,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, 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:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	27.13
Dual form			27.4.e.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.874714 - 4.96075i) q^{2} +(2.71299 - 4.43167i) q^{3} +(-16.3263 + 5.94230i) q^{4} +(11.9326 + 10.0126i) q^{5} +(-24.3575 - 9.58200i) q^{6} +(-5.29732 - 1.92807i) q^{7} +(23.6100 + 40.8938i) q^{8} +(-12.2794 - 24.0461i) q^{9} +O(q^{10})$	\(q+(-0.874714 - 4.96075i) q^{2} +(2.71299 - 4.43167i) q^{3} +(-16.3263 + 5.94230i) q^{4} +(11.9326 + 10.0126i) q^{5} +(-24.3575 - 9.58200i) q^{6} +(-5.29732 - 1.92807i) q^{7} +(23.6100 + 40.8938i) q^{8} +(-12.2794 - 24.0461i) q^{9} +(39.2325 - 67.9527i) q^{10} +(30.2222 - 25.3594i) q^{11} +(-17.9588 + 88.4744i) q^{12} +(-10.1763 + 57.7124i) q^{13} +(-4.93102 + 27.9652i) q^{14} +(76.7456 - 25.7172i) q^{15} +(75.7369 - 63.5508i) q^{16} +(8.53867 - 14.7894i) q^{17} +(-108.546 + 81.9485i) q^{18} +(10.5573 + 18.2858i) q^{19} +(-254.314 - 92.5626i) q^{20} +(-22.9161 + 18.2452i) q^{21} +(-152.238 - 127.742i) q^{22} +(-27.3949 + 9.97093i) q^{23} +(245.282 + 6.31238i) q^{24} +(20.4278 + 115.852i) q^{25} +295.198 q^{26} +(-139.878 - 10.8185i) q^{27} +97.9431 q^{28} +(34.8557 + 197.676i) q^{29} +(-194.707 - 358.220i) q^{30} +(36.3946 - 13.2466i) q^{31} +(-92.1260 - 77.3029i) q^{32} +(-30.3923 - 202.735i) q^{33} +(-80.8354 - 29.4217i) q^{34} +(-43.9057 - 76.0470i) q^{35} +(343.367 + 319.617i) q^{36} +(-144.366 + 250.048i) q^{37} +(81.4764 - 68.3668i) q^{38} +(228.154 + 201.671i) q^{39} +(-127.725 + 724.367i) q^{40} +(78.5187 - 445.302i) q^{41} +(110.555 + 97.7218i) q^{42} +(-12.7283 + 10.6803i) q^{43} +(-342.725 + 593.617i) q^{44} +(94.2398 - 409.881i) q^{45} +(73.4259 + 127.177i) q^{46} +(-101.430 - 36.9176i) q^{47} +(-76.1630 - 508.053i) q^{48} +(-238.409 - 200.049i) q^{49} +(556.844 - 202.675i) q^{50} +(-42.3765 - 77.9640i) q^{51} +(-176.804 - 1002.70i) q^{52} -540.581 q^{53} +(68.6856 + 703.364i) q^{54} +614.544 q^{55} +(-46.2240 - 262.150i) q^{56} +(109.678 + 2.82260i) q^{57} +(950.134 - 345.821i) q^{58} +(124.757 + 104.684i) q^{59} +(-1100.16 + 875.913i) q^{60} +(-425.952 - 155.034i) q^{61} +(-97.5477 - 168.958i) q^{62} +(18.6854 + 151.056i) q^{63} +(92.5737 - 160.342i) q^{64} +(-699.282 + 586.767i) q^{65} +(-979.131 + 328.103i) q^{66} +(53.9930 - 306.209i) q^{67} +(-51.5221 + 292.196i) q^{68} +(-30.1341 + 148.456i) q^{69} +(-338.845 + 284.325i) q^{70} +(207.996 - 360.260i) q^{71} +(693.420 - 1069.88i) q^{72} +(294.437 + 509.980i) q^{73} +(1366.71 + 497.440i) q^{74} +(568.838 + 223.775i) q^{75} +(-281.021 - 235.805i) q^{76} +(-208.992 + 76.0667i) q^{77} +(800.868 - 1308.22i) q^{78} +(81.7637 + 463.705i) q^{79} +1540.05 q^{80} +(-427.432 + 590.544i) q^{81} -2277.71 q^{82} +(43.8952 + 248.942i) q^{83} +(265.718 - 434.052i) q^{84} +(249.969 - 90.9813i) q^{85} +(64.1160 + 53.7997i) q^{86} +(970.600 + 381.825i) q^{87} +(1750.59 + 637.163i) q^{88} +(-468.388 - 811.272i) q^{89} +(-2115.75 - 108.971i) q^{90} +(165.180 - 286.101i) q^{91} +(388.008 - 325.578i) q^{92} +(40.0337 - 197.227i) q^{93} +(-94.4163 + 535.462i) q^{94} +(-57.1127 + 323.902i) q^{95} +(-592.518 + 198.550i) q^{96} +(247.545 - 207.715i) q^{97} +(-783.853 + 1357.67i) q^{98} +(-980.907 - 415.328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.874714	−	4.96075i	−0.309258	−	1.75389i	−0.602753	−	0.797928i	$-0.705929\pi$
$2$	−0.874714	−	4.96075i	−0.309258	−	1.75389i	0.293495	−	0.955961i	$-0.405182\pi$
$3$	2.71299	−	4.43167i	0.522115	−	0.852875i
$3$	2.71299	−	4.43167i	0.522115	−	0.852875i
$4$	−16.3263	+	5.94230i	−2.04079	+	0.742788i
$5$	11.9326	+	10.0126i	1.06728	+	0.895556i	0.994804	−	0.101813i	$-0.0324645\pi$
$5$	11.9326	+	10.0126i	1.06728	+	0.895556i	0.0724791	+	0.997370i	$0.476909\pi$
$6$	−24.3575	−	9.58200i	−1.65732	−	0.651972i
$7$	−5.29732	−	1.92807i	−0.286029	−	0.104106i	0.195022	−	0.980799i	$-0.437522\pi$
$7$	−5.29732	−	1.92807i	−0.286029	−	0.104106i	−0.481050	+	0.876693i	$0.659745\pi$
$8$	23.6100	+	40.8938i	1.04343	+	1.80727i
$9$	−12.2794	−	24.0461i	−0.454793	−	0.890597i
$10$	39.2325	−	67.9527i	1.24064	−	2.14885i
$11$	30.2222	−	25.3594i	0.828395	−	0.695106i	−0.126527	−	0.991963i	$-0.540383\pi$
$11$	30.2222	−	25.3594i	0.828395	−	0.695106i	0.954922	+	0.296858i	$0.0959387\pi$
$12$	−17.9588	+	88.4744i	−0.432022	+	2.12836i
$13$	−10.1763	+	57.7124i	−0.217106	+	1.23127i	0.660107	+	0.751172i	$0.270511\pi$
$13$	−10.1763	+	57.7124i	−0.217106	+	1.23127i	−0.877213	+	0.480100i	$0.840600\pi$
$14$	−4.93102	+	27.9652i	−0.0941336	+	0.533858i
$15$	76.7456	−	25.7172i	1.32104	−	0.442676i
$16$	75.7369	−	63.5508i	1.18339	−	0.992981i
$17$	8.53867	−	14.7894i	0.121819	−	0.210998i	−0.798666	−	0.601775i	$-0.794460\pi$
$17$	8.53867	−	14.7894i	0.121819	−	0.210998i	0.920485	+	0.390777i	$0.127794\pi$
$18$	−108.546	+	81.9485i	−1.42136	+	1.07308i
$19$	10.5573	+	18.2858i	0.127474	+	0.220792i	0.922697	−	0.385525i	$-0.125980\pi$
$19$	10.5573	+	18.2858i	0.127474	+	0.220792i	−0.795223	+	0.606317i	$0.792646\pi$
$20$	−254.314	−	92.5626i	−2.84331	−	1.03488i
$21$	−22.9161	+	18.2452i	−0.238129	+	0.189592i
$22$	−152.238	−	127.742i	−1.47533	−	1.23795i
$23$	−27.3949	+	9.97093i	−0.248358	+	0.0903949i	−0.463200	−	0.886254i	$-0.653299\pi$
$23$	−27.3949	+	9.97093i	−0.248358	+	0.0903949i	0.214842	+	0.976649i	$0.431076\pi$
$24$	245.282	+	6.31238i	2.08616	+	0.0536879i
$25$	20.4278	+	115.852i	0.163423	+	0.926816i
$26$	295.198			2.22666
$27$	−139.878	−	10.8185i	−0.997022	−	0.0771121i
$28$	97.9431			0.661054
$29$	34.8557	+	197.676i	0.223191	+	1.26578i	0.866113	+	0.499848i	$0.166611\pi$
$29$	34.8557	+	197.676i	0.223191	+	1.26578i	−0.642922	+	0.765931i	$0.722278\pi$
$30$	−194.707	−	358.220i	−1.18495	−	2.18006i
$31$	36.3946	−	13.2466i	0.210860	−	0.0767469i	−0.234430	−	0.972133i	$-0.575323\pi$
$31$	36.3946	−	13.2466i	0.210860	−	0.0767469i	0.445291	+	0.895386i	$0.353100\pi$
$32$	−92.1260	−	77.3029i	−0.508929	−	0.427042i
$33$	−30.3923	−	202.735i	−0.160322	−	1.06944i
$34$	−80.8354	−	29.4217i	−0.407740	−	0.148405i
$35$	−43.9057	−	76.0470i	−0.212041	−	0.367265i
$36$	343.367	+	319.617i	1.58966	+	1.47971i
$37$	−144.366	+	250.048i	−0.641447	+	1.11102i	0.343662	+	0.939093i	$0.388332\pi$
$37$	−144.366	+	250.048i	−0.641447	+	1.11102i	−0.985110	+	0.171926i	$0.945001\pi$
$38$	81.4764	−	68.3668i	0.347822	−	0.291857i
$39$	228.154	+	201.671i	0.936767	+	0.828030i
$40$	−127.725	+	724.367i	−0.504879	+	2.86331i
$41$	78.5187	−	445.302i	0.299087	−	1.69621i	−0.351023	−	0.936367i	$-0.614166\pi$
$41$	78.5187	−	445.302i	0.299087	−	1.69621i	0.650110	−	0.759840i	$-0.274723\pi$
$42$	110.555	+	97.7218i	0.406166	+	0.359019i
$43$	−12.7283	+	10.6803i	−0.0451407	+	0.0378775i	−0.665079	−	0.746773i	$-0.731602\pi$
$43$	−12.7283	+	10.6803i	−0.0451407	+	0.0378775i	0.619938	+	0.784651i	$0.287158\pi$
$44$	−342.725	+	593.617i	−1.17427	+	2.03389i
$45$	94.2398	−	409.881i	0.312188	−	1.35781i
$46$	73.4259	+	127.177i	0.235349	+	0.407637i
$47$	−101.430	−	36.9176i	−0.314790	−	0.114574i	0.179794	−	0.983704i	$-0.442457\pi$
$47$	−101.430	−	36.9176i	−0.314790	−	0.114574i	−0.494583	+	0.869130i	$0.664679\pi$
$48$	−76.1630	−	508.053i	−0.229025	−	1.52773i
$49$	−238.409	−	200.049i	−0.695070	−	0.583233i
$50$	556.844	−	202.675i	1.57499	−	0.573250i
$51$	−42.3765	−	77.9640i	−0.116351	−	0.214062i
$52$	−176.804	−	1002.70i	−0.471505	−	2.67404i
$53$	−540.581			−1.40103			−0.700514	−	0.713639i	$-0.747046\pi$
$53$	−540.581			−1.40103			−0.700514	+	0.713639i	$0.747046\pi$
$54$	68.6856	+	703.364i	0.173091	+	1.77251i
$55$	614.544			1.50664
$56$	−46.2240	−	262.150i	−0.110303	−	0.625557i
$57$	109.678	+	2.82260i	0.254864	+	0.00655898i
$58$	950.134	−	345.821i	2.15101	−	0.782905i
$59$	124.757	+	104.684i	0.275288	+	0.230994i	0.769970	−	0.638080i	$-0.220271\pi$
$59$	124.757	+	104.684i	0.275288	+	0.230994i	−0.494682	+	0.869074i	$0.664715\pi$
$60$	−1100.16	+	875.913i	−2.36716	+	1.88466i
$61$	−425.952	−	155.034i	−0.894058	−	0.325411i	−0.146189	−	0.989257i	$-0.546701\pi$
$61$	−425.952	−	155.034i	−0.894058	−	0.325411i	−0.747869	+	0.663846i	$0.768923\pi$
$62$	−97.5477	−	168.958i	−0.199816	−	0.346091i
$63$	18.6854	+	151.056i	0.0373674	+	0.302083i
$64$	92.5737	−	160.342i	0.180808	−	0.313169i
$65$	−699.282	+	586.767i	−1.33439	+	1.11968i
$66$	−979.131	+	328.103i	−1.82610	+	0.611920i
$67$	53.9930	−	306.209i	0.0984521	−	0.558350i	−0.895183	−	0.445700i	$-0.852955\pi$
$67$	53.9930	−	306.209i	0.0984521	−	0.558350i	0.993635	−	0.112650i	$-0.0359339\pi$
$68$	−51.5221	+	292.196i	−0.0918820	+	0.521088i
$69$	−30.1341	+	148.456i	−0.0525757	+	0.259015i
$70$	−338.845	+	284.325i	−0.578567	+	0.485476i
$71$	207.996	−	360.260i	0.347671	−	0.602183i	−0.638165	−	0.769900i	$-0.720306\pi$
$71$	207.996	−	360.260i	0.347671	−	0.602183i	0.985835	+	0.167717i	$0.0536394\pi$
$72$	693.420	−	1069.88i	1.13500	−	1.75121i
$73$	294.437	+	509.980i	0.472072	+	0.817652i	0.999489	−	0.0319540i	$-0.0101730\pi$
$73$	294.437	+	509.980i	0.472072	+	0.817652i	−0.527418	+	0.849606i	$0.676840\pi$
$74$	1366.71	+	497.440i	2.14698	+	0.781436i
$75$	568.838	+	223.775i	0.875784	+	0.344525i
$76$	−281.021	−	235.805i	−0.424150	−	0.355904i
$77$	−208.992	+	76.0667i	−0.309309	+	0.112579i
$78$	800.868	−	1308.22i	1.16257	−	1.89906i
$79$	81.7637	+	463.705i	0.116445	+	0.660391i	0.986025	+	0.166599i	$0.0532784\pi$
$79$	81.7637	+	463.705i	0.116445	+	0.660391i	−0.869580	+	0.493792i	$0.835610\pi$
$80$	1540.05			2.15228
$81$	−427.432	+	590.544i	−0.586327	+	0.810075i
$82$	−2277.71			−3.06745
$83$	43.8952	+	248.942i	0.0580496	+	0.329216i	0.999978	−	0.00659738i	$-0.00210003\pi$
$83$	43.8952	+	248.942i	0.0580496	+	0.329216i	−0.941929	+	0.335813i	$0.890989\pi$
$84$	265.718	−	434.052i	0.345146	−	0.563797i
$85$	249.969	−	90.9813i	0.318976	−	0.116098i
$86$	64.1160	+	53.7997i	0.0803931	+	0.0674578i
$87$	970.600	+	381.825i	1.19608	+	0.470528i
$88$	1750.59	+	637.163i	2.12061	+	0.771839i
$89$	−468.388	−	811.272i	−0.557854	−	0.966232i	−0.997675	−	0.0681465i	$-0.978291\pi$
$89$	−468.388	−	811.272i	−0.557854	−	0.966232i	0.439821	−	0.898085i	$-0.355042\pi$
$90$	−2115.75	−	108.971i	−2.47800	−	0.127628i
$91$	165.180	−	286.101i	0.190281	−	0.329577i
$92$	388.008	−	325.578i	0.439703	−	0.368955i
$93$	40.0337	−	197.227i	0.0446377	−	0.219908i
$94$	−94.4163	+	535.462i	−0.103599	+	0.587539i
$95$	−57.1127	+	323.902i	−0.0616805	+	0.349807i
$96$	−592.518	+	198.550i	−0.629933	+	0.211088i
$97$	247.545	−	207.715i	0.259117	−	0.217425i	−0.503969	−	0.863722i	$-0.668127\pi$
$97$	247.545	−	207.715i	0.259117	−	0.217425i	0.763087	+	0.646296i	$0.223683\pi$
$98$	−783.853	+	1357.67i	−0.807970	+	1.39945i
$99$	−980.907	−	415.328i	−0.995807	−	0.421637i
$100$	−1021.94	−	1770.05i	−1.02194	−	1.77005i
$101$	237.515	+	86.4486i	0.233997	+	0.0851678i	0.456357	−	0.889797i	$-0.349154\pi$
$101$	237.515	+	86.4486i	0.233997	+	0.0851678i	−0.222360	+	0.974965i	$0.571376\pi$
$102$	−349.693	+	278.415i	−0.339458	+	0.270267i
$103$	−1017.67	−	853.925i	−0.973533	−	0.816891i	0.00956859	−	0.999954i	$-0.496954\pi$
$103$	−1017.67	−	853.925i	−0.973533	−	0.816891i	−0.983101	+	0.183063i	$0.941399\pi$
$104$	−2600.34	+	946.447i	−2.45177	+	0.892372i
$105$	−456.131	−	11.7386i	−0.423941	−	0.0109102i
$106$	472.853	+	2681.68i	0.433279	+	2.45725i
$107$	1780.29			1.60848			0.804241	−	0.594303i	$-0.202572\pi$
$107$	1780.29			1.60848			0.804241	+	0.594303i	$0.202572\pi$
$108$	2347.99	−	654.573i	2.09199	−	0.583207i
$109$	1698.95			1.49293			0.746466	−	0.665424i	$-0.231749\pi$
$109$	1698.95			1.49293			0.746466	+	0.665424i	$0.231749\pi$
$110$	−537.550	−	3048.60i	−0.465940	−	2.64247i
$111$	716.471	+	1318.16i	0.612652	+	1.12715i
$112$	−523.733	+	190.623i	−0.441858	+	0.160823i
$113$	−420.449	−	352.799i	−0.350022	−	0.293704i	0.450777	−	0.892637i	$-0.351147\pi$
$113$	−420.449	−	352.799i	−0.350022	−	0.293704i	−0.800799	+	0.598933i	$0.795592\pi$
$114$	−81.9349	−	546.555i	−0.0673149	−	0.449031i
$115$	−426.727	−	155.316i	−0.346022	−	0.125942i
$116$	−1743.72	−	3020.21i	−1.39569	−	2.41741i
$117$	1512.72	−	463.975i	1.19531	−	0.366619i
$118$	410.182	−	710.457i	0.320003	−	0.554262i
$119$	−73.7471	+	61.8812i	−0.0568100	+	0.0476692i
$120$	2863.64	+	2531.24i	2.17844	+	1.92558i
$121$	39.1548	−	222.058i	0.0294176	−	0.166835i
$122$	−396.498	+	2248.65i	−0.294239	+	1.66871i
$123$	−1760.41	−	1556.07i	−1.29050	−	1.14070i
$124$	−515.476	+	432.536i	−0.373316	+	0.313249i
$125$	57.3291	−	99.2969i	0.0410214	−	0.0710511i
$126$	733.005	−	224.824i	0.518264	−	0.158960i
$127$	−222.595	−	385.545i	−0.155528	−	0.269383i	0.777723	−	0.628607i	$-0.216375\pi$
$127$	−222.595	−	385.545i	−0.155528	−	0.269383i	−0.933251	+	0.359224i	$0.883041\pi$
$128$	−1780.47	−	648.037i	−1.22947	−	0.447492i
$129$	12.7999	+	85.3832i	0.00873621	+	0.0582758i
$130$	3522.47	+	2955.71i	2.37647	+	1.99410i
$131$	1778.56	−	647.343i	1.18621	−	0.431745i	0.327819	−	0.944740i	$-0.393686\pi$
$131$	1778.56	−	647.343i	1.18621	−	0.431745i	0.858392	+	0.512995i	$0.171464\pi$
$132$	1700.91	+	3129.32i	1.12155	+	2.06343i
$133$	−20.6692	−	117.221i	−0.0134755	−	0.0764235i
$134$	−1566.26			−1.00973
$135$	−1560.79	−	1529.64i	−0.995047	−	0.975190i
$136$	806.394			0.508439
$137$	331.214	+	1878.41i	0.206551	+	1.17141i	0.894980	+	0.446106i	$0.147189\pi$
$137$	331.214	+	1878.41i	0.206551	+	1.17141i	−0.688429	+	0.725303i	$0.741699\pi$
$138$	762.812	+	19.6312i	0.470543	+	0.0121095i
$139$	−2876.67	+	1047.02i	−1.75537	+	0.638901i	−0.999868	−	0.0162483i	$-0.994828\pi$
$139$	−2876.67	+	1047.02i	−1.75537	+	0.638901i	−0.755499	+	0.655150i	$0.772606\pi$
$140$	1168.71	+	980.668i	0.705531	+	0.592011i
$141$	−438.785	+	349.348i	−0.262074	+	0.208655i
$142$	−1969.10	−	716.693i	−1.16368	−	0.423546i
$143$	1156.01	+	2002.26i	0.676014	+	1.17089i
$144$	−2458.15	−	1040.81i	−1.42254	−	0.602322i
$145$	−1563.34	+	2707.79i	−0.895369	+	1.55082i
$146$	2272.33	−	1906.71i	1.28808	−	1.08083i
$147$	−1533.35	+	513.820i	−0.860331	+	0.288294i
$148$	871.098	−	4940.24i	0.483810	−	2.74382i
$149$	192.006	−	1088.92i	0.105569	−	0.598711i	−0.885423	−	0.464787i	$-0.846131\pi$
$149$	192.006	−	1088.92i	0.105569	−	0.598711i	0.990992	−	0.133924i	$-0.0427580\pi$
$150$	612.523	−	3017.60i	0.333415	−	1.64257i
$151$	2116.76	−	1776.17i	1.14079	−	0.957235i	0.141324	−	0.989963i	$-0.454864\pi$
$151$	2116.76	−	1776.17i	1.14079	−	0.957235i	0.999464	+	0.0327280i	$0.0104195\pi$
$152$	−498.516	+	863.455i	−0.266020	+	0.460760i
$153$	−460.478	−	23.7167i	−0.243316	−	0.0125319i
$154$	560.156	+	970.218i	0.293108	+	0.507678i
$155$	566.915	+	206.340i	0.293779	+	0.106927i
$156$	−4923.31	−	1936.78i	−2.52680	−	0.994018i
$157$	843.686	+	707.937i	0.428876	+	0.359869i	0.831527	−	0.555484i	$-0.187467\pi$
$157$	843.686	+	707.937i	0.428876	+	0.359869i	−0.402652	+	0.915353i	$0.631911\pi$
$158$	2228.80	−	811.218i	1.12224	−	0.408462i
$159$	−1466.59	+	2395.68i	−0.731497	+	1.19490i
$160$	−325.296	−	1844.85i	−0.160731	−	0.911550i
$161$	164.344			0.0804481
$162$	3303.42	+	1603.83i	1.60211	+	0.777830i
$163$	−3204.18			−1.53970			−0.769849	−	0.638227i	$-0.779668\pi$
$163$	−3204.18			−1.53970			−0.769849	+	0.638227i	$0.779668\pi$
$164$	1364.20	+	7736.74i	0.649547	+	3.68377i
$165$	1667.25	−	2723.46i	0.786637	−	1.28497i
$166$	1196.54	−	435.506i	0.559456	−	0.203625i
$167$	−894.925	−	750.931i	−0.414679	−	0.347957i	0.411456	−	0.911430i	$-0.365021\pi$
$167$	−894.925	−	750.931i	−0.414679	−	0.347957i	−0.826135	+	0.563473i	$0.809465\pi$
$168$	−1287.17	−	506.358i	−0.591113	−	0.232538i
$169$	−1162.66	−	423.173i	−0.529203	−	0.192614i
$170$	−669.987	−	1160.45i	−0.302269	−	0.523544i
$171$	310.064	−	478.400i	0.138662	−	0.213943i
$172$	144.341	−	250.006i	0.0639878	−	0.110830i
$173$	1073.53	−	900.795i	0.471784	−	0.395874i	−0.375661	−	0.926757i	$-0.622584\pi$
$173$	1073.53	−	900.795i	0.471784	−	0.395874i	0.847445	+	0.530883i	$0.178140\pi$
$174$	1045.14	−	5148.89i	0.455355	−	2.24331i
$175$	115.158	−	653.092i	0.0497435	−	0.282109i
$176$	677.323	−	3841.29i	0.290086	−	1.64516i
$177$	802.388	−	268.877i	0.340741	−	0.114181i
$178$	−3614.81	+	3033.18i	−1.52214	+	1.27723i
$179$	720.190	−	1247.41i	0.300723	−	0.520868i	−0.675577	−	0.737290i	$-0.736105\pi$
$179$	720.190	−	1247.41i	0.300723	−	0.520868i	0.976300	+	0.216422i	$0.0694385\pi$
$180$	897.049	+	7251.87i	0.371456	+	3.00290i
$181$	448.108	+	776.145i	0.184020	+	0.318732i	0.943246	−	0.332095i	$-0.107756\pi$
$181$	448.108	+	776.145i	0.184020	+	0.318732i	−0.759226	+	0.650827i	$0.774422\pi$
$182$	−1563.76	−	569.162i	−0.636888	−	0.231808i
$183$	−1842.66	+	1467.07i	−0.744335	+	0.592619i
$184$	−1054.54	−	884.867i	−0.422511	−	0.354529i
$185$	−4226.30	+	1538.25i	−1.67959	+	0.611319i
$186$	−1013.41	−	26.0804i	−0.399499	−	0.0102812i
$187$	−116.994	−	663.505i	−0.0457510	−	0.259467i
$188$	1875.36			0.727525
$189$	720.122	+	327.004i	0.277149	+	0.125852i
$190$	1656.76			0.632598
$191$	−103.056	−	584.457i	−0.0390410	−	0.221413i	0.959045	−	0.283254i	$-0.0914139\pi$
$191$	−103.056	−	584.457i	−0.0390410	−	0.221413i	−0.998086	+	0.0618411i	$0.980303\pi$
$192$	−459.433	−	845.263i	−0.172691	−	0.317717i
$193$	1338.31	−	487.105i	0.499138	−	0.181671i	−0.0801683	−	0.996781i	$-0.525546\pi$
$193$	1338.31	−	487.105i	0.499138	−	0.181671i	0.579306	+	0.815110i	$0.303324\pi$
$194$	−1246.95	−	1046.32i	−0.461474	−	0.387223i
$195$	703.216	+	4690.88i	0.258248	+	1.72267i
$196$	5081.10	+	1849.37i	1.85171	+	0.673968i
$197$	384.953	+	666.759i	0.139222	+	0.241140i	0.927202	−	0.374561i	$-0.122206\pi$
$197$	384.953	+	666.759i	0.139222	+	0.241140i	−0.787980	+	0.615701i	$0.788873\pi$
$198$	−1202.32	+	5229.33i	−0.431543	+	1.87693i
$199$	2271.87	−	3935.00i	0.809290	−	1.40173i	−0.104066	−	0.994570i	$-0.533185\pi$
$199$	2271.87	−	3935.00i	0.809290	−	1.40173i	0.913356	−	0.407162i	$-0.133481\pi$
$200$	−4255.33	+	3570.64i	−1.50449	+	1.26241i
$201$	−1210.54	−	1070.02i	−0.424799	−	0.375490i
$202$	221.091	−	1253.87i	0.0770096	−	0.436743i
$203$	196.492	−	1114.36i	0.0679361	−	0.385285i
$204$	1155.14	+	1021.05i	0.396451	+	0.350432i
$205$	5395.57	−	4527.42i	1.83826	−	1.54248i
$206$	−3345.94	+	5795.34i	−1.13166	+	1.96010i
$207$	576.155	+	536.304i	0.193457	+	0.180076i
$208$	2896.95	+	5017.67i	0.965709	+	1.67266i
$209$	782.781	+	284.909i	0.259072	+	0.0942946i
$210$	340.751	+	2273.02i	0.111972	+	0.746920i
$211$	3083.97	+	2587.76i	1.00620	+	0.844306i	0.987832	−	0.155525i	$-0.0497070\pi$
$211$	3083.97	+	2587.76i	1.00620	+	0.844306i	0.0183727	+	0.999831i	$0.494151\pi$
$212$	8825.71	−	3212.30i	2.85921	−	1.04067i
$213$	−1032.26	−	1899.15i	−0.332063	−	0.610928i
$214$	−1557.25	−	8831.59i	−0.497436	−	2.82110i
$215$	−258.820			−0.0820993
$216$	−2860.12	−	5975.58i	−0.900957	−	1.88235i
$217$	−218.334			−0.0683019
$218$	−1486.09	−	8428.05i	−0.461701	−	2.61844i
$219$	3058.87	+	78.7206i	0.943831	+	0.0242897i
$220$	−10033.3	+	3651.81i	−3.07474	+	1.11911i
$221$	766.640	+	643.288i	0.233348	+	0.195802i
$222$	5912.35	−	4707.24i	1.78744	−	1.42311i
$223$	−4319.78	−	1572.27i	−1.29719	−	0.472140i	−0.401112	−	0.916029i	$-0.631376\pi$
$223$	−4319.78	−	1572.27i	−1.29719	−	0.472140i	−0.896082	+	0.443889i	$0.853598\pi$
$224$	338.976	+	587.124i	0.101111	+	0.175129i
$225$	2534.95	−	1913.80i	0.751096	−	0.567053i
$226$	−1382.37	+	2394.34i	−0.406876	+	0.704731i
$227$	−114.884	+	96.3994i	−0.0335909	+	0.0281861i	−0.659429	−	0.751767i	$-0.729202\pi$
$227$	−114.884	+	96.3994i	−0.0335909	+	0.0281861i	0.625838	+	0.779953i	$0.284757\pi$
$228$	−1807.42	+	605.659i	−0.524996	+	0.175924i
$229$	−898.844	+	5097.60i	−0.259377	+	1.47100i	0.525207	+	0.850975i	$0.323988\pi$
$229$	−898.844	+	5097.60i	−0.259377	+	1.47100i	−0.784583	+	0.620023i	$0.787123\pi$
$230$	−397.219	+	2252.74i	−0.113878	+	0.645832i
$231$	−229.889	+	1132.55i	−0.0654787	+	0.322581i
$232$	−7260.80	+	6092.53i	−2.05472	+	1.72411i
$233$	−247.239	+	428.230i	−0.0695157	+	0.120405i	−0.898688	−	0.438588i	$-0.855479\pi$
$233$	−247.239	+	428.230i	−0.0695157	+	0.120405i	0.829173	+	0.558993i	$0.188812\pi$
$234$	−3624.86	−	7098.37i	−1.01267	−	1.98305i
$235$	−840.682	−	1456.10i	−0.233362	−	0.404195i
$236$	−2658.89	−	967.757i	−0.733386	−	0.266931i
$237$	2276.81	+	895.675i	0.624028	+	0.245487i
$238$	371.484	+	311.712i	0.101175	+	0.0848963i
$239$	−5424.09	+	1974.21i	−1.46801	+	0.534314i	−0.947561	−	0.319576i	$-0.896459\pi$
$239$	−5424.09	+	1974.21i	−1.46801	+	0.534314i	−0.520454	+	0.853890i	$0.674237\pi$
$240$	4178.13	−	6824.98i	1.12374	−	1.83563i
$241$	1063.43	+	6031.02i	0.284239	+	1.61200i	0.707991	+	0.706221i	$0.249602\pi$
$241$	1063.43	+	6031.02i	0.284239	+	1.61200i	−0.423752	+	0.905778i	$0.639287\pi$
$242$	−1135.82			−0.301709
$243$	1457.48	+	3496.38i	0.384763	+	0.923015i
$244$	7875.50			2.06630
$245$	−841.820	−	4774.20i	−0.219518	−	1.24495i
$246$	−6179.40	+	10094.1i	−1.60156	+	2.61616i
$247$	−1162.75	+	423.206i	−0.299530	+	0.109020i
$248$	1400.98	+	1175.56i	0.358719	+	0.301001i
$249$	1222.32	+	480.847i	0.311089	+	0.122379i
$250$	−542.733	−	197.539i	−0.137302	−	0.0499738i
$251$	1154.86	+	2000.27i	0.290414	+	0.503011i	0.973908	−	0.226945i	$-0.0728737\pi$
$251$	1154.86	+	2000.27i	0.290414	+	0.503011i	−0.683494	+	0.729956i	$0.739540\pi$
$252$	−1202.68	−	2355.15i	−0.300643	−	0.588733i
$253$	−575.077	+	996.063i	−0.142904	+	0.247518i
$254$	−1717.89	+	1441.48i	−0.424369	+	0.356088i
$255$	274.964	−	1354.61i	0.0675251	−	0.332663i
$256$	−1400.15	+	7940.62i	−0.341832	+	1.93863i
$257$	94.4655	−	535.740i	0.0229284	−	0.130033i	−0.971195	−	0.238286i	$-0.923414\pi$
$257$	94.4655	−	535.740i	0.0229284	−	0.130033i	0.994123	+	0.108253i	$0.0345256\pi$
$258$	412.368	−	138.183i	0.0995075	−	0.0333446i
$259$	1246.86	−	1046.24i	0.299136	−	0.251005i
$260$	7929.97	−	13735.1i	1.89152	−	3.27621i
$261$	4325.35	−	3265.49i	1.02579	−	0.774441i
$262$	−4767.04	−	8256.75i	−1.12408	−	1.94696i
$263$	−3598.48	−	1309.74i	−0.843695	−	0.307080i	−0.116228	−	0.993223i	$-0.537080\pi$
$263$	−3598.48	−	1309.74i	−0.843695	−	0.307080i	−0.727467	+	0.686143i	$0.759303\pi$
$264$	7573.03	−	6029.43i	1.76548	−	1.40563i
$265$	−6450.52	−	5412.63i	−1.49529	−	1.25470i
$266$	−563.423	+	205.069i	−0.129871	+	0.0472692i
$267$	−4866.02	−	125.228i	−1.11534	−	0.0287035i
$268$	938.081	+	5320.12i	0.213815	+	1.21261i
$269$	3865.59			0.876169			0.438084	−	0.898934i	$-0.355657\pi$
$269$	3865.59			0.876169			0.438084	+	0.898934i	$0.355657\pi$
$270$	−6222.93	+	9080.68i	−1.40265	+	2.04679i
$271$	−46.0285			−0.0103175			−0.00515873	−	0.999987i	$-0.501642\pi$
$271$	−46.0285			−0.0103175			−0.00515873	+	0.999987i	$0.501642\pi$
$272$	−293.186	−	1662.74i	−0.0653568	−	0.370657i
$273$	−819.772	−	1508.21i	−0.181739	−	0.334363i
$274$	9028.58	−	3286.13i	1.99064	−	0.724535i
$275$	3555.32	+	2983.27i	0.779613	+	0.654173i
$276$	−390.191	−	2602.81i	−0.0850970	−	0.567648i
$277$	6335.30	+	2305.86i	1.37419	+	0.500165i	0.920412	−	0.390949i	$-0.127853\pi$
$277$	6335.30	+	2305.86i	1.37419	+	0.500165i	0.453780	+	0.891114i	$0.350075\pi$
$278$	7710.28	+	13354.6i	1.66342	+	2.88113i
$279$	−765.433	−	712.490i	−0.164248	−	0.152888i
$280$	2073.23	−	3590.94i	0.442498	−	0.766429i
$281$	−3634.72	+	3049.89i	−0.771634	+	0.647477i	−0.941127	−	0.338054i	$-0.890231\pi$
$281$	−3634.72	+	3049.89i	−0.771634	+	0.647477i	0.169493	+	0.985531i	$0.445787\pi$
$282$	2116.84	+	1871.12i	0.447007	+	0.395120i
$283$	623.179	−	3534.22i	0.130898	−	0.742360i	−0.846731	−	0.532022i	$-0.821432\pi$
$283$	623.179	−	3534.22i	0.130898	−	0.742360i	0.977629	−	0.210338i	$-0.0674564\pi$
$284$	−1255.04	+	7117.71i	−0.262230	+	1.48718i
$285$	1280.48	+	1131.85i	0.266138	+	0.235245i
$286$	8921.53	−	7486.05i	1.84455	−	1.54776i
$287$	−1274.51	+	2207.52i	−0.262133	+	0.454027i
$288$	−727.582	+	3164.51i	−0.148865	+	0.647467i
$289$	2310.68	+	4002.22i	0.470320	+	0.814618i
$290$	14800.1	+	5386.81i	2.99687	+	1.09077i
$291$	−248.938	−	1660.57i	−0.0501478	−	0.334516i
$292$	−7837.53	−	6576.47i	−1.57074	−	1.31801i
$293$	−6306.78	+	2295.48i	−1.25749	+	0.457691i	−0.882928	−	0.469509i	$-0.844431\pi$
$293$	−6306.78	+	2295.48i	−1.25749	+	0.457691i	−0.374567	+	0.927200i	$0.622209\pi$
$294$	3890.18	+	7157.12i	0.771700	+	1.41977i
$295$	440.517	+	2498.29i	0.0869419	+	0.493072i
$296$	−13633.9			−2.67721
$297$	−4501.79	+	3220.28i	−0.879529	+	0.629157i
$298$	−5569.82			−1.08272
$299$	−296.669	−	1682.49i	−0.0573806	−	0.325421i
$300$	−10616.8	−	273.226i	−2.04320	−	0.0525823i
$301$	88.0184	−	32.0361i	0.0168548	−	0.00613464i
$302$	−10662.7	−	8947.05i	−2.03168	−	1.70478i
$303$	1027.49	−	818.056i	0.194811	−	0.155103i
$304$	1961.65	+	713.982i	0.370093	+	0.134703i
$305$	−3530.41	−	6114.85i	−0.662789	−	1.14798i
$306$	285.133	+	2305.06i	0.0532680	+	0.430626i
$307$	−572.149	+	990.992i	−0.106366	+	0.184231i	−0.914295	−	0.405048i	$-0.867255\pi$
$307$	−572.149	+	990.992i	−0.106366	+	0.184231i	0.807930	+	0.589279i	$0.200588\pi$
$308$	2960.06	−	2483.78i	0.547614	−	0.459502i
$309$	−6545.24	+	2193.28i	−1.20500	+	0.403791i
$310$	527.713	−	2992.81i	0.0966842	−	0.548323i
$311$	1566.20	−	8882.39i	0.285567	−	1.61953i	−0.417686	−	0.908591i	$-0.637159\pi$
$311$	1566.20	−	8882.39i	0.285567	−	1.61953i	0.703253	−	0.710939i	$-0.251730\pi$
$312$	−2860.35	+	14091.6i	−0.519024	+	2.55698i
$313$	−892.475	+	748.876i	−0.161168	+	0.135236i	−0.719805	−	0.694176i	$-0.755769\pi$
$313$	−892.475	+	748.876i	−0.161168	+	0.135236i	0.558637	+	0.829412i	$0.311325\pi$
$314$	2773.91	−	4804.56i	0.498538	−	0.863493i
$315$	−1289.50	+	1989.57i	−0.230651	+	0.355872i
$316$	−4090.38	−	7084.74i	−0.728170	−	1.26123i
$317$	−26.5651	−	9.66891i	−0.00470677	−	0.00171312i	0.339666	−	0.940546i	$-0.389686\pi$
$317$	−26.5651	−	9.66891i	−0.00470677	−	0.00171312i	−0.344372	+	0.938833i	$0.611908\pi$
$318$	13167.2	+	5179.84i	2.32195	+	0.913431i
$319$	6066.38	+	5090.30i	1.06474	+	0.893423i
$320$	2710.09	−	986.393i	0.473433	−	0.172316i
$321$	4829.92	−	7889.68i	0.839812	−	1.37183i
$322$	−143.754	−	815.271i	−0.0248792	−	0.141097i
$323$	360.581			0.0621153
$324$	3469.21	−	12181.4i	0.594858	−	2.08871i
$325$	−6893.97			−1.17664
$326$	2802.74	+	15895.1i	0.476164	+	2.70046i
$327$	4609.22	−	7529.17i	0.779481	−	1.27329i
$328$	20063.9	−	7302.67i	3.37757	−	1.22934i
$329$	466.129	+	391.129i	0.0781110	+	0.0655429i
$330$	−14968.7	−	5888.56i	−2.49698	−	0.982286i
$331$	−10173.1	−	3702.70i	−1.68932	−	0.614861i	−0.694777	−	0.719225i	$-0.744497\pi$
$331$	−10173.1	−	3702.70i	−1.68932	−	0.614861i	−0.994539	+	0.104364i	$0.966719\pi$
$332$	−2195.94	−	3803.47i	−0.363005	−	0.628743i
$333$	7785.42	+	400.985i	1.28120	+	0.0659875i
$334$	−2942.38	+	5096.35i	−0.482035	+	0.834909i
$335$	3710.24	−	3113.26i	0.605110	−	0.507747i
$336$	−576.101	+	2838.17i	−0.0935384	+	0.460818i
$337$	−917.031	+	5200.74i	−0.148231	+	0.840660i	0.816485	+	0.577367i	$0.195920\pi$
$337$	−917.031	+	5200.74i	−0.148231	+	0.840660i	−0.964716	+	0.263293i	$0.915191\pi$
$338$	−1082.26	+	6137.81i	−0.174164	+	0.987731i
$339$	−2704.16	+	906.154i	−0.433244	+	0.145179i
$340$	−3540.44	+	2970.79i	−0.564728	+	0.473863i
$341$	764.001	−	1323.29i	0.121328	−	0.210147i
$342$	−2644.44	−	1119.69i	−0.418114	−	0.177034i
$343$	1844.02	+	3193.93i	0.290285	+	0.502788i
$344$	−737.275	−	268.346i	−0.115556	−	0.0420589i
$345$	−1846.01	+	1469.74i	−0.288076	+	0.229358i
$346$	−5407.65	−	4537.55i	−0.840222	−	0.705030i
$347$	9341.66	−	3400.09i	1.44521	−	0.526012i	0.503958	−	0.863728i	$-0.331876\pi$
$347$	9341.66	−	3400.09i	1.44521	−	0.526012i	0.941248	+	0.337716i	$0.109654\pi$
$348$	−18115.3	−	466.201i	−2.79046	−	0.0718132i
$349$	132.239	+	749.966i	0.0202825	+	0.115028i	0.993268	−	0.115838i	$-0.0369553\pi$
$349$	132.239	+	749.966i	0.0202825	+	0.115028i	−0.972986	+	0.230866i	$0.925844\pi$
$350$	−3340.55			−0.510172
$351$	2047.80	−	7962.62i	0.311406	−	1.21086i
$352$	−4744.61			−0.718434
$353$	597.423	+	3388.15i	0.0900782	+	0.510859i	0.996145	+	0.0877239i	$0.0279593\pi$
$353$	597.423	+	3388.15i	0.0900782	+	0.510859i	−0.906067	+	0.423135i	$0.860930\pi$
$354$	−2035.69	−	3745.25i	−0.305638	−	0.562311i
$355$	6089.08	−	2216.25i	0.910352	−	0.331341i
$356$	12467.9	+	10461.8i	1.85617	+	1.55751i
$357$	74.1620	+	494.706i	0.0109946	+	0.0733406i
$358$	−6818.02	−	2481.56i	−1.00655	−	0.366353i
$359$	38.5343	+	66.7434i	0.00566508	+	0.00981220i	0.868844	−	0.495086i	$-0.164863\pi$
$359$	38.5343	+	66.7434i	0.00566508	+	0.00981220i	−0.863179	+	0.504898i	$0.831530\pi$
$360$	18986.6	−	5823.50i	2.77967	−	0.852570i
$361$	3206.59	−	5553.97i	0.467501	−	0.809735i
$362$	3458.30	−	2901.85i	0.502110	−	0.421321i
$363$	−877.862	−	775.962i	−0.126931	−	0.112197i
$364$	−996.694	+	5652.53i	−0.143519	+	0.813937i
$365$	−1592.84	+	9033.46i	−0.228420	+	1.29543i
$366$	8889.58	+	7857.70i	1.26958	+	1.12221i
$367$	−9134.94	+	7665.13i	−1.29929	+	1.09024i	−0.309025	+	0.951054i	$0.600003\pi$
$367$	−9134.94	+	7665.13i	−1.29929	+	1.09024i	−0.990267	+	0.139181i	$0.955553\pi$
$368$	−1441.14	+	2496.13i	−0.204144	+	0.353587i
$369$	−11671.9	+	3579.97i	−1.64666	+	0.505057i
$370$	11327.6	+	19620.1i	1.59161	+	2.75675i
$371$	2863.63	+	1042.28i	0.400734	+	0.145855i
$372$	518.377	+	3457.89i	0.0722489	+	0.481944i
$373$	−2305.55	−	1934.59i	−0.320045	−	0.268550i	0.468584	−	0.883419i	$-0.344764\pi$
$373$	−2305.55	−	1934.59i	−0.320045	−	0.268550i	−0.788629	+	0.614869i	$0.789209\pi$
$374$	−3189.14	+	1160.75i	−0.440927	+	0.160484i
$375$	−284.518	−	523.455i	−0.0391799	−	0.0720829i
$376$	−885.071	−	5019.49i	−0.121394	−	0.688459i
$377$	−11763.1			−1.60697
$378$	992.285	−	3858.38i	0.135020	−	0.525010i
$379$	5072.56			0.687493			0.343747	−	0.939062i	$-0.388304\pi$
$379$	5072.56			0.687493			0.343747	+	0.939062i	$0.388304\pi$
$380$	−992.285	−	5627.53i	−0.133956	−	0.759700i
$381$	−2312.51	−	59.5129i	−0.310953	−	0.00800246i
$382$	−2809.20	+	1022.47i	−0.376260	+	0.136947i
$383$	9044.81	+	7589.50i	1.20671	+	1.01255i	0.999413	+	0.0342669i	$0.0109096\pi$
$383$	9044.81	+	7589.50i	1.20671	+	1.01255i	0.207293	+	0.978279i	$0.433535\pi$
$384$	−7702.27	+	6132.33i	−1.02358	+	0.814946i
$385$	−3255.44	−	1184.88i	−0.430941	−	0.156850i
$386$	−3587.04	−	6212.94i	−0.472994	−	0.819249i
$387$	413.116	+	174.918i	0.0542633	+	0.0229757i
$388$	−2807.20	+	4862.22i	−0.367304	+	0.636190i
$389$	7548.43	−	6333.88i	0.983857	−	0.825554i	−0.000809477	−	1.00000i	$-0.500258\pi$
$389$	7548.43	−	6333.88i	0.983857	−	0.825554i	0.984667	+	0.174445i	$0.0558132\pi$
$390$	22655.1	−	7591.65i	2.94151	−	0.985688i
$391$	−86.4519	+	490.293i	−0.0111817	+	0.0634148i
$392$	2551.91	−	14472.6i	0.328804	−	1.86474i
$393$	1956.40	−	9638.23i	0.251113	−	1.23711i
$394$	2970.90	−	2492.88i	0.379877	−	0.318755i
$395$	−3667.25	+	6351.86i	−0.467138	+	0.809106i
$396$	18482.6	+	951.941i	2.34542	+	0.120800i
$397$	−2489.64	−	4312.18i	−0.314739	−	0.545144i	0.664643	−	0.747161i	$-0.268584\pi$
$397$	−2489.64	−	4312.18i	−0.314739	−	0.545144i	−0.979382	+	0.202017i	$0.935250\pi$
$398$	−21507.8	−	7828.19i	−2.70876	−	0.985909i
$399$	−575.559	−	226.419i	−0.0722155	−	0.0284089i
$400$	8909.63	+	7476.07i	1.11370	+	0.934508i
$401$	3818.92	−	1389.97i	0.475580	−	0.173097i	−0.0930985	−	0.995657i	$-0.529677\pi$
$401$	3818.92	−	1389.97i	0.475580	−	0.173097i	0.568678	+	0.822560i	$0.307455\pi$
$402$	−4249.23	+	6941.13i	−0.527195	+	0.861174i
$403$	394.130	+	2235.22i	0.0487171	+	0.276289i
$404$	−4391.46			−0.540801
$405$	−11013.3	+	2767.00i	−1.35124	+	0.339490i
$406$	−5699.93			−0.696756
$407$	1978.04	+	11218.0i	0.240904	+	1.36624i
$408$	2187.73	−	3573.67i	0.265463	−	0.433635i
$409$	2611.57	−	950.534i	0.315731	−	0.114917i	−0.179294	−	0.983796i	$-0.557381\pi$
$409$	2611.57	−	950.534i	0.315731	−	0.114917i	0.495025	+	0.868879i	$0.335159\pi$
$410$	−27179.0	−	22805.9i	−3.27384	−	2.74708i
$411$	9223.05	+	3628.26i	1.10691	+	0.435447i
$412$	21689.1	+	7894.18i	2.59356	+	0.943977i
$413$	−459.042	−	795.084i	−0.0546924	−	0.0947301i
$414$	2156.50	−	3327.27i	0.256005	−	0.394992i
$415$	−1968.78	+	3410.02i	−0.232876	+	0.403353i
$416$	5398.83	−	4530.16i	0.636297	−	0.533917i
$417$	−3164.31	+	15589.0i	−0.371599	+	1.83069i
$418$	728.653	−	4132.39i	0.0852621	−	0.483545i
$419$	1910.84	−	10836.9i	0.222794	−	1.26353i	−0.644064	−	0.764971i	$-0.722753\pi$
$419$	1910.84	−	10836.9i	0.222794	−	1.26353i	0.866858	−	0.498555i	$-0.166136\pi$
$420$	7516.70	−	2518.82i	0.873280	−	0.292633i
$421$	680.336	−	570.869i	0.0787590	−	0.0660866i	−0.602558	−	0.798075i	$-0.705852\pi$
$421$	680.336	−	570.869i	0.0787590	−	0.0660866i	0.681317	+	0.731988i	$0.261407\pi$
$422$	10139.6	−	17562.3i	1.16964	−	2.02588i
$423$	357.778	+	2892.33i	0.0411247	+	0.332458i
$424$	−12763.1	−	22106.4i	−1.46187	−	2.53203i
$425$	1887.81	+	687.106i	0.215464	+	0.0784225i
$426$	−8518.28	+	6782.01i	−0.968807	+	0.771337i
$427$	1957.49	+	1642.53i	0.221849	+	0.186153i
$428$	−29065.7	+	10579.1i	−3.28258	+	1.19476i
$429$	12009.6	+	309.070i	1.35158	+	0.0347833i
$430$	226.393	+	1283.94i	0.0253899	+	0.143993i
$431$	−6010.51			−0.671731			−0.335866	−	0.941910i	$-0.609029\pi$
$431$	−6010.51			−0.671731			−0.335866	+	0.941910i	$0.609029\pi$
$432$	−11281.5	+	8070.02i	−1.25644	+	0.898771i
$433$	7426.23			0.824207			0.412104	−	0.911137i	$-0.364794\pi$
$433$	7426.23			0.824207			0.412104	+	0.911137i	$0.364794\pi$
$434$	190.980	+	1083.10i	0.0211229	+	0.119794i
$435$	7758.70	+	14274.4i	0.855175	+	1.57335i
$436$	−27737.6	+	10095.7i	−3.04677	+	1.10893i
$437$	−471.542	−	395.671i	−0.0516176	−	0.0433123i
$438$	−2285.12	−	15243.1i	−0.249286	−	1.66289i
$439$	9868.78	+	3591.94i	1.07292	+	0.390510i	0.817267	−	0.576259i	$-0.195488\pi$
$439$	9868.78	+	3591.94i	1.07292	+	0.390510i	0.255651	+	0.966769i	$0.417710\pi$
$440$	14509.4	+	25131.0i	1.57207	+	2.72290i
$441$	−1882.88	+	8189.30i	−0.203313	+	0.884278i
$442$	2520.60	−	4365.80i	0.271250	−	0.469819i
$443$	−7197.04	+	6039.03i	−0.771877	+	0.647682i	−0.941189	−	0.337881i	$-0.890290\pi$
$443$	−7197.04	+	6039.03i	−0.771877	+	0.647682i	0.169312	+	0.985563i	$0.445846\pi$
$444$	−19530.3	−	17263.2i	−2.08753	−	1.84522i
$445$	2533.88	−	14370.4i	0.269927	−	1.53083i
$446$	−4021.07	+	22804.6i	−0.426913	+	2.42115i
$447$	−4304.83	−	3805.14i	−0.455507	−	0.402633i
$448$	−799.544	+	670.897i	−0.0843190	+	0.0707520i
$449$	4004.86	−	6936.62i	0.420937	−	0.729085i	−0.575094	−	0.818087i	$-0.695035\pi$
$449$	4004.86	−	6936.62i	0.420937	−	0.729085i	0.996031	+	0.0890023i	$0.0283679\pi$
$450$	−11711.3	−	10901.2i	−1.22683	−	1.14197i
$451$	−8919.60	−	15449.2i	−0.931281	−	1.61303i
$452$	8960.84	+	3261.48i	0.932483	+	0.339396i
$453$	−2128.67	−	14199.5i	−0.220780	−	1.47274i
$454$	578.704	+	485.590i	0.0598236	+	0.0501980i
$455$	4835.65	−	1760.03i	0.498239	−	0.181344i
$456$	2474.08	+	4551.80i	0.254078	+	0.467451i
$457$	−618.137	−	3505.63i	−0.0632718	−	0.358832i	−0.999962	−	0.00867400i	$-0.997239\pi$
$457$	−618.137	−	3505.63i	−0.0632718	−	0.358832i	0.936691	−	0.350158i	$-0.113872\pi$
$458$	26074.1			2.66018
$459$	−1354.37	+	1976.34i	−0.137727	+	0.200976i
$460$	7889.83			0.799707
$461$	−433.570	−	2458.90i	−0.0438034	−	0.248422i	0.955041	−	0.296472i	$-0.0958102\pi$
$461$	−433.570	−	2458.90i	−0.0438034	−	0.248422i	−0.998845	+	0.0480506i	$0.984699\pi$
$462$	5819.38	+	149.763i	0.586022	+	0.0150814i
$463$	4975.36	−	1810.88i	0.499405	−	0.181769i	−0.0800212	−	0.996793i	$-0.525499\pi$
$463$	4975.36	−	1810.88i	0.499405	−	0.181769i	0.579426	+	0.815025i	$0.303277\pi$
$464$	15202.4	+	12756.3i	1.52102	+	1.27628i
$465$	2452.46	−	1952.58i	0.244581	−	0.194729i
$466$	2340.61	+	851.911i	0.232675	+	0.0846867i
$467$	342.837	+	593.811i	0.0339713	+	0.0588400i	0.882511	−	0.470291i	$-0.155851\pi$
$467$	342.837	+	593.811i	0.0339713	+	0.0588400i	−0.848540	+	0.529131i	$0.822518\pi$
$468$	−21940.1	+	16564.0i	−2.16705	+	1.63605i
$469$	−876.411	+	1517.99i	−0.0862876	+	0.149455i
$470$	−6488.01	+	5444.08i	−0.636744	+	0.534291i
$471$	5426.25	−	1818.32i	0.530846	−	0.177884i
$472$	−1335.39	+	7573.38i	−0.130225	+	0.738545i
$473$	−113.831	+	645.566i	−0.0110654	+	0.0627551i
$474$	2451.66	−	12078.1i	0.237571	−	1.17040i
$475$	−1902.78	+	1596.62i	−0.183801	+	0.154227i
$476$	836.304	−	1448.52i	0.0805293	−	0.139481i
$477$	6638.01	+	12998.9i	0.637177	+	1.24775i
$478$	14538.1	+	25180.7i	1.39112	+	2.40949i
$479$	−13552.8	−	4932.81i	−1.29278	−	0.470534i	−0.398143	−	0.917323i	$-0.630345\pi$
$479$	−13552.8	−	4932.81i	−1.29278	−	0.470534i	−0.894639	+	0.446789i	$0.852567\pi$
$480$	−9058.28	−	3563.44i	−0.861358	−	0.338850i
$481$	−12961.8	−	10876.2i	−1.22870	−	1.03101i
$482$	28988.1	−	10550.8i	2.73937	−	0.997047i
$483$	445.864	−	728.320i	0.0420031	−	0.0686122i
$484$	680.281	+	3858.07i	0.0638882	+	0.362328i
$485$	5033.63			0.471268
$486$	16069.8	−	10288.5i	1.49988	−	0.960281i
$487$	9613.07			0.894476			0.447238	−	0.894415i	$-0.352408\pi$
$487$	9613.07			0.894476			0.447238	+	0.894415i	$0.352408\pi$
$488$	−3716.82	−	21079.1i	−0.344780	−	1.95534i
$489$	−8692.89	+	14199.9i	−0.803898	+	1.31317i
$490$	−22947.3	+	8352.12i	−2.11561	+	0.770021i
$491$	2330.71	+	1955.70i	0.214223	+	0.179755i	0.743585	−	0.668642i	$-0.233124\pi$
$491$	2330.71	+	1955.70i	0.214223	+	0.179755i	−0.529361	+	0.848396i	$0.677568\pi$
$492$	37987.7	+	14944.0i	3.48093	+	1.36936i
$493$	3221.14	+	1172.40i	0.294265	+	0.107104i
$494$	3116.49	+	5397.92i	0.283841	+	0.491627i
$495$	−7546.23	−	14777.4i	−0.685208	−	1.34181i
$496$	1914.59	−	3316.16i	0.173322	−	0.300202i
$497$	−1796.43	+	1507.38i	−0.162135	+	0.136047i
$498$	1316.18	−	6484.20i	0.118433	−	0.583462i
$499$	2243.24	−	12722.0i	0.201244	−	1.14131i	−0.701996	−	0.712180i	$-0.747708\pi$
$499$	2243.24	−	12722.0i	0.201244	−	1.14131i	0.903241	−	0.429134i	$-0.141181\pi$
$500$	−345.922	+	1961.82i	−0.0309402	+	0.175471i
$501$	−5755.80	+	1928.75i	−0.513274	+	0.171996i
$502$	8912.66	−	7478.61i	0.792413	−	0.664914i
$503$	−5416.54	+	9381.72i	−0.480142	+	0.831631i	−0.999741	−	0.0227800i	$-0.992748\pi$
$503$	−5416.54	+	9381.72i	−0.480142	+	0.831631i	0.519598	+	0.854411i	$0.326082\pi$
$504$	−5736.08	+	4330.55i	−0.506955	+	0.382734i
$505$	1968.60	+	3409.71i	0.173468	+	0.300455i
$506$	5444.24	+	1981.54i	0.478313	+	0.174092i
$507$	−5029.64	+	4004.46i	−0.440580	+	0.350778i
$508$	5925.18	+	4971.82i	0.517495	+	0.434230i
$509$	−8799.04	+	3202.59i	−0.766229	+	0.278885i	−0.695418	−	0.718605i	$-0.744781\pi$
$509$	−8799.04	+	3202.59i	−0.766229	+	0.278885i	−0.0708109	+	0.997490i	$0.522559\pi$
$510$	−6960.40	−	179.128i	−0.604337	−	0.0155528i
$511$	−576.452	−	3269.22i	−0.0499036	−	0.283017i
$512$	25458.3			2.19747
$513$	−1278.91	−	2672.00i	−0.110069	−	0.229964i
$514$	−2740.30			−0.235155
$515$	−3593.38	−	20379.1i	−0.307463	−	1.74371i
$516$	−716.349	−	1317.94i	−0.0611153	−	0.112440i
$517$	−4001.65	+	1456.48i	−0.340411	+	0.123899i
$518$	−6280.79	−	5270.21i	−0.532745	−	0.447026i
$519$	−1079.57	−	7201.36i	−0.0913058	−	0.609065i
$520$	−40505.2	−	14742.7i	−3.41590	−	1.24329i
$521$	−2385.57	−	4131.92i	−0.200602	−	0.347453i	0.748121	−	0.663563i	$-0.230956\pi$
$521$	−2385.57	−	4131.92i	−0.200602	−	0.347453i	−0.948723	+	0.316110i	$0.897623\pi$
$522$	−19982.7	−	18600.6i	−1.67552	−	1.55963i
$523$	5149.38	−	8918.99i	0.430529	−	0.745698i	−0.566390	−	0.824137i	$-0.691660\pi$
$523$	5149.38	−	8918.99i	0.430529	−	0.745698i	0.996919	+	0.0784392i	$0.0249936\pi$
$524$	−25190.7	+	21137.5i	−2.10012	+	1.76221i
$525$	−2581.87	−	2282.17i	−0.214632	−	0.189718i
$526$	−3349.65	+	18996.8i	−0.277665	+	1.57471i
$527$	114.853	−	651.363i	0.00949349	−	0.0538403i
$528$	−15185.8	−	13423.0i	−1.25166	−	1.10637i
$529$	−8669.40	+	7274.49i	−0.712534	+	0.597887i
$530$	−21208.3	+	36733.9i	−1.73817	+	3.01060i
$531$	985.293	−	4285.38i	0.0805237	−	0.350225i
$532$	1034.01	+	1790.96i	0.0842673	+	0.145955i
$533$	24900.4	+	9063.01i	2.02356	+	0.736515i
$534$	3635.15	+	24248.6i	0.294585	+	1.96506i
$535$	21243.5	+	17825.4i	1.71671	+	1.44049i
$536$	13796.8	−	5021.64i	1.11181	−	0.404667i
$537$	−3574.22	−	6575.84i	−0.287224	−	0.528433i
$538$	−3381.29	−	19176.2i	−0.270962	−	1.53670i
$539$	−12278.4			−0.981201
$540$	34571.6	+	15698.8i	2.75504	+	1.25105i
$541$	−11070.6			−0.879783			−0.439892	−	0.898051i	$-0.644983\pi$
$541$	−11070.6			−0.879783			−0.439892	+	0.898051i	$0.644983\pi$
$542$	40.2618	+	228.336i	0.00319076	+	0.0180957i
$543$	4655.33	+	119.806i	0.367918	+	0.00946845i
$544$	−1929.90	+	702.425i	−0.152102	+	0.0553607i
$545$	20272.8	+	17010.9i	1.59338	+	1.33700i
$546$	−6764.79	+	5385.94i	−0.530232	+	0.422155i
$547$	−8326.61	−	3030.64i	−0.650860	−	0.236894i	−0.00457452	−	0.999990i	$-0.501456\pi$
$547$	−8326.61	−	3030.64i	−0.650860	−	0.236894i	−0.646285	+	0.763096i	$0.723678\pi$
$548$	−16569.6	−	28699.3i	−1.29164	−	2.23718i
$549$	1502.47	+	12146.2i	0.116802	+	0.944240i
$550$	11689.3	−	20246.5i	0.906246	−	1.56966i
$551$	−3246.68	+	2724.29i	−0.251022	+	0.210633i
$552$	−6782.40	+	2272.76i	−0.522968	+	0.175245i
$553$	460.926	−	2614.04i	0.0354441	−	0.201013i
$554$	5897.22	−	33444.8i	0.452254	−	2.56486i
$555$	−4648.89	+	22902.8i	−0.355557	+	1.75166i
$556$	40743.8	−	34188.1i	3.10777	−	2.60773i
$557$	2971.99	−	5147.64i	0.226081	−	0.391584i	−0.730562	−	0.682846i	$-0.760742\pi$
$557$	2971.99	−	5147.64i	0.226081	−	0.391584i	0.956643	+	0.291262i	$0.0940752\pi$
$558$	−2864.95	+	4420.34i	−0.217353	+	0.335355i
$559$	−486.860	−	843.267i	−0.0368372	−	0.0638039i
$560$	−8158.13	−	2969.32i	−0.615614	−	0.224065i
$561$	−3257.84	−	1281.60i	−0.245180	−	0.0964514i
$562$	18309.1	+	15363.1i	1.37424	+	1.15312i
$563$	−14554.1	+	5297.24i	−1.08949	+	0.396540i	−0.823430	−	0.567417i	$-0.807943\pi$
$563$	−14554.1	+	5297.24i	−1.08949	+	0.396540i	−0.266055	+	0.963958i	$0.585720\pi$
$564$	5087.82	−	8310.97i	0.379851	−	0.620488i
$565$	−1484.60	−	8419.60i	−0.110545	−	0.626930i
$566$	−18077.5			−1.34250
$567$	3402.86	−	2304.19i	0.252040	−	0.170664i
$568$	19643.2			1.45108
$569$	374.543	+	2124.14i	0.0275952	+	0.156500i	0.995492	−	0.0948491i	$-0.0302369\pi$
$569$	374.543	+	2124.14i	0.0275952	+	0.156500i	−0.967896	+	0.251349i	$0.919126\pi$
$570$	4494.76	−	7342.19i	0.330289	−	0.539528i
$571$	−14760.6	+	5372.44i	−1.08181	+	0.393747i	−0.820581	−	0.571530i	$-0.806350\pi$
$571$	−14760.6	+	5372.44i	−1.08181	+	0.393747i	−0.261229	+	0.965277i	$0.584128\pi$
$572$	−30771.4	−	25820.3i	−2.24933	−	1.88741i
$573$	−2869.71	−	1128.92i	−0.209221	−	0.0823057i
$574$	12065.8	+	4391.58i	0.877379	+	0.319340i
$575$	−1714.77	−	2970.07i	−0.124367	−	0.215409i
$576$	−4992.36	−	257.130i	−0.361137	−	0.0186002i
$577$	−5989.26	+	10373.7i	−0.432125	+	0.748462i	−0.997056	−	0.0766759i	$-0.975569\pi$
$577$	−5989.26	+	10373.7i	−0.432125	+	0.748462i	0.564931	+	0.825138i	$0.308903\pi$
$578$	17832.8	−	14963.5i	1.28330	−	1.07682i
$579$	1472.13	−	7252.46i	0.105664	−	0.520556i
$580$	9433.16	−	53498.1i	0.675329	−	3.82998i
$581$	247.450	−	1403.36i	0.0176695	−	0.100208i
$582$	−8019.90	+	2687.44i	−0.571195	+	0.191405i
$583$	−16337.5	+	13708.8i	−1.16060	+	0.973862i
$584$	−13903.3	+	24081.3i	−0.985144	+	1.70632i
$585$	22696.2	+	9609.86i	1.60406	+	0.679178i
$586$	16903.9	+	29278.4i	1.19163	+	2.06396i
$587$	−15576.6	−	5669.43i	−1.09526	−	0.398641i	−0.269692	−	0.962947i	$-0.586922\pi$
$587$	−15576.6	−	5669.43i	−1.09526	−	0.398641i	−0.825566	+	0.564305i	$0.809144\pi$
$588$	21980.8	−	17500.4i	1.54162	−	1.22739i
$589$	626.452	+	525.656i	0.0438243	+	0.0367729i
$590$	12008.1	−	4370.58i	0.837906	−	0.304973i
$591$	3999.23	+	102.921i	0.278352	+	0.00716347i
$592$	4956.98	+	28112.4i	0.344140	+	1.95171i
$593$	17790.1			1.23196			0.615981	−	0.787761i	$-0.288760\pi$
$593$	17790.1			1.23196			0.615981	+	0.787761i	$0.288760\pi$
$594$	19912.8	+	19515.4i	1.37547	+	1.34802i
$595$	−1499.59			−0.103323
$596$	3335.95	+	18919.1i	0.229271	+	1.30026i
$597$	−11275.1	−	20743.8i	−0.772961	−	1.42209i
$598$	−8086.92	+	2943.40i	−0.553008	+	0.201278i
$599$	−82.6583	−	69.3585i	−0.00563827	−	0.00473107i	0.639964	−	0.768405i	$-0.278949\pi$
$599$	−82.6583	−	69.3585i	−0.00563827	−	0.00473107i	−0.645602	+	0.763674i	$0.723394\pi$
$600$	4279.27	+	28545.3i	0.291167	+	1.94226i
$601$	2041.21	+	742.939i	0.138540	+	0.0504245i	0.410360	−	0.911924i	$-0.365403\pi$
$601$	2041.21	+	742.939i	0.138540	+	0.0504245i	−0.271820	+	0.962348i	$0.587625\pi$
$602$	−235.914	−	408.614i	−0.0159720	−	0.0276643i
$603$	−8026.15	+	2461.75i	−0.542040	+	0.166252i
$604$	−24004.3	+	41576.7i	−1.61709	+	2.80088i
$605$	2690.60	−	2257.68i	0.180808	−	0.151716i
$606$	−4956.93	−	4381.54i	−0.332280	−	0.293710i
$607$	−3759.63	+	21321.9i	−0.251398	+	1.42575i	0.553754	+	0.832680i	$0.313195\pi$
$607$	−3759.63	+	21321.9i	−0.251398	+	1.42575i	−0.805152	+	0.593069i	$0.797916\pi$
$608$	440.941	−	2500.70i	0.0294121	−	0.166804i
$609$	−4405.40	−	3894.03i	−0.293129	−	0.259104i
$610$	−27246.1	+	22862.2i	−1.80846	+	1.51748i
$611$	3162.78	−	5478.09i	0.209415	−	0.362717i
$612$	7658.85	−	2349.09i	0.505867	−	0.155158i
$613$	1475.96	+	2556.44i	0.0972490	+	0.168440i	0.910545	−	0.413410i	$-0.135662\pi$
$613$	1475.96	+	2556.44i	0.0972490	+	0.168440i	−0.813296	+	0.581850i	$0.802329\pi$
$614$	5416.53	+	1971.45i	0.356015	+	0.129579i
$615$	−5425.93	−	36194.2i	−0.355764	−	2.37316i
$616$	−8044.96	−	6750.52i	−0.526202	−	0.441536i
$617$	884.322	−	321.867i	0.0577009	−	0.0210014i	−0.313008	−	0.949750i	$-0.601337\pi$
$617$	884.322	−	321.867i	0.0577009	−	0.0210014i	0.370709	+	0.928749i	$0.379115\pi$
$618$	16605.5	+	30550.8i	1.08086	+	1.98856i
$619$	2619.16	+	14854.0i	0.170069	+	0.964511i	0.943682	+	0.330853i	$0.107336\pi$
$619$	2619.16	+	14854.0i	0.170069	+	0.964511i	−0.773613	+	0.633658i	$0.781552\pi$
$620$	−10481.8			−0.678966
$621$	3939.82	−	1098.34i	0.254589	−	0.0709743i
$622$	−45433.3			−2.92879
$623$	917.016	+	5200.65i	0.0589718	+	0.334446i
$624$	30096.0	+	774.529i	1.93078	+	0.0496890i
$625$	15496.4	−	5640.23i	0.991769	−	0.360974i
$626$	4495.64	+	3772.29i	0.287032	+	0.240848i
$627$	3386.30	−	2696.07i	0.215687	−	0.171724i
$628$	−17981.1	−	6544.58i	−1.14255	−	0.415855i
$629$	2465.38	+	4270.16i	0.156282	+	0.270688i
$630$	10997.7	+	4656.57i	0.695491	+	0.294480i
$631$	1917.22	−	3320.72i	0.120956	−	0.209502i	−0.799189	−	0.601080i	$-0.794737\pi$
$631$	1917.22	−	3320.72i	0.120956	−	0.209502i	0.920145	+	0.391578i	$0.128071\pi$
$632$	−17032.2	+	14291.7i	−1.07200	+	0.899516i
$633$	19834.9	−	6646.58i	1.24544	−	0.417343i
$634$	−24.7282	+	140.240i	−0.00154902	+	0.00878495i
$635$	1204.19	−	6829.31i	0.0752549	−	0.426792i
$636$	9708.19	−	47827.5i	0.605275	−	2.98190i
$637$	13971.4	−	11723.4i	0.869023	−	0.729197i
$638$	19945.3	−	34546.3i	1.23769	−	2.14373i
$639$	−11216.9	−	577.724i	−0.694421	−	0.0357659i
$640$	−14757.0	−	25559.9i	−0.911441	−	1.57866i
$641$	23949.5	+	8716.91i	1.47574	+	0.537125i	0.949652	−	0.313306i	$-0.101437\pi$
$641$	23949.5	+	8716.91i	1.47574	+	0.537125i	0.526087	+	0.850431i	$0.323659\pi$
$642$	−43363.5	−	17058.8i	−2.66576	−	1.04869i
$643$	−2158.26	−	1811.00i	−0.132369	−	0.111071i	0.574199	−	0.818716i	$-0.305313\pi$
$643$	−2158.26	−	1811.00i	−0.132369	−	0.111071i	−0.706569	+	0.707644i	$0.749758\pi$
$644$	−2683.14	+	976.584i	−0.164178	+	0.0597559i
$645$	−702.174	+	1147.00i	−0.0428652	+	0.0700205i
$646$	−315.405	−	1788.75i	−0.0192097	−	0.108943i
$647$	4835.21			0.293805			0.146902	−	0.989151i	$-0.453070\pi$
$647$	4835.21			0.293805			0.146902	+	0.989151i	$0.453070\pi$
$648$	−34241.3	−	3536.55i	−2.07581	−	0.214396i
$649$	6425.16			0.388612
$650$	6030.25	+	34199.3i	0.363886	+	2.06370i
$651$	−592.339	+	967.587i	−0.0356614	+	0.0582530i
$652$	52312.5	−	19040.2i	3.14220	−	1.14367i
$653$	−5275.81	−	4426.93i	−0.316169	−	0.265297i	0.470867	−	0.882204i	$-0.343941\pi$
$653$	−5275.81	−	4426.93i	−0.316169	−	0.265297i	−0.787036	+	0.616907i	$0.788386\pi$
$654$	−41382.1	−	16279.3i	−2.47426	−	0.973350i
$655$	27704.4	+	10083.6i	1.65267	+	0.601524i
$656$	−22352.5	−	38715.7i	−1.33037	−	2.30426i
$657$	8647.52	−	13342.3i	0.513504	−	0.792288i
$658$	1532.56	−	2654.47i	0.0907985	−	0.157268i
$659$	17755.3	−	14898.5i	1.04954	−	0.880670i	0.0564962	−	0.998403i	$-0.482007\pi$
$659$	17755.3	−	14898.5i	1.04954	−	0.880670i	0.993045	+	0.117733i	$0.0375627\pi$
$660$	−11036.5	+	54371.4i	−0.650901	+	3.20667i
$661$	−922.380	+	5231.08i	−0.0542760	+	0.307814i	−0.999845	−	0.0176073i	$-0.994395\pi$
$661$	−922.380	+	5231.08i	−0.0542760	+	0.307814i	0.945569	+	0.325422i	$0.105506\pi$
$662$	−9469.63	+	53704.9i	−0.555963	+	3.15302i
$663$	4930.72	−	1652.27i	0.288829	−	0.0967854i
$664$	−9143.81	+	7672.57i	−0.534411	+	0.448424i
$665$	927.051	−	1605.70i	0.0540594	−	0.0936336i
$666$	−4820.83	−	38972.3i	−0.280485	−	2.26748i
$667$	−2925.89	−	5067.78i	−0.169851	−	0.294191i
$668$	19073.1	+	6942.05i	1.10473	+	0.402090i
$669$	−18687.3	+	14878.3i	−1.07996	+	0.859833i
$670$	−18689.5	−	15682.3i	−1.07767	−	0.904271i
$671$	−16804.8	+	6116.44i	−0.966828	+	0.351896i
$672$	3521.58	+	90.6286i	0.202154	+	0.00520249i
$673$	−4766.72	−	27033.4i	−0.273022	−	1.54838i	−0.745176	−	0.666868i	$-0.767635\pi$
$673$	−4766.72	−	27033.4i	−0.273022	−	1.54838i	0.472154	−	0.881516i	$-0.343477\pi$
$674$	26601.7			1.52027
$675$	−1604.06	−	16426.2i	−0.0914674	−	0.936658i
$676$	21496.6			1.22307
$677$	−1476.95	−	8376.18i	−0.0838459	−	0.475514i	−0.997600	−	0.0692452i	$-0.977941\pi$
$677$	−1476.95	−	8376.18i	−0.0838459	−	0.475514i	0.913754	−	0.406268i	$-0.133170\pi$
$678$	6860.57	+	12622.0i	0.388611	+	0.714965i
$679$	−1711.82	+	623.050i	−0.0967503	+	0.0352142i
$680$	9622.36	+	8074.12i	0.542648	+	0.455336i
$681$	115.531	+	770.660i	0.00650095	+	0.0433653i
$682$	−7232.78	−	2632.52i	−0.406096	−	0.147807i
$683$	15369.6	+	26621.0i	0.861059	+	1.49140i	0.870908	+	0.491446i	$0.163532\pi$
$683$	15369.6	+	26621.0i	0.861059	+	1.49140i	−0.00984920	+	0.999951i	$0.503135\pi$
$684$	−2219.42	+	9653.02i	−0.124067	+	0.539609i
$685$	−14855.5	+	25730.6i	−0.828615	+	1.43520i
$686$	14231.3	−	11941.5i	0.792061	−	0.664618i
$687$	20152.3	+	17813.1i	1.11915	+	0.989245i
$688$	−285.260	+	1617.79i	−0.0158073	+	0.0896477i
$689$	5501.09	−	31198.2i	0.304172	−	1.72505i
$690$	8905.76	+	7872.00i	0.491357	+	0.434322i
$691$	−7723.56	+	6480.84i	−0.425207	+	0.356791i	−0.830140	−	0.557555i	$-0.811739\pi$
$691$	−7723.56	+	6480.84i	−0.425207	+	0.356791i	0.404933	+	0.914347i	$0.367295\pi$
$692$	−12174.0	+	21085.9i	−0.668764	+	1.15833i
$693$	4395.40	+	4091.38i	0.240934	+	0.224270i
$694$	−25038.3	−	43367.5i	−1.36951	−	2.37206i
$695$	−44809.6	−	16309.3i	−2.44565	−	0.890142i
$696$	7301.65	+	48706.4i	0.397656	+	2.65260i
$697$	−5915.31	−	4963.53i	−0.321461	−	0.269738i
$698$	3604.72	−	1312.01i	0.195474	−	0.0711466i
$699$	1227.02	+	2257.47i	0.0663951	+	0.122153i
$700$	2000.77	+	11346.9i	0.108031	+	0.612675i
$701$	−17040.1			−0.918108			−0.459054	−	0.888408i	$-0.651812\pi$
$701$	−17040.1			−0.918108			−0.459054	+	0.888408i	$0.651812\pi$
$702$	−41291.8	−	3193.61i	−2.22003	−	0.171702i
$703$	−6096.43			−0.327072
$704$	−1268.41	−	7193.52i	−0.0679049	−	0.385108i
$705$	−8733.73	−	224.765i	−0.466569	−	0.0120073i
$706$	16285.2	−	5927.33i	0.868132	−	0.315974i
$707$	−1091.52	−	915.892i	−0.0580633	−	0.0487209i
$708$	−11502.3	+	9157.82i	−0.610570	+	0.486118i
$709$	35055.7	+	12759.2i	1.85690	+	0.675858i	0.981195	+	0.193021i	$0.0618287\pi$
$709$	35055.7	+	12759.2i	1.85690	+	0.675858i	0.875710	+	0.482837i	$0.160394\pi$
$710$	−16320.4	−	28267.8i	−0.862669	−	1.49419i
$711$	10146.3	−	7660.12i	0.535184	−	0.404046i
$712$	22117.3	−	38308.3i	1.16416	−	2.01638i
$713$	−864.947	+	725.777i	−0.0454313	+	0.0381214i
$714$	2389.24	−	800.625i	0.125231	−	0.0419645i
$715$	−6253.75	+	35466.8i	−0.327101	+	1.85508i
$716$	−4345.61	+	24645.2i	−0.226820	+	1.28636i
$717$	−5966.45	+	29393.8i	−0.310769	+	1.53101i
$718$	297.390	−	249.540i	0.0154575	−	0.0129704i
$719$	−10784.5	+	18679.3i	−0.559380	+	0.968874i	0.438168	+	0.898893i	$0.355627\pi$
$719$	−10784.5	+	18679.3i	−0.559380	+	0.968874i	−0.997548	+	0.0699815i	$0.977706\pi$
$720$	−18910.9	−	37032.2i	−0.978842	−	1.91682i
$721$	3744.49	+	6485.65i	0.193415	+	0.335005i
$722$	−30356.7	−	11048.9i	−1.56476	−	0.569527i
$723$	29612.5	+	11649.3i	1.52324	+	0.599228i
$724$	−11928.1	−	10008.8i	−0.612296	−	0.513778i
$725$	−22189.2	+	8076.20i	−1.13667	+	0.413714i
$726$	−3081.47	+	5033.59i	−0.157526	+	0.257320i
$727$	−4038.36	−	22902.7i	−0.206017	−	1.16838i	−0.895831	−	0.444395i	$-0.853419\pi$
$727$	−4038.36	−	22902.7i	−0.206017	−	1.16838i	0.689813	−	0.723987i	$-0.257693\pi$
$728$	15599.7			0.794179
$729$	19448.9	+	3026.55i	0.988107	+	0.153765i
$730$	46206.0			2.34269
$731$	49.2728	+	279.440i	0.00249305	+	0.0141388i
$732$	21366.1	−	34901.6i	1.07884	−	1.76230i
$733$	−17275.4	+	6287.72i	−0.870505	+	0.316838i	−0.738372	−	0.674394i	$-0.764405\pi$
$733$	−17275.4	+	6287.72i	−0.870505	+	0.316838i	−0.132133	+	0.991232i	$0.542183\pi$
$734$	46015.2	+	38611.3i	2.31397	+	1.94165i
$735$	−23441.5	−	9221.67i	−1.17640	−	0.462784i
$736$	3294.56	+	1199.12i	0.164999	+	0.0600547i
$737$	−6133.51	−	10623.6i	−0.306555	−	0.530968i
$738$	27968.9	+	54770.1i	1.39506	+	2.73187i
$739$	7296.65	−	12638.2i	0.363209	−	0.629096i	−0.625278	−	0.780402i	$-0.715014\pi$
$739$	7296.65	−	12638.2i	0.363209	−	0.629096i	0.988487	+	0.151306i	$0.0483478\pi$
$740$	59859.3	−	50227.9i	2.97361	−	2.49515i
$741$	−1279.01	+	6301.07i	−0.0634085	+	0.312383i
$742$	2665.61	−	15117.4i	0.131884	−	0.747950i
$743$	−3626.20	+	20565.2i	−0.179048	+	1.01543i	0.754319	+	0.656508i	$0.227967\pi$
$743$	−3626.20	+	20565.2i	−0.179048	+	1.01543i	−0.933367	+	0.358923i	$0.883144\pi$
$744$	9010.55	−	3019.40i	0.444009	−	0.148786i
$745$	13194.1	−	11071.2i	0.648852	−	0.544451i
$746$	−7580.30	+	13129.5i	−0.372030	+	0.644375i
$747$	5447.08	−	4112.37i	0.266798	−	0.201424i
$748$	5852.83	+	10137.4i	0.286097	+	0.495535i
$749$	−9430.80	−	3432.53i	−0.460072	−	0.167453i
$750$	−2347.86	+	1869.30i	−0.114309	+	0.0910094i
$751$	7637.96	+	6409.01i	0.371123	+	0.311409i	0.809205	−	0.587526i	$-0.199898\pi$
$751$	7637.96	+	6409.01i	0.371123	+	0.311409i	−0.438083	+	0.898935i	$0.644342\pi$
$752$	−10028.1	+	3649.95i	−0.486288	+	0.176994i
$753$	11997.6	+	308.762i	0.580635	+	0.0149428i
$754$	10289.3	+	58353.7i	0.496970	+	2.81846i
$755$	43042.5			2.07480
$756$	−13700.1	−	1059.60i	−0.659086	−	0.0509752i
$757$	−32639.5			−1.56711			−0.783556	−	0.621321i	$-0.786596\pi$
$757$	−32639.5			−1.56711			−0.783556	+	0.621321i	$0.786596\pi$
$758$	−4437.04	−	25163.7i	−0.212613	−	1.20579i
$759$	2854.05	+	5250.86i	0.136489	+	0.251112i
$760$	−14594.0	+	5311.80i	−0.696554	+	0.253525i
$761$	−20219.3	−	16966.0i	−0.963138	−	0.808169i	0.0183225	−	0.999832i	$-0.494167\pi$
$761$	−20219.3	−	16966.0i	−0.963138	−	0.808169i	−0.981461	+	0.191663i	$0.938612\pi$
$762$	1727.55	+	11523.8i	0.0821294	+	0.547853i
$763$	−8999.87	−	3275.69i	−0.427021	−	0.155423i
$764$	5155.54	+	8929.66i	0.244137	+	0.422858i
$765$	−5257.22	−	4893.59i	−0.248464	−	0.231279i
$766$	29738.0	−	51507.6i	1.40271	−	2.42956i
$767$	−7311.11	+	6134.75i	−0.344183	+	0.288804i
$768$	31391.6	+	27747.8i	1.47493	+	1.30373i
$769$	978.862	−	5551.40i	0.0459020	−	0.260323i	−0.953217	−	0.302286i	$-0.902250\pi$
$769$	978.862	−	5551.40i	0.0459020	−	0.260323i	0.999119	+	0.0419631i	$0.0133612\pi$
$770$	−3030.33	+	17185.8i	−0.141825	+	0.804331i
$771$	−2117.94	−	1872.10i	−0.0989310	−	0.0874473i
$772$	−18955.2	+	15905.3i	−0.883694	+	0.741507i
$773$	706.977	−	1224.52i	0.0328955	−	0.0569766i	−0.849109	−	0.528218i	$-0.822860\pi$
$773$	706.977	−	1224.52i	0.0328955	−	0.0569766i	0.882004	+	0.471241i	$0.156194\pi$
$774$	506.368	−	2202.37i	0.0235155	−	0.102277i
$775$	2278.10	+	3945.79i	0.105590	+	0.182887i
$776$	14338.8	+	5218.90i	0.663316	+	0.241427i
$777$	−1253.88	−	8364.12i	−0.0578927	−	0.386179i
$778$	−38023.5	−	31905.5i	−1.75220	−	1.47027i
$779$	8971.63	−	3265.41i	0.412634	−	0.150186i
$780$	−39355.6	−	72406.1i	−1.80661	−	3.32379i
$781$	−2849.89	−	16162.5i	−0.130572	−	0.740513i
$782$	2507.84			0.114680
$783$	−2736.99	−	28027.7i	−0.124920	−	1.27922i
$784$	−30769.6			−1.40168
$785$	2979.05	+	16895.0i	0.135448	+	0.768165i
$786$	−49524.1	−	1274.52i	−2.24741	−	0.0578377i
$787$	14099.4	−	5131.76i	0.638613	−	0.232436i	−0.00236264	−	0.999997i	$-0.500752\pi$
$787$	14099.4	−	5131.76i	0.638613	−	0.232436i	0.640976	+	0.767561i	$0.278530\pi$
$788$	−10247.0	−	8598.22i	−0.463240	−	0.388704i
$789$	−15567.0	+	12394.0i	−0.702406	+	0.559236i
$790$	34717.8	+	12636.2i	1.56355	+	0.569085i
$791$	1547.04	+	2679.54i	0.0695401	+	0.120447i
$792$	−6174.92	−	49918.9i	−0.277041	−	2.23964i
$793$	13282.0	−	23005.0i	0.594775	−	1.03018i
$794$	−19213.9	+	16122.4i	−0.858787	+	0.720607i
$795$	−41487.2	+	13902.2i	−1.85082	+	0.620202i
$796$	−13708.4	+	77744.3i	−0.610405	+	3.46178i
$797$	−4310.64	+	24446.8i	−0.191582	+	1.08651i	0.725622	+	0.688094i	$0.241552\pi$
$797$	−4310.64	+	24446.8i	−0.191582	+	1.08651i	−0.917203	+	0.398420i	$0.869559\pi$
$798$	−619.760	+	3053.25i	−0.0274928	+	0.135444i
$799$	−1412.07	+	1184.87i	−0.0625223	+	0.0524625i
$800$	7073.76	−	12252.1i	0.312619	−	0.541472i
$801$	−13756.4	+	21224.9i	−0.606815	+	0.936259i
$802$	−10235.8	−	17728.8i	−0.450670	−	0.780583i
$803$	21831.3	+	7945.96i	0.959416	+	0.349199i
$804$	26122.0	+	10276.2i	1.14584	+	0.450761i
$805$	1961.05	+	1645.52i	0.0858609	+	0.0720458i
$806$	10743.6	−	3910.36i	0.469513	−	0.170889i
$807$	10487.3	−	17131.0i	0.457460	−	0.747263i
$808$	2072.54	+	11754.0i	0.0902373	+	0.511761i
$809$	−9052.45			−0.393408			−0.196704	−	0.980463i	$-0.563024\pi$
$809$	−9052.45			−0.393408			−0.196704	+	0.980463i	$0.563024\pi$
$810$	23359.8	+	52213.7i	1.01331	+	2.26494i
$811$	−6428.27			−0.278332			−0.139166	−	0.990269i	$-0.544442\pi$
$811$	−6428.27			−0.278332			−0.139166	+	0.990269i	$0.544442\pi$
$812$	3413.88	+	19361.0i	0.147541	+	0.836748i
$813$	−124.875	+	203.983i	−0.00538690	+	0.00879951i
$814$	53919.7	−	19625.2i	2.32172	−	0.845039i
$815$	−38234.1	−	32082.2i	−1.64329	−	1.37889i
$816$	−8164.14	−	3211.69i	−0.350248	−	0.137784i
$817$	−329.674	−	119.992i	−0.0141173	−	0.00513828i
$818$	−6999.74	−	12123.9i	−0.299193	−	0.518218i
$819$	−8907.93	−	458.799i	−0.380059	−	0.0195748i
$820$	−61186.7	+	105978.i	−2.60577	+	4.51332i
$821$	−12683.5	+	10642.7i	−0.539169	+	0.452416i	−0.871254	−	0.490833i	$-0.836692\pi$
$821$	−12683.5	+	10642.7i	−0.539169	+	0.452416i	0.332085	+	0.943250i	$0.392248\pi$
$822$	9931.35	−	48926.9i	0.421406	−	2.07606i
$823$	113.108	−	641.466i	0.00479063	−	0.0271690i	−0.982319	−	0.187216i	$-0.940054\pi$
$823$	113.108	−	641.466i	0.00479063	−	0.0271690i	0.987109	+	0.160047i	$0.0511646\pi$
$824$	10893.0	−	61777.5i	0.460531	−	2.61180i
$825$	22866.4	−	7662.44i	0.964976	−	0.323360i
$826$	−3542.68	+	2972.66i	−0.149232	+	0.125220i
$827$	8305.20	−	14385.0i	0.349214	−	0.604857i	−0.636896	−	0.770950i	$-0.719782\pi$
$827$	8305.20	−	14385.0i	0.349214	−	0.604857i	0.986110	+	0.166093i	$0.0531152\pi$
$828$	−12593.4	−	5332.20i	−0.528564	−	0.223800i
$829$	2843.11	+	4924.42i	0.119114	+	0.206311i	0.919417	−	0.393285i	$-0.128661\pi$
$829$	2843.11	+	4924.42i	0.119114	+	0.206311i	−0.800303	+	0.599596i	$0.795328\pi$
$830$	18638.4	+	6783.82i	0.779455	+	0.283698i
$831$	27406.4	−	21820.2i	1.14406	−	0.910871i
$832$	8311.69	+	6974.33i	0.346341	+	0.290615i
$833$	−4994.30	+	1817.78i	−0.207734	+	0.0756089i
$834$	80101.0	+	2061.42i	3.32575	+	0.0855889i
$835$	−3159.97	−	17921.1i	−0.130965	−	0.742737i
$836$	−14473.0			−0.598754
$837$	−5234.13	+	1459.17i	−0.216151	+	0.0602585i
$838$	−55430.6			−2.28499
$839$	−1690.50	−	9587.29i	−0.0695619	−	0.394505i	−0.999632	−	0.0271234i	$-0.991365\pi$
$839$	−1690.50	−	9587.29i	−0.0695619	−	0.394505i	0.930070	−	0.367382i	$-0.119746\pi$
$840$	−10289.2	−	18930.1i	−0.422634	−	0.777559i
$841$	−14942.9	+	5438.77i	−0.612690	+	0.223001i
$842$	−3427.04	−	2875.63i	−0.140265	−	0.117697i
$843$	3655.17	+	24382.2i	0.149337	+	0.996165i
$844$	−65727.2	−	23922.7i	−2.68060	−	0.975657i
$845$	−9636.45	−	16690.8i	−0.392312	−	0.679505i
$846$	14035.2	−	4304.80i	0.570377	−	0.174944i
$847$	−635.559	+	1100.82i	−0.0257828	+	0.0446572i
$848$	−40941.9	+	34354.3i	−1.65796	+	1.39119i
$849$	−13971.8	−	12350.0i	−0.564797	−	0.499236i
$850$	1757.27	−	9965.96i	0.0709104	−	0.402153i
$851$	1461.66	−	8289.51i	0.0588780	−	0.333914i
$852$	28138.4	+	24872.2i	1.13146	+	1.00013i
$853$	−1463.20	+	1227.77i	−0.0587327	+	0.0492826i	−0.671681	−	0.740840i	$-0.734428\pi$
$853$	−1463.20	+	1227.77i	−0.0587327	+	0.0492826i	0.612949	+	0.790123i	$0.289983\pi$
$854$	6435.93	−	11147.4i	0.257884	−	0.446668i
$855$	8489.91	−	2603.99i	0.339589	−	0.104157i
$856$	42032.8	+	72803.0i	1.67833	+	2.90696i
$857$	28454.4	+	10356.5i	1.13417	+	0.412804i	0.839804	−	0.542889i	$-0.182670\pi$
$857$	28454.4	+	10356.5i	1.13417	+	0.412804i	0.294365	+	0.955693i	$0.404892\pi$
$858$	−8971.73	−	59846.9i	−0.356981	−	2.38128i
$859$	−30617.0	−	25690.7i	−1.21611	−	1.02044i	−0.999019	−	0.0442875i	$-0.985898\pi$
$859$	−30617.0	−	25690.7i	−1.21611	−	1.02044i	−0.217092	−	0.976151i	$-0.569657\pi$
$860$	4225.58	−	1537.98i	0.167548	−	0.0609824i
$861$	6325.26	+	11637.2i	0.250365	+	0.460620i
$862$	5257.48	+	29816.6i	0.207738	+	1.17814i
$863$	−19731.1			−0.778278			−0.389139	−	0.921179i	$-0.627227\pi$
$863$	−19731.1			−0.778278			−0.389139	+	0.921179i	$0.627227\pi$
$864$	12050.1	+	11809.7i	0.474484	+	0.465015i
$865$	21829.3			0.858055
$866$	−6495.82	−	36839.6i	−0.254893	−	1.44557i
$867$	24005.4	+	617.784i	0.940329	+	0.0241996i
$868$	3564.60	−	1297.41i	0.139390	−	0.0507338i
$869$	14230.4	+	11940.7i	0.555503	+	0.466123i
$870$	64025.1	−	50975.0i	2.49500	−	1.98645i
$871$	17122.6	+	6232.13i	0.666106	+	0.242443i
$872$	40112.2	+	69476.4i	1.55776	+	2.69813i
$873$	−8034.45	−	3401.88i	−0.311483	−	0.131886i
$874$	−1550.36	+	2685.30i	−0.0600019	+	0.103926i
$875$	−495.142	+	415.474i	−0.0191301	+	0.0160521i
$876$	−50407.9	+	16891.5i	−1.94421	+	0.651496i
$877$	5986.23	−	33949.6i	0.230491	−	1.30718i	−0.621414	−	0.783483i	$-0.713441\pi$
$877$	5986.23	−	33949.6i	0.230491	−	1.30718i	0.851905	−	0.523697i	$-0.175448\pi$
$878$	9186.36	−	52098.4i	0.353103	−	2.00255i
$879$	−6937.40	+	34177.2i	−0.266203	+	1.31145i
$880$	46543.6	−	39054.7i	1.78294	−	1.49606i
$881$	10736.5	−	18596.2i	0.410582	−	0.711149i	−0.584371	−	0.811486i	$-0.698659\pi$
$881$	10736.5	−	18596.2i	0.410582	−	0.711149i	0.994953	+	0.100337i	$0.0319922\pi$
$882$	42272.0	+	2177.20i	1.61380	+	0.0831182i
$883$	8801.45	+	15244.6i	0.335439	+	0.580997i	0.983569	−	0.180533i	$-0.0577822\pi$
$883$	8801.45	+	15244.6i	0.335439	+	0.580997i	−0.648130	+	0.761529i	$0.724449\pi$
$884$	−16339.0	−	5946.93i	−0.621654	−	0.226263i
$885$	12266.7	+	4825.61i	0.465923	+	0.183289i
$886$	36253.5	+	30420.3i	1.37467	+	1.15349i
$887$	35840.9	−	13045.0i	1.35673	−	0.493809i	0.441688	−	0.897169i	$-0.354380\pi$
$887$	35840.9	−	13045.0i	1.35673	−	0.493809i	0.915042	+	0.403360i	$0.132158\pi$
$888$	−36988.6	+	60421.0i	−1.39781	+	2.28333i
$889$	435.798	+	2471.54i	0.0164412	+	0.0932426i
$890$	−73504.2			−2.76839
$891$	2057.93	+	28687.0i	0.0773774	+	1.07862i
$892$	79869.2			2.99800
$893$	−395.762	−	2244.48i	−0.0148305	−	0.0841081i
$894$	−15110.8	+	24683.6i	−0.565305	+	0.923426i
$895$	21083.5	−	7673.77i	0.787424	−	0.286599i
$896$	8182.25	+	6865.73i	0.305078	+	0.255991i
$897$	−8261.11	−	3249.84i	−0.307503	−	0.120969i
$898$	−37913.9	−	13799.5i	−1.40891	−	0.512802i
$899$	3887.09	+	6732.64i	0.144207	+	0.249773i
$900$	−30014.1	+	46308.9i	−1.11163	+	1.71514i
$901$	−4615.84	+	7994.87i	−0.170673	+	0.295613i
$902$	−68837.5	+	57761.5i	−2.54106	+	2.13220i
$903$	96.8194	−	476.982i	0.00356805	−	0.0175780i
$904$	4500.46	−	25523.4i	0.165579	−	0.939042i
$905$	−2424.17	+	13748.2i	−0.0890411	+	0.504977i
$906$	−68578.1	+	22980.2i	−2.51474	+	0.842680i
$907$	6572.14	−	5514.68i	0.240600	−	0.201887i	−0.514512	−	0.857483i	$-0.672027\pi$
$907$	6572.14	−	5514.68i	0.240600	−	0.201887i	0.755112	+	0.655596i	$0.227582\pi$
$908$	1302.81	−	2256.53i	0.0476158	−	0.0824731i
$909$	−837.796	−	6772.86i	−0.0305698	−	0.247131i
$910$	−12960.9	−	22448.9i	−0.472142	−	0.817773i
$911$	−7446.92	−	2710.46i	−0.270832	−	0.0985746i	0.203034	−	0.979172i	$-0.434920\pi$
$911$	−7446.92	−	2710.46i	−0.270832	−	0.0985746i	−0.473866	+	0.880597i	$0.657142\pi$
$912$	8486.07	−	6756.36i	0.308116	−	0.245313i
$913$	7639.64	+	6410.42i	0.276928	+	0.232370i
$914$	−16849.8	+	6132.84i	−0.609784	+	0.221943i
$915$	−36677.0	−	943.890i	−1.32514	−	0.0341028i
$916$	−15616.6	−	88566.3i	−0.563306	−	3.19467i
$917$	−10669.7			−0.384238
$918$	10988.8	+	4989.98i	0.395082	+	0.179405i
$919$	26507.1			0.951457			0.475729	−	0.879592i	$-0.342184\pi$
$919$	26507.1			0.951457			0.475729	+	0.879592i	$0.342184\pi$
$920$	−3723.59	−	21117.5i	−0.133438	−	0.756765i
$921$	2839.52	+	5224.12i	0.101591	+	0.186906i
$922$	−11818.7	+	4301.67i	−0.422157	+	0.153653i
$923$	18674.9	+	15670.1i	0.665970	+	0.558815i
$924$	−2976.71	−	19856.5i	−0.105981	−	0.706959i
$925$	−31917.7	−	11617.1i	−1.13454	−	0.412938i
$926$	−13335.3	−	23097.5i	−0.473247	−	0.819688i
$927$	−8037.23	+	34956.7i	−0.284765	+	1.23854i
$928$	12069.8	−	20905.6i	0.426953	−	0.739504i
$929$	−8939.44	+	7501.08i	−0.315709	+	0.264911i	−0.786847	−	0.617148i	$-0.788288\pi$
$929$	−8939.44	+	7501.08i	−0.315709	+	0.264911i	0.471138	+	0.882060i	$0.343843\pi$
$930$	−11831.5	−	10458.1i	−0.417171	−	0.368747i
$931$	1141.09	−	6471.46i	0.0401695	−	0.227813i
$932$	1491.83	−	8460.61i	0.0524320	−	0.297357i
$933$	−35114.7	−	31038.7i	−1.23216	−	1.08913i
$934$	2645.86	−	2220.14i	0.0926930	−	0.0777787i
$935$	5247.39	−	9088.74i	0.183538	−	0.317897i
$936$	54689.0	+	50906.3i	1.90979	+	1.77770i
$937$	11020.7	+	19088.4i	0.384237	+	0.665518i	0.991663	−	0.128858i	$-0.0411312\pi$
$937$	11020.7	+	19088.4i	0.384237	+	0.665518i	−0.607426	+	0.794376i	$0.707798\pi$
$938$	8296.96	+	3019.85i	0.288812	+	0.105119i
$939$	897.497	+	5986.85i	0.0311914	+	0.208065i
$940$	22377.9	+	18777.3i	0.776474	+	0.651539i
$941$	13109.7	−	4771.52i	0.454158	−	0.165300i	−0.104805	−	0.994493i	$-0.533422\pi$
$941$	13109.7	−	4771.52i	0.454158	−	0.165300i	0.558963	+	0.829193i	$0.311200\pi$
$942$	−13766.6	−	25327.8i	−0.476158	−	0.876033i
$943$	2289.06	+	12981.9i	0.0790478	+	0.448302i
$944$	16101.5			0.555146
$945$	5318.75	+	11112.3i	0.183089	+	0.382523i
$946$	3302.06			0.113487
$947$	7841.27	+	44470.0i	0.269068	+	1.52596i	0.757197	+	0.653187i	$0.226568\pi$
$947$	7841.27	+	44470.0i	0.269068	+	1.52596i	−0.488129	+	0.872771i	$0.662321\pi$
$948$	−42494.4	−	1093.60i	−1.45586	−	0.0374668i
$949$	−32428.4	+	11803.0i	−1.10924	+	0.403731i
$950$	9584.82	+	8042.62i	0.327340	+	0.274671i
$951$	−114.920	+	91.4962i	−0.00391855	+	0.00311984i
$952$	−4271.73	−	1554.78i	−0.145428	−	0.0529315i
$953$	12599.8	+	21823.6i	0.428278	+	0.741799i	0.996720	−	0.0809240i	$-0.0257871\pi$
$953$	12599.8	+	21823.6i	0.428278	+	0.741799i	−0.568442	+	0.822723i	$0.692454\pi$
$954$	58677.8	−	44299.8i	1.99137	−	1.50342i
$955$	4622.23	−	8005.94i	0.156620	−	0.271273i
$956$	76824.3	−	64463.2i	2.59903	−	2.18085i
$957$	39016.5	−	13074.3i	1.31790	−	0.441622i
$958$	−12615.6	+	71546.7i	−0.425462	+	2.41291i
$959$	1867.15	−	10589.1i	0.0628711	−	0.356560i
$960$	2981.07	−	14686.3i	0.100223	−	0.493748i
$961$	−21672.1	+	18185.1i	−0.727472	+	0.610422i
$962$	−42616.4	+	73813.8i	−1.42828	+	2.47386i
$963$	−21861.0	−	42809.2i	−0.731526	−	1.43251i
$964$	−53200.1	−	92145.2i	−1.77745	−	3.07863i
$965$	20846.7	+	7587.57i	0.695418	+	0.253112i
$966$	−4003.01	−	1574.75i	−0.133328	−	0.0524499i
$967$	−13960.8	−	11714.5i	−0.464270	−	0.389569i	0.380429	−	0.924810i	$-0.375776\pi$
$967$	−13960.8	−	11714.5i	−0.464270	−	0.389569i	−0.844699	+	0.535241i	$0.820221\pi$
$968$	10005.2	−	3641.61i	0.332212	−	0.120915i
$969$	978.251	−	1597.97i	0.0324313	−	0.0529766i
$970$	−4402.98	−	24970.5i	−0.145743	−	0.826552i
$971$	31852.0			1.05271			0.526355	−	0.850265i	$-0.323558\pi$
$971$	31852.0			1.05271			0.526355	+	0.850265i	$0.323558\pi$
$972$	−44571.9	−	48422.3i	−1.47083	−	1.59789i
$973$	17257.4			0.568599
$974$	−8408.68	−	47688.0i	−0.276624	−	1.56881i
$975$	−18703.3	+	30551.8i	−0.614342	+	1.00353i
$976$	−42112.8	+	15327.8i	−1.38115	+	0.502696i
$977$	−11203.4	−	9400.78i	−0.366867	−	0.307838i	0.440654	−	0.897677i	$-0.354747\pi$
$977$	−11203.4	−	9400.78i	−0.366867	−	0.307838i	−0.807521	+	0.589839i	$0.799191\pi$
$978$	78045.7	+	30702.4i	2.55177	+	1.00384i
$979$	−34729.1	−	12640.4i	−1.13376	−	0.412654i
$980$	42113.6	+	72942.9i	1.37272	+	2.37763i
$981$	−20862.1	−	40853.1i	−0.678975	−	1.32960i
$982$	7663.04	−	13272.8i	0.249020	−	0.431315i
$983$	−16132.4	+	13536.7i	−0.523442	+	0.439220i	−0.865830	−	0.500339i	$-0.833209\pi$
$983$	−16132.4	+	13536.7i	−0.523442	+	0.439220i	0.342388	+	0.939559i	$0.388764\pi$
$984$	22070.1	−	108729.i	0.715010	−	3.52250i
$985$	−2082.52	+	11810.5i	−0.0673650	+	0.382046i
$986$	2998.40	−	17004.8i	0.0968443	−	0.549231i
$987$	2997.95	−	1004.60i	0.0966828	−	0.0323980i
$988$	16468.6	−	13818.8i	0.530300	−	0.444975i
$989$	242.198	−	419.499i	0.00778711	−	0.0134877i
$990$	−66706.1	+	50360.9i	−2.14147	+	1.61674i
$991$	7051.45	+	12213.5i	0.226031	+	0.391497i	0.956628	−	0.291311i	$-0.0940916\pi$
$991$	7051.45	+	12213.5i	0.226031	+	0.391497i	−0.730597	+	0.682809i	$0.760758\pi$
$992$	−4376.89	−	1593.06i	−0.140087	−	0.0509875i
$993$	−44008.6	+	35038.4i	−1.40642	+	1.11975i
$994$	9049.11	+	7593.11i	0.288753	+	0.242293i
$995$	66509.0	−	24207.3i	2.11907	−	0.771279i
$996$	−22813.3	−	587.105i	−0.725769	−	0.0186779i
$997$	7222.56	+	40961.2i	0.229429	+	1.30116i	0.854034	+	0.520217i	$0.174149\pi$
$997$	7222.56	+	40961.2i	0.229429	+	1.30116i	−0.624605	+	0.780941i	$0.714740\pi$
$998$	−65072.9			−2.06397
$999$	22898.8	−	33414.6i	0.725210	−	1.05825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.13.1	✓	48
3.2	odd	2		81.4.e.a.10.8		48
9.2	odd	6		243.4.e.b.109.8		48
9.4	even	3		243.4.e.d.190.8		48
9.5	odd	6		243.4.e.a.190.1		48
9.7	even	3		243.4.e.c.109.1		48
27.2	odd	18		81.4.e.a.73.8		48
27.5	odd	18		729.4.a.c.1.24		24
27.7	even	9		243.4.e.c.136.1		48
27.11	odd	18		243.4.e.a.55.1		48
27.16	even	9		243.4.e.d.55.8		48
27.20	odd	18		243.4.e.b.136.8		48
27.22	even	9		729.4.a.d.1.1		24
27.25	even	9	inner	27.4.e.a.25.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.1	✓	48	1.1	even	1	trivial
27.4.e.a.25.1	yes	48	27.25	even	9	inner
81.4.e.a.10.8		48	3.2	odd	2
81.4.e.a.73.8		48	27.2	odd	18
243.4.e.a.55.1		48	27.11	odd	18
243.4.e.a.190.1		48	9.5	odd	6
243.4.e.b.109.8		48	9.2	odd	6
243.4.e.b.136.8		48	27.20	odd	18
243.4.e.c.109.1		48	9.7	even	3
243.4.e.c.136.1		48	27.7	even	9
243.4.e.d.55.8		48	27.16	even	9
243.4.e.d.190.8		48	9.4	even	3
729.4.a.c.1.24		24	27.5	odd	18
729.4.a.d.1.1		24	27.22	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.874714 - 4.96075i) q^{2} +(2.71299 - 4.43167i) q^{3} +(-16.3263 + 5.94230i) q^{4} +(11.9326 + 10.0126i) q^{5} +(-24.3575 - 9.58200i) q^{6} +(-5.29732 - 1.92807i) q^{7} +(23.6100 + 40.8938i) q^{8} +(-12.2794 - 24.0461i) q^{9} +O(q^{10})\)	\(q+(-0.874714 - 4.96075i) q^{2} +(2.71299 - 4.43167i) q^{3} +(-16.3263 + 5.94230i) q^{4} +(11.9326 + 10.0126i) q^{5} +(-24.3575 - 9.58200i) q^{6} +(-5.29732 - 1.92807i) q^{7} +(23.6100 + 40.8938i) q^{8} +(-12.2794 - 24.0461i) q^{9} +(39.2325 - 67.9527i) q^{10} +(30.2222 - 25.3594i) q^{11} +(-17.9588 + 88.4744i) q^{12} +(-10.1763 + 57.7124i) q^{13} +(-4.93102 + 27.9652i) q^{14} +(76.7456 - 25.7172i) q^{15} +(75.7369 - 63.5508i) q^{16} +(8.53867 - 14.7894i) q^{17} +(-108.546 + 81.9485i) q^{18} +(10.5573 + 18.2858i) q^{19} +(-254.314 - 92.5626i) q^{20} +(-22.9161 + 18.2452i) q^{21} +(-152.238 - 127.742i) q^{22} +(-27.3949 + 9.97093i) q^{23} +(245.282 + 6.31238i) q^{24} +(20.4278 + 115.852i) q^{25} +295.198 q^{26} +(-139.878 - 10.8185i) q^{27} +97.9431 q^{28} +(34.8557 + 197.676i) q^{29} +(-194.707 - 358.220i) q^{30} +(36.3946 - 13.2466i) q^{31} +(-92.1260 - 77.3029i) q^{32} +(-30.3923 - 202.735i) q^{33} +(-80.8354 - 29.4217i) q^{34} +(-43.9057 - 76.0470i) q^{35} +(343.367 + 319.617i) q^{36} +(-144.366 + 250.048i) q^{37} +(81.4764 - 68.3668i) q^{38} +(228.154 + 201.671i) q^{39} +(-127.725 + 724.367i) q^{40} +(78.5187 - 445.302i) q^{41} +(110.555 + 97.7218i) q^{42} +(-12.7283 + 10.6803i) q^{43} +(-342.725 + 593.617i) q^{44} +(94.2398 - 409.881i) q^{45} +(73.4259 + 127.177i) q^{46} +(-101.430 - 36.9176i) q^{47} +(-76.1630 - 508.053i) q^{48} +(-238.409 - 200.049i) q^{49} +(556.844 - 202.675i) q^{50} +(-42.3765 - 77.9640i) q^{51} +(-176.804 - 1002.70i) q^{52} -540.581 q^{53} +(68.6856 + 703.364i) q^{54} +614.544 q^{55} +(-46.2240 - 262.150i) q^{56} +(109.678 + 2.82260i) q^{57} +(950.134 - 345.821i) q^{58} +(124.757 + 104.684i) q^{59} +(-1100.16 + 875.913i) q^{60} +(-425.952 - 155.034i) q^{61} +(-97.5477 - 168.958i) q^{62} +(18.6854 + 151.056i) q^{63} +(92.5737 - 160.342i) q^{64} +(-699.282 + 586.767i) q^{65} +(-979.131 + 328.103i) q^{66} +(53.9930 - 306.209i) q^{67} +(-51.5221 + 292.196i) q^{68} +(-30.1341 + 148.456i) q^{69} +(-338.845 + 284.325i) q^{70} +(207.996 - 360.260i) q^{71} +(693.420 - 1069.88i) q^{72} +(294.437 + 509.980i) q^{73} +(1366.71 + 497.440i) q^{74} +(568.838 + 223.775i) q^{75} +(-281.021 - 235.805i) q^{76} +(-208.992 + 76.0667i) q^{77} +(800.868 - 1308.22i) q^{78} +(81.7637 + 463.705i) q^{79} +1540.05 q^{80} +(-427.432 + 590.544i) q^{81} -2277.71 q^{82} +(43.8952 + 248.942i) q^{83} +(265.718 - 434.052i) q^{84} +(249.969 - 90.9813i) q^{85} +(64.1160 + 53.7997i) q^{86} +(970.600 + 381.825i) q^{87} +(1750.59 + 637.163i) q^{88} +(-468.388 - 811.272i) q^{89} +(-2115.75 - 108.971i) q^{90} +(165.180 - 286.101i) q^{91} +(388.008 - 325.578i) q^{92} +(40.0337 - 197.227i) q^{93} +(-94.4163 + 535.462i) q^{94} +(-57.1127 + 323.902i) q^{95} +(-592.518 + 198.550i) q^{96} +(247.545 - 207.715i) q^{97} +(-783.853 + 1357.67i) q^{98} +(-980.907 - 415.328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Introduction

L-functions

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