LMFDB - Embedded newform 27.4.e.a.25.1

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			25.1
Character	$\chi$	$=$	27.25
Dual form			27.4.e.a.13.1

$q$-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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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	0.293495	+	0.955961i	$0.405182\pi$
$2$	−0.874714	+	4.96075i	−0.309258	+	1.75389i	−0.602753	+	0.797928i	$0.705929\pi$
$3$	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	0.0724791	−	0.997370i	$-0.476909\pi$
$5$	11.9326	−	10.0126i	1.06728	−	0.895556i	0.994804	+	0.101813i	$0.0324645\pi$
$6$	−24.3575	+	9.58200i	−1.65732	+	0.651972i
$7$	−5.29732	+	1.92807i	−0.286029	+	0.104106i	−0.481050	−	0.876693i	$-0.659745\pi$
$7$	−5.29732	+	1.92807i	−0.286029	+	0.104106i	0.195022	+	0.980799i	$0.437522\pi$
$8$	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	0.954922	−	0.296858i	$-0.0959387\pi$
$11$	30.2222	+	25.3594i	0.828395	+	0.695106i	−0.126527	+	0.991963i	$0.540383\pi$
$12$	−17.9588	−	88.4744i	−0.432022	−	2.12836i
$13$	−10.1763	−	57.7124i	−0.217106	−	1.23127i	−0.877213	−	0.480100i	$-0.840600\pi$
$13$	−10.1763	−	57.7124i	−0.217106	−	1.23127i	0.660107	−	0.751172i	$-0.270511\pi$
$14$	−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	0.920485	−	0.390777i	$-0.127794\pi$
$17$	8.53867	+	14.7894i	0.121819	+	0.210998i	−0.798666	+	0.601775i	$0.794460\pi$
$18$	−108.546	−	81.9485i	−1.42136	−	1.07308i
$19$	10.5573	−	18.2858i	0.127474	−	0.220792i	−0.795223	−	0.606317i	$-0.792646\pi$
$19$	10.5573	−	18.2858i	0.127474	−	0.220792i	0.922697	+	0.385525i	$0.125980\pi$
$20$	−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	0.214842	−	0.976649i	$-0.431076\pi$
$23$	−27.3949	−	9.97093i	−0.248358	−	0.0903949i	−0.463200	+	0.886254i	$0.653299\pi$
$24$	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	−0.642922	−	0.765931i	$-0.722278\pi$
$29$	34.8557	−	197.676i	0.223191	−	1.26578i	0.866113	−	0.499848i	$-0.166611\pi$
$30$	−194.707	+	358.220i	−1.18495	+	2.18006i
$31$	36.3946	+	13.2466i	0.210860	+	0.0767469i	0.445291	−	0.895386i	$-0.353100\pi$
$31$	36.3946	+	13.2466i	0.210860	+	0.0767469i	−0.234430	+	0.972133i	$0.575323\pi$
$32$	−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	−0.985110	−	0.171926i	$-0.945001\pi$
$37$	−144.366	−	250.048i	−0.641447	−	1.11102i	0.343662	−	0.939093i	$-0.388332\pi$
$38$	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	0.650110	+	0.759840i	$0.274723\pi$
$41$	78.5187	+	445.302i	0.299087	+	1.69621i	−0.351023	+	0.936367i	$0.614166\pi$
$42$	110.555	−	97.7218i	0.406166	−	0.359019i
$43$	−12.7283	−	10.6803i	−0.0451407	−	0.0378775i	0.619938	−	0.784651i	$-0.287158\pi$
$43$	−12.7283	−	10.6803i	−0.0451407	−	0.0378775i	−0.665079	+	0.746773i	$0.731602\pi$
$44$	−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	−0.494583	−	0.869130i	$-0.664679\pi$
$47$	−101.430	+	36.9176i	−0.314790	+	0.114574i	0.179794	+	0.983704i	$0.442457\pi$
$48$	−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	−0.494682	−	0.869074i	$-0.664715\pi$
$59$	124.757	−	104.684i	0.275288	−	0.230994i	0.769970	+	0.638080i	$0.220271\pi$
$60$	−1100.16	−	875.913i	−2.36716	−	1.88466i
$61$	−425.952	+	155.034i	−0.894058	+	0.325411i	−0.747869	−	0.663846i	$-0.768923\pi$
$61$	−425.952	+	155.034i	−0.894058	+	0.325411i	−0.146189	+	0.989257i	$0.546701\pi$
$62$	−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	0.993635	+	0.112650i	$0.0359339\pi$
$67$	53.9930	+	306.209i	0.0984521	+	0.558350i	−0.895183	+	0.445700i	$0.852955\pi$
$68$	−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	0.985835	−	0.167717i	$-0.0536394\pi$
$71$	207.996	+	360.260i	0.347671	+	0.602183i	−0.638165	+	0.769900i	$0.720306\pi$
$72$	693.420	+	1069.88i	1.13500	+	1.75121i
$73$	294.437	−	509.980i	0.472072	−	0.817652i	−0.527418	−	0.849606i	$-0.676840\pi$
$73$	294.437	−	509.980i	0.472072	−	0.817652i	0.999489	+	0.0319540i	$0.0101730\pi$
$74$	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	−0.869580	−	0.493792i	$-0.835610\pi$
$79$	81.7637	−	463.705i	0.116445	−	0.660391i	0.986025	−	0.166599i	$-0.0532784\pi$
$80$	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	−0.941929	−	0.335813i	$-0.890989\pi$
$83$	43.8952	−	248.942i	0.0580496	−	0.329216i	0.999978	+	0.00659738i	$0.00210003\pi$
$84$	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	0.439821	+	0.898085i	$0.355042\pi$
$89$	−468.388	+	811.272i	−0.557854	+	0.966232i	−0.997675	+	0.0681465i	$0.978291\pi$
$90$	−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	0.763087	−	0.646296i	$-0.223683\pi$
$97$	247.545	+	207.715i	0.259117	+	0.217425i	−0.503969	+	0.863722i	$0.668127\pi$
$98$	−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	−0.222360	−	0.974965i	$-0.571376\pi$
$101$	237.515	−	86.4486i	0.233997	−	0.0851678i	0.456357	+	0.889797i	$0.349154\pi$
$102$	−349.693	−	278.415i	−0.339458	−	0.270267i
$103$	−1017.67	+	853.925i	−0.973533	+	0.816891i	−0.983101	−	0.183063i	$-0.941399\pi$
$103$	−1017.67	+	853.925i	−0.973533	+	0.816891i	0.00956859	+	0.999954i	$0.496954\pi$
$104$	−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	−0.800799	−	0.598933i	$-0.795592\pi$
$113$	−420.449	+	352.799i	−0.350022	+	0.293704i	0.450777	+	0.892637i	$0.351147\pi$
$114$	−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	−0.933251	−	0.359224i	$-0.883041\pi$
$127$	−222.595	+	385.545i	−0.155528	+	0.269383i	0.777723	+	0.628607i	$0.216375\pi$
$128$	−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	0.858392	−	0.512995i	$-0.171464\pi$
$131$	1778.56	+	647.343i	1.18621	+	0.431745i	0.327819	+	0.944740i	$0.393686\pi$
$132$	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	−0.688429	−	0.725303i	$-0.741699\pi$
$137$	331.214	−	1878.41i	0.206551	−	1.17141i	0.894980	−	0.446106i	$-0.147189\pi$
$138$	762.812	−	19.6312i	0.470543	−	0.0121095i
$139$	−2876.67	−	1047.02i	−1.75537	−	0.638901i	−0.755499	−	0.655150i	$-0.772606\pi$
$139$	−2876.67	−	1047.02i	−1.75537	−	0.638901i	−0.999868	+	0.0162483i	$0.994828\pi$
$140$	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	0.990992	+	0.133924i	$0.0427580\pi$
$149$	192.006	+	1088.92i	0.105569	+	0.598711i	−0.885423	+	0.464787i	$0.846131\pi$
$150$	612.523	+	3017.60i	0.333415	+	1.64257i
$151$	2116.76	+	1776.17i	1.14079	+	0.957235i	0.999464	−	0.0327280i	$-0.0104195\pi$
$151$	2116.76	+	1776.17i	1.14079	+	0.957235i	0.141324	+	0.989963i	$0.454864\pi$
$152$	−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	−0.402652	−	0.915353i	$-0.631911\pi$
$157$	843.686	−	707.937i	0.428876	−	0.359869i	0.831527	+	0.555484i	$0.187467\pi$
$158$	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	−0.826135	−	0.563473i	$-0.809465\pi$
$167$	−894.925	+	750.931i	−0.414679	+	0.347957i	0.411456	+	0.911430i	$0.365021\pi$
$168$	−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	0.847445	−	0.530883i	$-0.178140\pi$
$173$	1073.53	+	900.795i	0.471784	+	0.395874i	−0.375661	+	0.926757i	$0.622584\pi$
$174$	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	0.976300	−	0.216422i	$-0.0694385\pi$
$179$	720.190	+	1247.41i	0.300723	+	0.520868i	−0.675577	+	0.737290i	$0.736105\pi$
$180$	897.049	−	7251.87i	0.371456	−	3.00290i
$181$	448.108	−	776.145i	0.184020	−	0.318732i	−0.759226	−	0.650827i	$-0.774422\pi$
$181$	448.108	−	776.145i	0.184020	−	0.318732i	0.943246	+	0.332095i	$0.107756\pi$
$182$	−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	−0.998086	−	0.0618411i	$-0.980303\pi$
$191$	−103.056	+	584.457i	−0.0390410	+	0.221413i	0.959045	+	0.283254i	$0.0914139\pi$
$192$	−459.433	+	845.263i	−0.172691	+	0.317717i
$193$	1338.31	+	487.105i	0.499138	+	0.181671i	0.579306	−	0.815110i	$-0.303324\pi$
$193$	1338.31	+	487.105i	0.499138	+	0.181671i	−0.0801683	+	0.996781i	$0.525546\pi$
$194$	−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	−0.787980	−	0.615701i	$-0.788873\pi$
$197$	384.953	−	666.759i	0.139222	−	0.241140i	0.927202	+	0.374561i	$0.122206\pi$
$198$	−1202.32	−	5229.33i	−0.431543	−	1.87693i
$199$	2271.87	+	3935.00i	0.809290	+	1.40173i	0.913356	+	0.407162i	$0.133481\pi$
$199$	2271.87	+	3935.00i	0.809290	+	1.40173i	−0.104066	+	0.994570i	$0.533185\pi$
$200$	−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	0.0183727	−	0.999831i	$-0.494151\pi$
$211$	3083.97	−	2587.76i	1.00620	−	0.844306i	0.987832	+	0.155525i	$0.0497070\pi$
$212$	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	−0.896082	−	0.443889i	$-0.853598\pi$
$223$	−4319.78	+	1572.27i	−1.29719	+	0.472140i	−0.401112	+	0.916029i	$0.631376\pi$
$224$	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	0.625838	−	0.779953i	$-0.284757\pi$
$227$	−114.884	−	96.3994i	−0.0335909	−	0.0281861i	−0.659429	+	0.751767i	$0.729202\pi$
$228$	−1807.42	−	605.659i	−0.524996	−	0.175924i
$229$	−898.844	−	5097.60i	−0.259377	−	1.47100i	−0.784583	−	0.620023i	$-0.787123\pi$
$229$	−898.844	−	5097.60i	−0.259377	−	1.47100i	0.525207	−	0.850975i	$-0.323988\pi$
$230$	−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	0.829173	−	0.558993i	$-0.188812\pi$
$233$	−247.239	−	428.230i	−0.0695157	−	0.120405i	−0.898688	+	0.438588i	$0.855479\pi$
$234$	−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	−0.520454	−	0.853890i	$-0.674237\pi$
$239$	−5424.09	−	1974.21i	−1.46801	−	0.534314i	−0.947561	+	0.319576i	$0.896459\pi$
$240$	4178.13	+	6824.98i	1.12374	+	1.83563i
$241$	1063.43	−	6031.02i	0.284239	−	1.61200i	−0.423752	−	0.905778i	$-0.639287\pi$
$241$	1063.43	−	6031.02i	0.284239	−	1.61200i	0.707991	−	0.706221i	$-0.249602\pi$
$242$	−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	−0.683494	−	0.729956i	$-0.739540\pi$
$251$	1154.86	−	2000.27i	0.290414	−	0.503011i	0.973908	+	0.226945i	$0.0728737\pi$
$252$	−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	0.994123	−	0.108253i	$-0.0345256\pi$
$257$	94.4655	+	535.740i	0.0229284	+	0.130033i	−0.971195	+	0.238286i	$0.923414\pi$
$258$	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	−0.727467	−	0.686143i	$-0.759303\pi$
$263$	−3598.48	+	1309.74i	−0.843695	+	0.307080i	−0.116228	+	0.993223i	$0.537080\pi$
$264$	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	0.453780	−	0.891114i	$-0.350075\pi$
$277$	6335.30	−	2305.86i	1.37419	−	0.500165i	0.920412	+	0.390949i	$0.127853\pi$
$278$	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	0.169493	−	0.985531i	$-0.445787\pi$
$281$	−3634.72	−	3049.89i	−0.771634	−	0.647477i	−0.941127	+	0.338054i	$0.890231\pi$
$282$	2116.84	−	1871.12i	0.447007	−	0.395120i
$283$	623.179	+	3534.22i	0.130898	+	0.742360i	0.977629	+	0.210338i	$0.0674564\pi$
$283$	623.179	+	3534.22i	0.130898	+	0.742360i	−0.846731	+	0.532022i	$0.821432\pi$
$284$	−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	−0.374567	−	0.927200i	$-0.622209\pi$
$293$	−6306.78	−	2295.48i	−1.25749	−	0.457691i	−0.882928	+	0.469509i	$0.844431\pi$
$294$	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	0.807930	−	0.589279i	$-0.200588\pi$
$307$	−572.149	−	990.992i	−0.106366	−	0.184231i	−0.914295	+	0.405048i	$0.867255\pi$
$308$	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	0.703253	+	0.710939i	$0.251730\pi$
$311$	1566.20	+	8882.39i	0.285567	+	1.61953i	−0.417686	+	0.908591i	$0.637159\pi$
$312$	−2860.35	−	14091.6i	−0.519024	−	2.55698i
$313$	−892.475	−	748.876i	−0.161168	−	0.135236i	0.558637	−	0.829412i	$-0.311325\pi$
$313$	−892.475	−	748.876i	−0.161168	−	0.135236i	−0.719805	+	0.694176i	$0.755769\pi$
$314$	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	−0.344372	−	0.938833i	$-0.611908\pi$
$317$	−26.5651	+	9.66891i	−0.00470677	+	0.00171312i	0.339666	+	0.940546i	$0.389686\pi$
$318$	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	−0.994539	−	0.104364i	$-0.966719\pi$
$331$	−10173.1	+	3702.70i	−1.68932	+	0.614861i	−0.694777	+	0.719225i	$0.744497\pi$
$332$	−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	−0.964716	−	0.263293i	$-0.915191\pi$
$337$	−917.031	−	5200.74i	−0.148231	−	0.840660i	0.816485	−	0.577367i	$-0.195920\pi$
$338$	−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	0.941248	−	0.337716i	$-0.109654\pi$
$347$	9341.66	+	3400.09i	1.44521	+	0.526012i	0.503958	+	0.863728i	$0.331876\pi$
$348$	−18115.3	+	466.201i	−2.79046	+	0.0718132i
$349$	132.239	−	749.966i	0.0202825	−	0.115028i	−0.972986	−	0.230866i	$-0.925844\pi$
$349$	132.239	−	749.966i	0.0202825	−	0.115028i	0.993268	+	0.115838i	$0.0369553\pi$
$350$	−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	−0.906067	−	0.423135i	$-0.860930\pi$
$353$	597.423	−	3388.15i	0.0900782	−	0.510859i	0.996145	−	0.0877239i	$-0.0279593\pi$
$354$	−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	−0.863179	−	0.504898i	$-0.831530\pi$
$359$	38.5343	−	66.7434i	0.00566508	−	0.00981220i	0.868844	+	0.495086i	$0.164863\pi$
$360$	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	−0.990267	−	0.139181i	$-0.955553\pi$
$367$	−9134.94	−	7665.13i	−1.29929	−	1.09024i	−0.309025	−	0.951054i	$-0.600003\pi$
$368$	−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	−0.788629	−	0.614869i	$-0.789209\pi$
$373$	−2305.55	+	1934.59i	−0.320045	+	0.268550i	0.468584	+	0.883419i	$0.344764\pi$
$374$	−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	0.207293	−	0.978279i	$-0.433535\pi$
$383$	9044.81	−	7589.50i	1.20671	−	1.01255i	0.999413	−	0.0342669i	$-0.0109096\pi$
$384$	−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	0.984667	−	0.174445i	$-0.0558132\pi$
$389$	7548.43	+	6333.88i	0.983857	+	0.825554i	−0.000809477		1.00000i	$0.500258\pi$
$390$	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	−0.979382	−	0.202017i	$-0.935250\pi$
$397$	−2489.64	+	4312.18i	−0.314739	+	0.545144i	0.664643	+	0.747161i	$0.268584\pi$
$398$	−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	0.568678	−	0.822560i	$-0.307455\pi$
$401$	3818.92	+	1389.97i	0.475580	+	0.173097i	−0.0930985	+	0.995657i	$0.529677\pi$
$402$	−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	0.495025	−	0.868879i	$-0.335159\pi$
$409$	2611.57	+	950.534i	0.315731	+	0.114917i	−0.179294	+	0.983796i	$0.557381\pi$
$410$	−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	0.866858	+	0.498555i	$0.166136\pi$
$419$	1910.84	+	10836.9i	0.222794	+	1.26353i	−0.644064	+	0.764971i	$0.722753\pi$
$420$	7516.70	+	2518.82i	0.873280	+	0.292633i
$421$	680.336	+	570.869i	0.0787590	+	0.0660866i	0.681317	−	0.731988i	$-0.261407\pi$
$421$	680.336	+	570.869i	0.0787590	+	0.0660866i	−0.602558	+	0.798075i	$0.705852\pi$
$422$	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	0.255651	−	0.966769i	$-0.417710\pi$
$439$	9868.78	−	3591.94i	1.07292	−	0.390510i	0.817267	+	0.576259i	$0.195488\pi$
$440$	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	0.169312	−	0.985563i	$-0.445846\pi$
$443$	−7197.04	−	6039.03i	−0.771877	−	0.647682i	−0.941189	+	0.337881i	$0.890290\pi$
$444$	−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	0.996031	−	0.0890023i	$-0.0283679\pi$
$449$	4004.86	+	6936.62i	0.420937	+	0.729085i	−0.575094	+	0.818087i	$0.695035\pi$
$450$	−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	0.936691	+	0.350158i	$0.113872\pi$
$457$	−618.137	+	3505.63i	−0.0632718	+	0.358832i	−0.999962	+	0.00867400i	$0.997239\pi$
$458$	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	−0.998845	−	0.0480506i	$-0.984699\pi$
$461$	−433.570	+	2458.90i	−0.0438034	+	0.248422i	0.955041	+	0.296472i	$0.0958102\pi$
$462$	5819.38	−	149.763i	0.586022	−	0.0150814i
$463$	4975.36	+	1810.88i	0.499405	+	0.181769i	0.579426	−	0.815025i	$-0.303277\pi$
$463$	4975.36	+	1810.88i	0.499405	+	0.181769i	−0.0800212	+	0.996793i	$0.525499\pi$
$464$	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	−0.848540	−	0.529131i	$-0.822518\pi$
$467$	342.837	−	593.811i	0.0339713	−	0.0588400i	0.882511	+	0.470291i	$0.155851\pi$
$468$	−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	−0.894639	−	0.446789i	$-0.852567\pi$
$479$	−13552.8	+	4932.81i	−1.29278	+	0.470534i	−0.398143	+	0.917323i	$0.630345\pi$
$480$	−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	−0.529361	−	0.848396i	$-0.677568\pi$
$491$	2330.71	−	1955.70i	0.214223	−	0.179755i	0.743585	+	0.668642i	$0.233124\pi$
$492$	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	0.903241	+	0.429134i	$0.141181\pi$
$499$	2243.24	+	12722.0i	0.201244	+	1.14131i	−0.701996	+	0.712180i	$0.747708\pi$
$500$	−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	0.519598	−	0.854411i	$-0.326082\pi$
$503$	−5416.54	−	9381.72i	−0.480142	−	0.831631i	−0.999741	+	0.0227800i	$0.992748\pi$
$504$	−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	−0.0708109	−	0.997490i	$-0.522559\pi$
$509$	−8799.04	−	3202.59i	−0.766229	−	0.278885i	−0.695418	+	0.718605i	$0.744781\pi$
$510$	−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	−0.948723	−	0.316110i	$-0.897623\pi$
$521$	−2385.57	+	4131.92i	−0.200602	+	0.347453i	0.748121	+	0.663563i	$0.230956\pi$
$522$	−19982.7	+	18600.6i	−1.67552	+	1.55963i
$523$	5149.38	+	8918.99i	0.430529	+	0.745698i	0.996919	−	0.0784392i	$-0.0249936\pi$
$523$	5149.38	+	8918.99i	0.430529	+	0.745698i	−0.566390	+	0.824137i	$0.691660\pi$
$524$	−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	−0.646285	−	0.763096i	$-0.723678\pi$
$547$	−8326.61	+	3030.64i	−0.650860	+	0.236894i	−0.00457452	+	0.999990i	$0.501456\pi$
$548$	−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	0.956643	−	0.291262i	$-0.0940752\pi$
$557$	2971.99	+	5147.64i	0.226081	+	0.391584i	−0.730562	+	0.682846i	$0.760742\pi$
$558$	−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	−0.266055	−	0.963958i	$-0.585720\pi$
$563$	−14554.1	−	5297.24i	−1.08949	−	0.396540i	−0.823430	+	0.567417i	$0.807943\pi$
$564$	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	−0.967896	−	0.251349i	$-0.919126\pi$
$569$	374.543	−	2124.14i	0.0275952	−	0.156500i	0.995492	+	0.0948491i	$0.0302369\pi$
$570$	4494.76	+	7342.19i	0.330289	+	0.539528i
$571$	−14760.6	−	5372.44i	−1.08181	−	0.393747i	−0.261229	−	0.965277i	$-0.584128\pi$
$571$	−14760.6	−	5372.44i	−1.08181	−	0.393747i	−0.820581	+	0.571530i	$0.806350\pi$
$572$	−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	0.564931	−	0.825138i	$-0.308903\pi$
$577$	−5989.26	−	10373.7i	−0.432125	−	0.748462i	−0.997056	+	0.0766759i	$0.975569\pi$
$578$	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	−0.825566	−	0.564305i	$-0.809144\pi$
$587$	−15576.6	+	5669.43i	−1.09526	+	0.398641i	−0.269692	+	0.962947i	$0.586922\pi$
$588$	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	−0.645602	−	0.763674i	$-0.723394\pi$
$599$	−82.6583	+	69.3585i	−0.00563827	+	0.00473107i	0.639964	+	0.768405i	$0.278949\pi$
$600$	4279.27	−	28545.3i	0.291167	−	1.94226i
$601$	2041.21	−	742.939i	0.138540	−	0.0504245i	−0.271820	−	0.962348i	$-0.587625\pi$
$601$	2041.21	−	742.939i	0.138540	−	0.0504245i	0.410360	+	0.911924i	$0.365403\pi$
$602$	−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	−0.805152	−	0.593069i	$-0.797916\pi$
$607$	−3759.63	−	21321.9i	−0.251398	−	1.42575i	0.553754	−	0.832680i	$-0.313195\pi$
$608$	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	−0.813296	−	0.581850i	$-0.802329\pi$
$613$	1475.96	−	2556.44i	0.0972490	−	0.168440i	0.910545	+	0.413410i	$0.135662\pi$
$614$	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	0.370709	−	0.928749i	$-0.379115\pi$
$617$	884.322	+	321.867i	0.0577009	+	0.0210014i	−0.313008	+	0.949750i	$0.601337\pi$
$618$	16605.5	−	30550.8i	1.08086	−	1.98856i
$619$	2619.16	−	14854.0i	0.170069	−	0.964511i	−0.773613	−	0.633658i	$-0.781552\pi$
$619$	2619.16	−	14854.0i	0.170069	−	0.964511i	0.943682	−	0.330853i	$-0.107336\pi$
$620$	−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	0.920145	−	0.391578i	$-0.128071\pi$
$631$	1917.22	+	3320.72i	0.120956	+	0.209502i	−0.799189	+	0.601080i	$0.794737\pi$
$632$	−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	0.526087	−	0.850431i	$-0.323659\pi$
$641$	23949.5	−	8716.91i	1.47574	−	0.537125i	0.949652	+	0.313306i	$0.101437\pi$
$642$	−43363.5	+	17058.8i	−2.66576	+	1.04869i
$643$	−2158.26	+	1811.00i	−0.132369	+	0.111071i	−0.706569	−	0.707644i	$-0.749758\pi$
$643$	−2158.26	+	1811.00i	−0.132369	+	0.111071i	0.574199	+	0.818716i	$0.305313\pi$
$644$	−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	−0.787036	−	0.616907i	$-0.788386\pi$
$653$	−5275.81	+	4426.93i	−0.316169	+	0.265297i	0.470867	+	0.882204i	$0.343941\pi$
$654$	−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	0.993045	−	0.117733i	$-0.0375627\pi$
$659$	17755.3	+	14898.5i	1.04954	+	0.880670i	0.0564962	+	0.998403i	$0.482007\pi$
$660$	−11036.5	−	54371.4i	−0.650901	−	3.20667i
$661$	−922.380	−	5231.08i	−0.0542760	−	0.307814i	0.945569	−	0.325422i	$-0.105506\pi$
$661$	−922.380	−	5231.08i	−0.0542760	−	0.307814i	−0.999845	+	0.0176073i	$0.994395\pi$
$662$	−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	0.472154	+	0.881516i	$0.343477\pi$
$673$	−4766.72	+	27033.4i	−0.273022	+	1.54838i	−0.745176	+	0.666868i	$0.767635\pi$
$674$	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	0.913754	+	0.406268i	$0.133170\pi$
$677$	−1476.95	+	8376.18i	−0.0838459	+	0.475514i	−0.997600	+	0.0692452i	$0.977941\pi$
$678$	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	−0.00984920	−	0.999951i	$-0.503135\pi$
$683$	15369.6	−	26621.0i	0.861059	−	1.49140i	0.870908	−	0.491446i	$-0.163532\pi$
$684$	−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	0.404933	−	0.914347i	$-0.367295\pi$
$691$	−7723.56	−	6480.84i	−0.425207	−	0.356791i	−0.830140	+	0.557555i	$0.811739\pi$
$692$	−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	0.875710	−	0.482837i	$-0.160394\pi$
$709$	35055.7	−	12759.2i	1.85690	−	0.675858i	0.981195	−	0.193021i	$-0.0618287\pi$
$710$	−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	−0.997548	−	0.0699815i	$-0.977706\pi$
$719$	−10784.5	−	18679.3i	−0.559380	−	0.968874i	0.438168	−	0.898893i	$-0.355627\pi$
$720$	−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	0.689813	+	0.723987i	$0.257693\pi$
$727$	−4038.36	+	22902.7i	−0.206017	+	1.16838i	−0.895831	+	0.444395i	$0.853419\pi$
$728$	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	−0.132133	−	0.991232i	$-0.542183\pi$
$733$	−17275.4	−	6287.72i	−0.870505	−	0.316838i	−0.738372	+	0.674394i	$0.764405\pi$
$734$	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	0.988487	−	0.151306i	$-0.0483478\pi$
$739$	7296.65	+	12638.2i	0.363209	+	0.629096i	−0.625278	+	0.780402i	$0.715014\pi$
$740$	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	−0.933367	−	0.358923i	$-0.883144\pi$
$743$	−3626.20	−	20565.2i	−0.179048	−	1.01543i	0.754319	−	0.656508i	$-0.227967\pi$
$744$	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	−0.438083	−	0.898935i	$-0.644342\pi$
$751$	7637.96	−	6409.01i	0.371123	−	0.311409i	0.809205	+	0.587526i	$0.199898\pi$
$752$	−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	−0.981461	−	0.191663i	$-0.938612\pi$
$761$	−20219.3	+	16966.0i	−0.963138	+	0.808169i	0.0183225	+	0.999832i	$0.494167\pi$
$762$	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	0.999119	−	0.0419631i	$-0.0133612\pi$
$769$	978.862	+	5551.40i	0.0459020	+	0.260323i	−0.953217	+	0.302286i	$0.902250\pi$
$770$	−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	0.882004	−	0.471241i	$-0.156194\pi$
$773$	706.977	+	1224.52i	0.0328955	+	0.0569766i	−0.849109	+	0.528218i	$0.822860\pi$
$774$	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	0.640976	−	0.767561i	$-0.278530\pi$
$787$	14099.4	+	5131.76i	0.638613	+	0.232436i	−0.00236264	+	0.999997i	$0.500752\pi$
$788$	−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	−0.917203	−	0.398420i	$-0.869559\pi$
$797$	−4310.64	−	24446.8i	−0.191582	−	1.08651i	0.725622	−	0.688094i	$-0.241552\pi$
$798$	−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	0.332085	−	0.943250i	$-0.392248\pi$
$821$	−12683.5	−	10642.7i	−0.539169	−	0.452416i	−0.871254	+	0.490833i	$0.836692\pi$
$822$	9931.35	+	48926.9i	0.421406	+	2.07606i
$823$	113.108	+	641.466i	0.00479063	+	0.0271690i	0.987109	−	0.160047i	$-0.0511646\pi$
$823$	113.108	+	641.466i	0.00479063	+	0.0271690i	−0.982319	+	0.187216i	$0.940054\pi$
$824$	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	0.986110	−	0.166093i	$-0.0531152\pi$
$827$	8305.20	+	14385.0i	0.349214	+	0.604857i	−0.636896	+	0.770950i	$0.719782\pi$
$828$	−12593.4	+	5332.20i	−0.528564	+	0.223800i
$829$	2843.11	−	4924.42i	0.119114	−	0.206311i	−0.800303	−	0.599596i	$-0.795328\pi$
$829$	2843.11	−	4924.42i	0.119114	−	0.206311i	0.919417	+	0.393285i	$0.128661\pi$
$830$	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	0.930070	+	0.367382i	$0.119746\pi$
$839$	−1690.50	+	9587.29i	−0.0695619	+	0.394505i	−0.999632	+	0.0271234i	$0.991365\pi$
$840$	−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	0.612949	−	0.790123i	$-0.289983\pi$
$853$	−1463.20	−	1227.77i	−0.0587327	−	0.0492826i	−0.671681	+	0.740840i	$0.734428\pi$
$854$	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	0.294365	−	0.955693i	$-0.404892\pi$
$857$	28454.4	−	10356.5i	1.13417	−	0.412804i	0.839804	+	0.542889i	$0.182670\pi$
$858$	−8971.73	+	59846.9i	−0.356981	+	2.38128i
$859$	−30617.0	+	25690.7i	−1.21611	+	1.02044i	−0.217092	+	0.976151i	$0.569657\pi$
$859$	−30617.0	+	25690.7i	−1.21611	+	1.02044i	−0.999019	+	0.0442875i	$0.985898\pi$
$860$	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	0.851905	+	0.523697i	$0.175448\pi$
$877$	5986.23	+	33949.6i	0.230491	+	1.30718i	−0.621414	+	0.783483i	$0.713441\pi$
$878$	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	0.994953	−	0.100337i	$-0.0319922\pi$
$881$	10736.5	+	18596.2i	0.410582	+	0.711149i	−0.584371	+	0.811486i	$0.698659\pi$
$882$	42272.0	−	2177.20i	1.61380	−	0.0831182i
$883$	8801.45	−	15244.6i	0.335439	−	0.580997i	−0.648130	−	0.761529i	$-0.724449\pi$
$883$	8801.45	−	15244.6i	0.335439	−	0.580997i	0.983569	+	0.180533i	$0.0577822\pi$
$884$	−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	0.915042	−	0.403360i	$-0.132158\pi$
$887$	35840.9	+	13045.0i	1.35673	+	0.493809i	0.441688	+	0.897169i	$0.354380\pi$
$888$	−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	0.755112	−	0.655596i	$-0.227582\pi$
$907$	6572.14	+	5514.68i	0.240600	+	0.201887i	−0.514512	+	0.857483i	$0.672027\pi$
$908$	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	−0.473866	−	0.880597i	$-0.657142\pi$
$911$	−7446.92	+	2710.46i	−0.270832	+	0.0985746i	0.203034	+	0.979172i	$0.434920\pi$
$912$	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	0.471138	−	0.882060i	$-0.343843\pi$
$929$	−8939.44	−	7501.08i	−0.315709	−	0.264911i	−0.786847	+	0.617148i	$0.788288\pi$
$930$	−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	−0.607426	−	0.794376i	$-0.707798\pi$
$937$	11020.7	−	19088.4i	0.384237	−	0.665518i	0.991663	+	0.128858i	$0.0411312\pi$
$938$	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	0.558963	−	0.829193i	$-0.311200\pi$
$941$	13109.7	+	4771.52i	0.454158	+	0.165300i	−0.104805	+	0.994493i	$0.533422\pi$
$942$	−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	−0.488129	−	0.872771i	$-0.662321\pi$
$947$	7841.27	−	44470.0i	0.269068	−	1.52596i	0.757197	−	0.653187i	$-0.226568\pi$
$948$	−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	−0.568442	−	0.822723i	$-0.692454\pi$
$953$	12599.8	−	21823.6i	0.428278	−	0.741799i	0.996720	+	0.0809240i	$0.0257871\pi$
$954$	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	−0.844699	−	0.535241i	$-0.820221\pi$
$967$	−13960.8	+	11714.5i	−0.464270	+	0.389569i	0.380429	+	0.924810i	$0.375776\pi$
$968$	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	−0.807521	−	0.589839i	$-0.799191\pi$
$977$	−11203.4	+	9400.78i	−0.366867	+	0.307838i	0.440654	+	0.897677i	$0.354747\pi$
$978$	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	0.342388	−	0.939559i	$-0.388764\pi$
$983$	−16132.4	−	13536.7i	−0.523442	−	0.439220i	−0.865830	+	0.500339i	$0.833209\pi$
$984$	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	−0.730597	−	0.682809i	$-0.760758\pi$
$991$	7051.45	−	12213.5i	0.226031	−	0.391497i	0.956628	+	0.291311i	$0.0940916\pi$
$992$	−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	−0.624605	−	0.780941i	$-0.714740\pi$
$997$	7222.56	−	40961.2i	0.229429	−	1.30116i	0.854034	−	0.520217i	$-0.174149\pi$
$998$	−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.25.1	yes	48
3.2	odd	2		81.4.e.a.73.8		48
9.2	odd	6		243.4.e.a.55.1		48
9.4	even	3		243.4.e.c.136.1		48
9.5	odd	6		243.4.e.b.136.8		48
9.7	even	3		243.4.e.d.55.8		48
27.4	even	9		243.4.e.c.109.1		48
27.5	odd	18		243.4.e.a.190.1		48
27.11	odd	18		729.4.a.c.1.24		24
27.13	even	9	inner	27.4.e.a.13.1	✓	48
27.14	odd	18		81.4.e.a.10.8		48
27.16	even	9		729.4.a.d.1.1		24
27.22	even	9		243.4.e.d.190.8		48
27.23	odd	18		243.4.e.b.109.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.1	✓	48	27.13	even	9	inner
27.4.e.a.25.1	yes	48	1.1	even	1	trivial
81.4.e.a.10.8		48	27.14	odd	18
81.4.e.a.73.8		48	3.2	odd	2
243.4.e.a.55.1		48	9.2	odd	6
243.4.e.a.190.1		48	27.5	odd	18
243.4.e.b.109.8		48	27.23	odd	18
243.4.e.b.136.8		48	9.5	odd	6
243.4.e.c.109.1		48	27.4	even	9
243.4.e.c.136.1		48	9.4	even	3
243.4.e.d.55.8		48	9.7	even	3
243.4.e.d.190.8		48	27.22	even	9
729.4.a.c.1.24		24	27.11	odd	18
729.4.a.d.1.1		24	27.16	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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