LMFDB - Embedded newform 114.4.i.c.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,4,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	114.i (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:	$6.72621774065$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 1488 x^{16} + 4798 x^{15} + 939930 x^{14} - 421443 x^{13} - 319752461 x^{12} + \cdots + 20\!\cdots\!49 $ x^18 - 6x^17 - 1488x^16 + 4798x^15 + 939930x^14 - 421443x^13 - 319752461x^12 - 722235969x^11 + 60651236964x^10 + 300466233870x^9 - 5754248160525x^8 - 46793226683178x^7 + 141508710385350x^6 + 2567891527205481x^5 + 9930325439050983x^4 + 15397443154057401x^3 + 9475016573038698x^2 + 12035110299066666*x + 20915625186935649
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.3
Root			$-14.5992 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	114.61
Dual form			114.4.i.c.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87939 + 0.684040i) q^{2} +(0.520945 + 2.95442i) q^{3} +(3.06418 + 2.57115i) q^{4} +(12.4903 - 10.4806i) q^{5} +(-1.04189 + 5.90885i) q^{6} +(11.3068 - 19.5839i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-8.45723 + 3.07818i) q^{9} +O(q^{10})$	\(q+(1.87939 + 0.684040i) q^{2} +(0.520945 + 2.95442i) q^{3} +(3.06418 + 2.57115i) q^{4} +(12.4903 - 10.4806i) q^{5} +(-1.04189 + 5.90885i) q^{6} +(11.3068 - 19.5839i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-8.45723 + 3.07818i) q^{9} +(30.6433 - 11.1532i) q^{10} +(-1.75525 - 3.04019i) q^{11} +(-6.00000 + 10.3923i) q^{12} +(-7.05919 + 40.0347i) q^{13} +(34.6460 - 29.0715i) q^{14} +(37.4710 + 31.4419i) q^{15} +(2.77837 + 15.7569i) q^{16} +(37.4787 + 13.6411i) q^{17} -18.0000 q^{18} +(-55.4820 + 61.4878i) q^{19} +65.2198 q^{20} +(63.7494 + 23.2029i) q^{21} +(-1.21919 - 6.91435i) q^{22} +(8.49929 + 7.13175i) q^{23} +(-18.3851 + 15.4269i) q^{24} +(24.4586 - 138.712i) q^{25} +(-40.6523 + 70.4118i) q^{26} +(-13.5000 - 23.3827i) q^{27} +(84.9993 - 30.9372i) q^{28} +(-226.376 + 82.3942i) q^{29} +(48.9149 + 84.7230i) q^{30} +(123.967 - 214.717i) q^{31} +(-5.55674 + 31.5138i) q^{32} +(8.06762 - 6.76953i) q^{33} +(61.1058 + 51.2739i) q^{34} +(-64.0264 - 363.112i) q^{35} +(-33.8289 - 12.3127i) q^{36} -391.300 q^{37} +(-146.332 + 77.6073i) q^{38} -121.957 q^{39} +(122.573 + 44.6130i) q^{40} +(50.4490 + 286.111i) q^{41} +(103.938 + 87.2144i) q^{42} +(387.790 - 325.394i) q^{43} +(2.43837 - 13.8287i) q^{44} +(-73.3723 + 127.085i) q^{45} +(11.0950 + 19.2172i) q^{46} +(-335.300 + 122.039i) q^{47} +(-45.1052 + 16.4170i) q^{48} +(-84.1871 - 145.816i) q^{49} +(140.852 - 243.962i) q^{50} +(-20.7774 + 117.834i) q^{51} +(-124.566 + 104.523i) q^{52} +(210.297 + 176.460i) q^{53} +(-9.37700 - 53.1796i) q^{54} +(-53.7868 - 19.5768i) q^{55} +180.909 q^{56} +(-210.564 - 131.886i) q^{57} -481.809 q^{58} +(-168.745 - 61.4182i) q^{59} +(33.9759 + 192.687i) q^{60} +(-404.241 - 339.198i) q^{61} +(379.857 - 318.738i) q^{62} +(-35.3413 + 200.430i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(331.417 + 574.030i) q^{65} +(19.7928 - 7.20399i) q^{66} +(152.486 - 55.5002i) q^{67} +(79.7680 + 138.162i) q^{68} +(-16.6426 + 28.8258i) q^{69} +(128.053 - 726.224i) q^{70} +(-393.759 + 330.403i) q^{71} +(-55.1552 - 46.2807i) q^{72} +(-70.1760 - 397.988i) q^{73} +(-735.403 - 267.665i) q^{74} +422.555 q^{75} +(-328.101 + 45.7569i) q^{76} -79.3852 q^{77} +(-229.204 - 83.4233i) q^{78} +(-126.815 - 719.203i) q^{79} +(199.845 + 167.690i) q^{80} +(62.0496 - 52.0658i) q^{81} +(-100.898 + 572.221i) q^{82} +(-18.5134 + 32.0661i) q^{83} +(135.681 + 235.007i) q^{84} +(611.089 - 222.418i) q^{85} +(951.390 - 346.277i) q^{86} +(-361.357 - 625.889i) q^{87} +(14.0420 - 24.3215i) q^{88} +(-218.928 + 1241.60i) q^{89} +(-224.826 + 188.651i) q^{90} +(704.219 + 590.910i) q^{91} +(7.70653 + 43.7059i) q^{92} +(698.946 + 254.396i) q^{93} -713.638 q^{94} +(-48.5577 + 1349.49i) q^{95} -96.0000 q^{96} +(1542.87 + 561.558i) q^{97} +(-58.4757 - 331.632i) q^{98} +(24.2029 + 20.3086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 9 q^{5} - 30 q^{7} + 72 q^{8}+O(q^{10}) $ 18 * q + 9 * q^5 - 30 * q^7 + 72 * q^8	\( 18 q + 9 q^{5} - 30 q^{7} + 72 q^{8} + 18 q^{10} + 57 q^{11} - 108 q^{12} - 228 q^{13} + 6 q^{14} + 27 q^{15} + 27 q^{17} - 324 q^{18} + 105 q^{19} - 24 q^{20} + 45 q^{21} + 222 q^{22} - 576 q^{23} - 243 q^{25} - 186 q^{26} - 243 q^{27} + 60 q^{28} - 339 q^{29} - 18 q^{30} + 429 q^{31} + 288 q^{33} - 450 q^{34} + 1680 q^{35} - 318 q^{37} + 114 q^{38} - 558 q^{39} + 72 q^{40} + 531 q^{41} + 18 q^{42} + 2172 q^{43} - 444 q^{44} + 27 q^{45} - 48 q^{46} - 816 q^{47} - 249 q^{49} + 780 q^{50} - 756 q^{51} + 276 q^{52} - 744 q^{53} + 2862 q^{55} - 480 q^{56} - 171 q^{57} + 900 q^{58} - 2307 q^{59} + 168 q^{61} + 1770 q^{62} - 108 q^{63} - 576 q^{64} + 1209 q^{65} - 90 q^{66} + 1944 q^{67} + 588 q^{68} + 72 q^{69} - 3360 q^{70} - 1011 q^{71} + 4152 q^{73} + 1854 q^{74} + 2340 q^{75} - 276 q^{76} - 7686 q^{77} - 954 q^{78} - 4929 q^{79} + 144 q^{80} - 1062 q^{82} + 156 q^{83} - 360 q^{84} - 2049 q^{85} + 2064 q^{86} + 675 q^{87} - 456 q^{88} - 4785 q^{89} - 162 q^{90} + 5166 q^{91} + 3852 q^{92} + 315 q^{93} + 1368 q^{94} - 1350 q^{95} - 1728 q^{96} + 2247 q^{97} - 2538 q^{98} + 864 q^{99}+O(q^{100}) \) 18 * q + 9 * q^5 - 30 * q^7 + 72 * q^8 + 18 * q^10 + 57 * q^11 - 108 * q^12 - 228 * q^13 + 6 * q^14 + 27 * q^15 + 27 * q^17 - 324 * q^18 + 105 * q^19 - 24 * q^20 + 45 * q^21 + 222 * q^22 - 576 * q^23 - 243 * q^25 - 186 * q^26 - 243 * q^27 + 60 * q^28 - 339 * q^29 - 18 * q^30 + 429 * q^31 + 288 * q^33 - 450 * q^34 + 1680 * q^35 - 318 * q^37 + 114 * q^38 - 558 * q^39 + 72 * q^40 + 531 * q^41 + 18 * q^42 + 2172 * q^43 - 444 * q^44 + 27 * q^45 - 48 * q^46 - 816 * q^47 - 249 * q^49 + 780 * q^50 - 756 * q^51 + 276 * q^52 - 744 * q^53 + 2862 * q^55 - 480 * q^56 - 171 * q^57 + 900 * q^58 - 2307 * q^59 + 168 * q^61 + 1770 * q^62 - 108 * q^63 - 576 * q^64 + 1209 * q^65 - 90 * q^66 + 1944 * q^67 + 588 * q^68 + 72 * q^69 - 3360 * q^70 - 1011 * q^71 + 4152 * q^73 + 1854 * q^74 + 2340 * q^75 - 276 * q^76 - 7686 * q^77 - 954 * q^78 - 4929 * q^79 + 144 * q^80 - 1062 * q^82 + 156 * q^83 - 360 * q^84 - 2049 * q^85 + 2064 * q^86 + 675 * q^87 - 456 * q^88 - 4785 * q^89 - 162 * q^90 + 5166 * q^91 + 3852 * q^92 + 315 * q^93 + 1368 * q^94 - 1350 * q^95 - 1728 * q^96 + 2247 * q^97 - 2538 * q^98 + 864 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	1.87939	+	0.684040i	0.664463	+	0.241845i
$2$	1.87939	+	0.684040i	0.664463	+	0.241845i
$3$	0.520945	+	2.95442i	0.100256	+	0.568579i
$3$	0.520945	+	2.95442i	0.100256	+	0.568579i
$4$	3.06418	+	2.57115i	0.383022	+	0.321394i
$5$	12.4903	−	10.4806i	1.11717	−	0.937415i	0.118710	−	0.992929i	$-0.462124\pi$
$5$	12.4903	−	10.4806i	1.11717	−	0.937415i	0.998458	+	0.0555136i	$0.0176796\pi$
$6$	−1.04189	+	5.90885i	−0.0708916	+	0.402046i
$7$	11.3068	−	19.5839i	0.610509	−	1.05743i	−0.380645	−	0.924721i	$-0.624298\pi$
$7$	11.3068	−	19.5839i	0.610509	−	1.05743i	0.991155	−	0.132712i	$-0.0423686\pi$
$8$	4.00000	+	6.92820i	0.176777	+	0.306186i
$9$	−8.45723	+	3.07818i	−0.313231	+	0.114007i
$10$	30.6433	−	11.1532i	0.969026	−	0.352697i
$11$	−1.75525	−	3.04019i	−0.0481117	−	0.0833320i	0.840967	−	0.541087i	$-0.181987\pi$
$11$	−1.75525	−	3.04019i	−0.0481117	−	0.0833320i	−0.889078	+	0.457755i	$0.848654\pi$
$12$	−6.00000	+	10.3923i	−0.144338	+	0.250000i
$13$	−7.05919	+	40.0347i	−0.150605	+	0.854124i	0.812089	+	0.583533i	$0.198330\pi$
$13$	−7.05919	+	40.0347i	−0.150605	+	0.854124i	−0.962694	+	0.270591i	$0.912781\pi$
$14$	34.6460	−	29.0715i	0.661396	−	0.554977i
$15$	37.4710	+	31.4419i	0.644997	+	0.541217i
$16$	2.77837	+	15.7569i	0.0434120	+	0.246202i
$17$	37.4787	+	13.6411i	0.534701	+	0.194615i	0.595236	−	0.803551i	$-0.297058\pi$
$17$	37.4787	+	13.6411i	0.534701	+	0.194615i	−0.0605350	+	0.998166i	$0.519281\pi$
$18$	−18.0000			−0.235702
$19$	−55.4820	+	61.4878i	−0.669918	+	0.742435i
$19$	−55.4820	+	61.4878i	−0.669918	+	0.742435i
$20$	65.2198			0.729180
$21$	63.7494	+	23.2029i	0.662441	+	0.241109i
$22$	−1.21919	−	6.91435i	−0.0118151	−	0.0670066i
$23$	8.49929	+	7.13175i	0.0770533	+	0.0646554i	0.680501	−	0.732747i	$-0.261762\pi$
$23$	8.49929	+	7.13175i	0.0770533	+	0.0646554i	−0.603448	+	0.797403i	$0.706207\pi$
$24$	−18.3851	+	15.4269i	−0.156368	+	0.131208i
$25$	24.4586	−	138.712i	0.195669	−	1.10969i
$26$	−40.6523	+	70.4118i	−0.306637	+	0.531111i
$27$	−13.5000	−	23.3827i	−0.0962250	−	0.166667i
$28$	84.9993	−	30.9372i	0.573691	−	0.208806i
$29$	−226.376	+	82.3942i	−1.44955	+	0.527594i	−0.942466	−	0.334301i	$-0.891500\pi$
$29$	−226.376	+	82.3942i	−1.44955	+	0.527594i	−0.507086	+	0.861895i	$0.669277\pi$
$30$	48.9149	+	84.7230i	0.297686	+	0.515608i
$31$	123.967	−	214.717i	0.718231	−	1.24401i	−0.243469	−	0.969909i	$-0.578285\pi$
$31$	123.967	−	214.717i	0.718231	−	1.24401i	0.961700	−	0.274104i	$-0.0883813\pi$
$32$	−5.55674	+	31.5138i	−0.0306970	+	0.174091i
$33$	8.06762	−	6.76953i	0.0425573	−	0.0357098i
$34$	61.1058	+	51.2739i	0.308223	+	0.258629i
$35$	−64.0264	−	363.112i	−0.309213	−	1.75363i
$36$	−33.8289	−	12.3127i	−0.156615	−	0.0570034i
$37$	−391.300			−1.73863			−0.869315	−	0.494259i	$-0.835439\pi$
$37$	−391.300			−1.73863			−0.869315	+	0.494259i	$0.835439\pi$
$38$	−146.332	+	77.6073i	−0.624690	+	0.331304i
$39$	−121.957			−0.500736
$40$	122.573	+	44.6130i	0.484513	+	0.176348i
$41$	50.4490	+	286.111i	0.192166	+	1.08983i	0.916397	+	0.400271i	$0.131084\pi$
$41$	50.4490	+	286.111i	0.192166	+	1.08983i	−0.724231	+	0.689558i	$0.757805\pi$
$42$	103.938	+	87.2144i	0.381857	+	0.320416i
$43$	387.790	−	325.394i	1.37529	−	1.15400i	0.404370	−	0.914596i	$-0.367491\pi$
$43$	387.790	−	325.394i	1.37529	−	1.15400i	0.970919	−	0.239409i	$-0.0769535\pi$
$44$	2.43837	−	13.8287i	0.00835452	−	0.0473808i
$45$	−73.3723	+	127.085i	−0.243060	+	0.420992i
$46$	11.0950	+	19.2172i	0.0355625	+	0.0615960i
$47$	−335.300	+	122.039i	−1.04061	+	0.378750i	−0.805111	−	0.593125i	$-0.797894\pi$
$47$	−335.300	+	122.039i	−1.04061	+	0.378750i	−0.235497	+	0.971875i	$0.575672\pi$
$48$	−45.1052	+	16.4170i	−0.135633	+	0.0493664i
$49$	−84.1871	−	145.816i	−0.245443	−	0.425120i
$50$	140.852	−	243.962i	0.398388	−	0.690029i
$51$	−20.7774	+	117.834i	−0.0570473	+	0.323531i
$52$	−124.566	+	104.523i	−0.332195	+	0.278745i
$53$	210.297	+	176.460i	0.545028	+	0.457332i	0.873253	−	0.487267i	$-0.162006\pi$
$53$	210.297	+	176.460i	0.545028	+	0.457332i	−0.328225	+	0.944599i	$0.606451\pi$
$54$	−9.37700	−	53.1796i	−0.0236305	−	0.134015i
$55$	−53.7868	−	19.5768i	−0.131866	−	0.0479951i
$56$	180.909			0.431695
$57$	−210.564	−	131.886i	−0.489296	−	0.306468i
$58$	−481.809			−1.09077
$59$	−168.745	−	61.4182i	−0.372352	−	0.135525i	0.149064	−	0.988827i	$-0.452374\pi$
$59$	−168.745	−	61.4182i	−0.372352	−	0.135525i	−0.521416	+	0.853303i	$0.674596\pi$
$60$	33.9759	+	192.687i	0.0731045	+	0.414596i
$61$	−404.241	−	339.198i	−0.848487	−	0.711965i	0.110969	−	0.993824i	$-0.464605\pi$
$61$	−404.241	−	339.198i	−0.848487	−	0.711965i	−0.959456	+	0.281859i	$0.909049\pi$
$62$	379.857	−	318.738i	0.778096	−	0.652900i
$63$	−35.3413	+	200.430i	−0.0706759	+	0.400823i
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	331.417	+	574.030i	0.632418	+	1.09538i
$66$	19.7928	−	7.20399i	0.0369140	−	0.0134356i
$67$	152.486	−	55.5002i	0.278046	−	0.101200i	−0.199233	−	0.979952i	$-0.563845\pi$
$67$	152.486	−	55.5002i	0.278046	−	0.101200i	0.477279	+	0.878752i	$0.341623\pi$
$68$	79.7680	+	138.162i	0.142254	+	0.246392i
$69$	−16.6426	+	28.8258i	−0.0290366	+	0.0502929i
$70$	128.053	−	726.224i	0.218646	−	1.24000i
$71$	−393.759	+	330.403i	−0.658177	+	0.552276i	−0.909540	−	0.415617i	$-0.863566\pi$
$71$	−393.759	+	330.403i	−0.658177	+	0.552276i	0.251363	+	0.967893i	$0.419121\pi$
$72$	−55.1552	−	46.2807i	−0.0902792	−	0.0757532i
$73$	−70.1760	−	397.988i	−0.112513	−	0.638095i	−0.987951	−	0.154765i	$-0.950538\pi$
$73$	−70.1760	−	397.988i	−0.112513	−	0.638095i	0.875438	−	0.483330i	$-0.160573\pi$
$74$	−735.403	−	267.665i	−1.15525	−	0.420478i
$75$	422.555			0.650565
$76$	−328.101	+	45.7569i	−0.495208	+	0.0690616i
$77$	−79.3852			−0.117491
$78$	−229.204	−	83.4233i	−0.332721	−	0.121100i
$79$	−126.815	−	719.203i	−0.180605	−	1.02426i	−0.931473	−	0.363810i	$-0.881476\pi$
$79$	−126.815	−	719.203i	−0.180605	−	1.02426i	0.750868	−	0.660452i	$-0.229635\pi$
$80$	199.845	+	167.690i	0.279292	+	0.234354i
$81$	62.0496	−	52.0658i	0.0851160	−	0.0714208i
$82$	−100.898	+	572.221i	−0.135882	+	0.770625i
$83$	−18.5134	+	32.0661i	−0.0244832	+	0.0424062i	−0.878007	−	0.478647i	$-0.841127\pi$
$83$	−18.5134	+	32.0661i	−0.0244832	+	0.0424062i	0.853524	+	0.521053i	$0.174461\pi$
$84$	135.681	+	235.007i	0.176239	+	0.305255i
$85$	611.089	−	222.418i	0.779787	−	0.283819i
$86$	951.390	−	346.277i	1.19292	−	0.434187i
$87$	−361.357	−	625.889i	−0.445305	−	0.771291i
$88$	14.0420	−	24.3215i	0.0170101	−	0.0294623i
$89$	−218.928	+	1241.60i	−0.260745	+	1.47876i	0.520138	+	0.854082i	$0.325881\pi$
$89$	−218.928	+	1241.60i	−0.260745	+	1.47876i	−0.780883	+	0.624677i	$0.785230\pi$
$90$	−224.826	+	188.651i	−0.263319	+	0.220951i
$91$	704.219	+	590.910i	0.811233	+	0.680706i
$92$	7.70653	+	43.7059i	0.00873328	+	0.0495289i
$93$	698.946	+	254.396i	0.779326	+	0.283652i
$94$	−713.638			−0.783044
$95$	−48.5577	+	1349.49i	−0.0524412	+	1.45742i
$96$	−96.0000			−0.102062
$97$	1542.87	+	561.558i	1.61500	+	0.587810i	0.982419	−	0.186687i	$-0.0597752\pi$
$97$	1542.87	+	561.558i	1.61500	+	0.587810i	0.632577	+	0.774498i	$0.281997\pi$
$98$	−58.4757	−	331.632i	−0.0602749	−	0.341836i
$99$	24.2029	+	20.3086i	0.0245705	+	0.0206171i
$100$	431.594	−	362.150i	0.431594	−	0.362150i
$101$	−10.1256	+	57.4249i	−0.00997555	+	0.0565741i	−0.989389	−	0.145289i	$-0.953589\pi$
$101$	−10.1256	+	57.4249i	−0.00997555	+	0.0565741i	0.979414	+	0.201864i	$0.0646998\pi$
$102$	−119.652	+	207.243i	−0.116150	+	0.201178i
$103$	−22.7815	−	39.4586i	−0.0217934	−	0.0377473i	0.854923	−	0.518755i	$-0.173604\pi$
$103$	−22.7815	−	39.4586i	−0.0217934	−	0.0377473i	−0.876716	+	0.481008i	$0.840271\pi$
$104$	−305.605	+	111.231i	−0.288145	+	0.104876i
$105$	1039.43	−	378.322i	0.966078	−	0.351624i
$106$	274.523	+	475.487i	0.251547	+	0.435693i
$107$	478.566	−	828.900i	0.432380	−	0.748905i	−0.564697	−	0.825298i	$-0.691007\pi$
$107$	478.566	−	828.900i	0.432380	−	0.748905i	0.997078	+	0.0763932i	$0.0243404\pi$
$108$	18.7540	−	106.359i	0.0167093	−	0.0947632i
$109$	−743.427	+	623.809i	−0.653278	+	0.548166i	−0.908064	−	0.418832i	$-0.862440\pi$
$109$	−743.427	+	623.809i	−0.653278	+	0.548166i	0.254785	+	0.966998i	$0.417995\pi$
$110$	−87.6948	−	73.5846i	−0.0760124	−	0.0637820i
$111$	−203.845	−	1156.07i	−0.174308	−	0.988548i
$112$	339.997	+	123.749i	0.286846	+	0.104403i
$113$	1052.17			0.875929			0.437964	−	0.898992i	$-0.355700\pi$
$113$	1052.17			0.875929			0.437964	+	0.898992i	$0.355700\pi$
$114$	−305.516	−	391.898i	−0.251002	−	0.321970i
$115$	180.904			0.146690
$116$	−905.505	−	329.577i	−0.724776	−	0.263797i
$117$	−63.5327	−	360.312i	−0.0502017	−	0.284708i
$118$	−275.125	−	230.857i	−0.214638	−	0.180103i
$119$	690.911	−	579.743i	0.532233	−	0.446596i
$120$	−67.9518	+	385.374i	−0.0516927	+	0.293164i
$121$	659.338	−	1142.01i	0.495371	−	0.858007i
$122$	−527.699	−	914.001i	−0.391603	−	0.678277i
$123$	−819.011	+	298.096i	−0.600388	+	0.218523i
$124$	931.928	−	339.194i	0.674916	−	0.245649i
$125$	−129.229	−	223.832i	−0.0924689	−	0.160161i
$126$	−203.522	+	352.511i	−0.143898	+	0.249239i
$127$	−201.322	+	1141.75i	−0.140665	+	0.797748i	0.830082	+	0.557641i	$0.188294\pi$
$127$	−201.322	+	1141.75i	−0.140665	+	0.797748i	−0.970746	+	0.240107i	$0.922818\pi$
$128$	−98.0537	+	82.2768i	−0.0677094	+	0.0568149i
$129$	1163.37	+	976.183i	0.794023	+	0.666265i
$130$	230.200	+	1305.53i	0.155306	+	0.880786i
$131$	557.139	+	202.782i	0.371584	+	0.135245i	0.521060	−	0.853520i	$-0.325537\pi$
$131$	557.139	+	202.782i	0.371584	+	0.135245i	−0.149477	+	0.988765i	$0.547759\pi$
$132$	42.1261			0.0277773
$133$	576.849	+	1781.79i	0.376084	+	1.16166i
$134$	324.543			0.209226
$135$	−413.684	−	150.569i	−0.263735	−	0.0959919i
$136$	55.4063	+	314.225i	0.0349342	+	0.198122i
$137$	227.805	+	191.151i	0.142063	+	0.119205i	0.711050	−	0.703141i	$-0.248220\pi$
$137$	227.805	+	191.151i	0.142063	+	0.119205i	−0.568987	+	0.822347i	$0.692664\pi$
$138$	−50.9958	+	42.7905i	−0.0314569	+	0.0263954i
$139$	35.2869	−	200.122i	0.0215323	−	0.122116i	−0.972147	−	0.234372i	$-0.924697\pi$
$139$	35.2869	−	200.122i	0.0215323	−	0.122116i	0.993679	+	0.112256i	$0.0358077\pi$
$140$	737.427	−	1277.26i	0.445171	−	0.771059i
$141$	−535.229	−	927.043i	−0.319677	−	0.553696i
$142$	−966.033	+	351.607i	−0.570899	+	0.207790i
$143$	134.104	−	48.8097i	0.0784217	−	0.0285432i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	−1963.97	+	3401.69i	−1.12482	+	1.94824i
$146$	140.352	−	795.975i	0.0795590	−	0.451201i
$147$	386.946	−	324.686i	0.217107	−	0.182175i
$148$	−1199.01	−	1006.09i	−0.665934	−	0.558785i
$149$	−43.3239	−	245.702i	−0.0238203	−	0.135092i	0.970578	−	0.240785i	$-0.0774049\pi$
$149$	−43.3239	−	245.702i	−0.0238203	−	0.135092i	−0.994399	+	0.105693i	$0.966294\pi$
$150$	794.143	+	289.044i	0.432277	+	0.157336i
$151$	−1838.05			−0.990585			−0.495293	−	0.868726i	$-0.664939\pi$
$151$	−1838.05			−0.990585			−0.495293	+	0.868726i	$0.664939\pi$
$152$	−647.928	−	138.439i	−0.345749	−	0.0738745i
$153$	−358.956			−0.189672
$154$	−149.195	−	54.3027i	−0.0780682	−	0.0284145i
$155$	−701.983	−	3981.14i	−0.363772	−	2.06305i
$156$	−373.697	−	313.569i	−0.191793	−	0.160934i
$157$	−2472.02	+	2074.27i	−1.25662	+	1.05443i	−0.260581	+	0.965452i	$0.583914\pi$
$157$	−2472.02	+	2074.27i	−1.25662	+	1.05443i	−0.996034	+	0.0889736i	$0.971641\pi$
$158$	253.630	−	1438.41i	0.127707	−	0.724263i
$159$	−411.784	+	713.231i	−0.205387	+	0.355742i
$160$	260.879	+	451.856i	0.128902	+	0.223265i
$161$	235.768	−	85.8124i	0.115410	−	0.0420060i
$162$	152.230	−	55.4073i	0.0738292	−	0.0268716i
$163$	−950.738	−	1646.73i	−0.456856	−	0.791298i	0.541937	−	0.840419i	$-0.317691\pi$
$163$	−950.738	−	1646.73i	−0.456856	−	0.791298i	−0.998793	+	0.0491211i	$0.984358\pi$
$164$	−581.049	+	1006.41i	−0.276660	+	0.479190i
$165$	29.8182	−	169.107i	0.0140687	−	0.0797878i
$166$	−56.7283	+	47.6007i	−0.0265239	+	0.0222562i
$167$	−3048.16	−	2557.71i	−1.41242	−	1.18516i	−0.955257	−	0.295778i	$-0.904421\pi$
$167$	−3048.16	−	2557.71i	−1.41242	−	1.18516i	−0.457163	−	0.889383i	$-0.651134\pi$
$168$	94.2434	+	534.481i	0.0432800	+	0.245453i
$169$	511.563	+	186.194i	0.232846	+	0.0847491i
$170$	1300.61			0.586780
$171$	279.954	−	690.800i	0.125196	−	0.308929i
$172$	2024.90			0.897656
$173$	−3185.00	−	1159.25i	−1.39972	−	0.509456i	−0.471624	−	0.881800i	$-0.656332\pi$
$173$	−3185.00	−	1159.25i	−1.39972	−	0.509456i	−0.928095	+	0.372344i	$0.878554\pi$
$174$	−250.996	−	1423.47i	−0.109356	−	0.620189i
$175$	−2439.97	−	2047.38i	−1.05397	−	0.884385i
$176$	43.0273	−	36.1042i	0.0184279	−	0.0154628i
$177$	93.5485	−	530.540i	0.0397262	−	0.225298i
$178$	−1260.76	+	2183.69i	−0.530886	+	0.919521i
$179$	−19.1983	−	33.2525i	−0.00801649	−	0.0138850i	0.861989	−	0.506926i	$-0.169218\pi$
$179$	−19.1983	−	33.2525i	−0.00801649	−	0.0138850i	−0.870006	+	0.493041i	$0.835885\pi$
$180$	−551.579	+	200.758i	−0.228402	+	0.0831314i
$181$	4241.42	−	1543.75i	1.74178	−	0.633956i	0.742427	−	0.669927i	$-0.233675\pi$
$181$	4241.42	−	1543.75i	1.74178	−	0.633956i	0.999353	+	0.0359711i	$0.0114524\pi$
$182$	919.293	+	1592.26i	0.374410	+	0.648496i
$183$	791.548	−	1371.00i	0.319743	−	0.553811i
$184$	−15.4131	+	87.4118i	−0.00617536	+	0.0350222i
$185$	−4887.46	+	4101.07i	−1.94234	+	1.62982i
$186$	1139.57	+	956.215i	0.449234	+	0.376952i
$187$	−24.3130	−	137.886i	−0.00950773	−	0.0539210i
$188$	−1341.20	−	488.157i	−0.520304	−	0.189375i
$189$	−610.567			−0.234985
$190$	−1014.36	+	2502.99i	−0.387314	+	0.955717i
$191$	3291.59			1.24697			0.623484	−	0.781836i	$-0.285717\pi$
$191$	3291.59			1.24697			0.623484	+	0.781836i	$0.285717\pi$
$192$	−180.421	−	65.6679i	−0.0678165	−	0.0246832i
$193$	−89.7998	−	509.280i	−0.0334919	−	0.189942i	0.963472	−	0.267810i	$-0.0862999\pi$
$193$	−89.7998	−	509.280i	−0.0334919	−	0.189942i	−0.996964	+	0.0778679i	$0.975189\pi$
$194$	2515.52	+	2110.77i	0.930946	+	0.781157i
$195$	−1523.28	+	1278.18i	−0.559407	+	0.469398i
$196$	116.951	−	663.265i	0.0426208	−	0.241714i
$197$	−898.675	+	1556.55i	−0.325015	+	0.562943i	−0.981515	−	0.191383i	$-0.938703\pi$
$197$	−898.675	+	1556.55i	−0.325015	+	0.562943i	0.656500	+	0.754326i	$0.272036\pi$
$198$	31.5946	+	54.7234i	0.0113400	+	0.0196415i
$199$	2037.88	−	741.726i	0.725936	−	0.264219i	0.0474923	−	0.998872i	$-0.484877\pi$
$199$	2037.88	−	741.726i	0.725936	−	0.264219i	0.678443	+	0.734653i	$0.262655\pi$
$200$	1058.86	−	385.392i	0.374363	−	0.136257i
$201$	243.408	+	421.594i	0.0854162	+	0.147945i
$202$	−58.3107	+	100.997i	−0.0203105	+	0.0351789i
$203$	−945.986	+	5364.95i	−0.327070	+	1.85491i
$204$	−366.635	+	307.643i	−0.125831	+	0.105585i
$205$	3628.74	+	3044.88i	1.23630	+	1.03738i
$206$	−15.8238	−	89.7414i	−0.00535194	−	0.0303523i
$207$	−93.8333	−	34.1525i	−0.0315066	−	0.0114675i
$208$	−650.436			−0.216825
$209$	284.320	+	60.7491i	0.0940995	+	0.0201058i
$210$	2212.28			0.726961
$211$	127.769	+	46.5042i	0.0416872	+	0.0151729i	0.362780	−	0.931875i	$-0.381828\pi$
$211$	127.769	+	46.5042i	0.0416872	+	0.0151729i	−0.321092	+	0.947048i	$0.604050\pi$
$212$	190.681	+	1081.41i	0.0617739	+	0.350337i
$213$	−1181.28	−	991.208i	−0.379999	−	0.318857i
$214$	1466.41	−	1230.46i	0.468420	−	0.393051i
$215$	1433.28	−	8128.56i	0.454647	−	2.57843i
$216$	108.000	−	187.061i	0.0340207	−	0.0589256i
$217$	−2803.34	−	4855.53i	−0.876974	−	1.51896i
$218$	−1823.90	+	663.844i	−0.566650	+	0.206244i
$219$	1139.27	−	414.659i	0.351527	−	0.127945i
$220$	−114.477	−	198.281i	−0.0350821	−	0.0607640i
$221$	−810.687	+	1404.15i	−0.246754	+	0.427391i
$222$	407.691	−	2312.13i	0.123254	−	0.699009i
$223$	894.562	−	750.627i	0.268629	−	0.225407i	−0.498515	−	0.866881i	$-0.666121\pi$
$223$	894.562	−	750.627i	0.268629	−	0.225407i	0.767145	+	0.641474i	$0.221677\pi$
$224$	554.336	+	465.143i	0.165349	+	0.138744i
$225$	220.127	+	1248.41i	0.0652230	+	0.369898i
$226$	1977.43	+	719.727i	0.582022	+	0.211839i
$227$	6684.51			1.95448			0.977238	−	0.212144i	$-0.0680446\pi$
$227$	6684.51			1.95448			0.977238	+	0.212144i	$0.0680446\pi$
$228$	−306.108	−	945.513i	−0.0889144	−	0.274641i
$229$	3123.34			0.901293			0.450647	−	0.892702i	$-0.351193\pi$
$229$	3123.34			0.901293			0.450647	+	0.892702i	$0.351193\pi$
$230$	339.989	+	123.746i	0.0974703	+	0.0354763i
$231$	−41.3553	−	234.537i	−0.0117791	−	0.0668027i
$232$	−1476.35	−	1238.80i	−0.417789	−	0.350567i
$233$	2946.57	−	2472.46i	0.828480	−	0.695178i	−0.126461	−	0.991972i	$-0.540362\pi$
$233$	2946.57	−	2472.46i	0.828480	−	0.695178i	0.954942	+	0.296794i	$0.0959175\pi$
$234$	127.065	−	720.624i	0.0354980	−	0.201319i
$235$	−2908.96	+	5038.47i	−0.807488	+	1.39861i
$236$	−359.150	−	622.065i	−0.0990621	−	0.171581i
$237$	2058.77	−	749.330i	0.564267	−	0.205376i
$238$	1695.06	−	616.950i	0.461656	−	0.168029i
$239$	3367.08	+	5831.96i	0.911291	+	1.57840i	0.812243	+	0.583320i	$0.198247\pi$
$239$	3367.08	+	5831.96i	0.911291	+	1.57840i	0.0990486	+	0.995083i	$0.468420\pi$
$240$	−391.319	+	677.784i	−0.105248	+	0.182295i
$241$	282.534	−	1602.33i	0.0755172	−	0.428279i	−0.923486	−	0.383633i	$-0.874673\pi$
$241$	282.534	−	1602.33i	0.0755172	−	0.428279i	0.999003	−	0.0446463i	$-0.0142161\pi$
$242$	2020.33	−	1695.26i	0.536660	−	0.450311i
$243$	186.149	+	156.197i	0.0491418	+	0.0412348i
$244$	−366.536	−	2078.73i	−0.0961682	−	0.545397i
$245$	−2579.77	−	938.959i	−0.672716	−	0.244848i
$246$	−1743.15			−0.451784
$247$	−2069.98	−	2655.26i	−0.533239	−	0.684008i
$248$	1983.47			0.507866
$249$	−104.381	−	37.9917i	−0.0265658	−	0.00966917i
$250$	−89.7616	−	509.064i	−0.0227081	−	0.128784i
$251$	−3420.74	−	2870.34i	−0.860220	−	0.721811i	0.101795	−	0.994805i	$-0.467541\pi$
$251$	−3420.74	−	2870.34i	−0.860220	−	0.721811i	−0.962016	+	0.272995i	$0.911986\pi$
$252$	−623.628	+	523.286i	−0.155892	+	0.130809i
$253$	6.76346	−	38.3575i	0.00168069	−	0.00953168i
$254$	−1159.36	+	2008.08i	−0.286398	+	0.496055i
$255$	975.460	+	1689.55i	0.239552	+	0.414916i
$256$	−240.561	+	87.5572i	−0.0587308	+	0.0213763i
$257$	3011.50	−	1096.10i	0.730944	−	0.266042i	0.0503794	−	0.998730i	$-0.483957\pi$
$257$	3011.50	−	1096.10i	0.730944	−	0.266042i	0.680564	+	0.732688i	$0.261735\pi$
$258$	1518.67	+	2630.42i	0.366466	+	0.634739i
$259$	−4424.34	+	7663.19i	−1.06145	+	1.83848i
$260$	−460.399	+	2611.05i	−0.109818	+	0.622810i
$261$	1660.89	−	1393.65i	0.393895	−	0.330517i
$262$	908.367	+	762.211i	0.214195	+	0.179731i
$263$	1100.75	+	6242.65i	0.258080	+	1.46364i	0.788042	+	0.615621i	$0.211095\pi$
$263$	1100.75	+	6242.65i	0.258080	+	1.46364i	−0.529962	+	0.848021i	$0.677794\pi$
$264$	79.1712	+	28.8160i	0.0184570	+	0.00671780i
$265$	4476.08			1.03760
$266$	−134.691	+	3743.25i	−0.0310467	+	0.862832i
$267$	−3782.27			−0.866933
$268$	609.942	+	222.001i	0.139023	+	0.0506002i
$269$	−1402.08	−	7951.58i	−0.317793	−	1.80229i	−0.556115	−	0.831105i	$-0.687709\pi$
$269$	−1402.08	−	7951.58i	−0.317793	−	1.80229i	0.238322	−	0.971186i	$-0.423403\pi$
$270$	−674.477	−	565.954i	−0.152027	−	0.127566i
$271$	5571.20	−	4674.79i	1.24880	−	1.04787i	0.252022	−	0.967722i	$-0.418905\pi$
$271$	5571.20	−	4674.79i	1.24880	−	1.04787i	0.996783	−	0.0801499i	$-0.0255399\pi$
$272$	−110.813	+	628.449i	−0.0247022	+	0.140093i
$273$	−1378.94	+	2388.39i	−0.305704	+	0.529495i
$274$	297.378	+	515.074i	0.0655667	+	0.113565i
$275$	−464.641	+	169.115i	−0.101887	+	0.0370838i
$276$	−125.111	+	45.5367i	−0.0272855	+	0.00993112i
$277$	2603.89	+	4510.08i	0.564812	+	0.978282i	0.997067	+	0.0765313i	$0.0243845\pi$
$277$	2603.89	+	4510.08i	0.564812	+	0.978282i	−0.432256	+	0.901751i	$0.642282\pi$
$278$	203.209	−	351.968i	0.0438405	−	0.0759340i
$279$	−387.480	+	2197.51i	−0.0831463	+	0.471546i
$280$	2259.61	−	1896.04i	0.482276	−	0.404678i
$281$	1069.77	+	897.640i	0.227106	+	0.190565i	0.749240	−	0.662299i	$-0.230419\pi$
$281$	1069.77	+	897.640i	0.227106	+	0.190565i	−0.522133	+	0.852864i	$0.674864\pi$
$282$	−371.766	−	2108.39i	−0.0785048	−	0.445223i
$283$	−7781.02	−	2832.06i	−1.63439	−	0.594871i	−0.648349	−	0.761343i	$-0.724540\pi$
$283$	−7781.02	−	2832.06i	−1.63439	−	0.594871i	−0.986046	+	0.166472i	$0.946762\pi$
$284$	−2056.06			−0.429594
$285$	−4012.25	+	559.548i	−0.833914	+	0.116297i
$286$	285.420			0.0590114
$287$	6173.59	+	2247.00i	1.26974	+	0.462148i
$288$	−50.0107	−	283.625i	−0.0102323	−	0.0580304i
$289$	−2545.00	−	2135.51i	−0.518014	−	0.434665i
$290$	−6017.95	+	5049.66i	−1.21857	+	1.02250i
$291$	−855.332	+	4850.83i	−0.172304	+	0.977184i
$292$	808.255	−	1399.94i	0.161985	−	0.280566i
$293$	2455.26	+	4252.63i	0.489548	+	0.847922i	0.999928	−	0.0120270i	$-0.00382840\pi$
$293$	2455.26	+	4252.63i	0.489548	+	0.847922i	−0.510380	+	0.859949i	$0.670495\pi$
$294$	949.319	−	345.524i	0.188318	−	0.0685421i
$295$	−2751.38	+	1001.42i	−0.543022	+	0.197644i
$296$	−1565.20	−	2711.00i	−0.307349	−	0.532344i
$297$	−47.3919	+	82.0851i	−0.00925911	+	0.0160372i
$298$	86.6478	−	491.404i	0.0168435	−	0.0955244i
$299$	−345.515	+	289.922i	−0.0668283	+	0.0560756i
$300$	1294.78	+	1086.45i	0.249181	+	0.209088i
$301$	−1987.84	−	11273.6i	−0.380656	−	2.15881i
$302$	−3454.40	−	1257.30i	−0.658207	−	0.239568i
$303$	−174.932			−0.0331670
$304$	−1123.01	−	703.390i	−0.211871	−	0.132705i
$305$	−8604.10			−1.61531
$306$	−674.617	−	245.540i	−0.126030	−	0.0458713i
$307$	−1067.77	−	6055.60i	−0.198504	−	1.12577i	−0.907340	−	0.420398i	$-0.861891\pi$
$307$	−1067.77	−	6055.60i	−0.198504	−	1.12577i	0.708836	−	0.705373i	$-0.249220\pi$
$308$	−243.250	−	204.111i	−0.0450015	−	0.0377608i
$309$	104.710	−	87.8618i	0.0192774	−	0.0161757i
$310$	1403.97	−	7962.29i	0.257225	−	1.45880i
$311$	3804.85	−	6590.20i	0.693741	−	1.20159i	−0.276862	−	0.960910i	$-0.589295\pi$
$311$	3804.85	−	6590.20i	0.693741	−	1.20159i	0.970603	−	0.240685i	$-0.0773721\pi$
$312$	−487.827	−	844.941i	−0.0885185	−	0.153319i
$313$	−6513.41	+	2370.69i	−1.17623	+	0.428113i	−0.854869	−	0.518844i	$-0.826362\pi$
$313$	−6513.41	+	2370.69i	−1.17623	+	0.428113i	−0.321361	+	0.946957i	$0.604140\pi$
$314$	−6064.76	+	2207.39i	−1.08998	+	0.396721i
$315$	1659.21	+	2873.84i	0.296781	+	0.514039i
$316$	1460.60	−	2529.83i	0.260016	−	0.450360i
$317$	114.284	−	648.134i	0.0202486	−	0.114836i	−0.973008	−	0.230771i	$-0.925875\pi$
$317$	114.284	−	648.134i	0.0202486	−	0.114836i	0.993257	+	0.115935i	$0.0369864\pi$
$318$	−1261.78	+	1058.76i	−0.222507	+	0.186705i
$319$	647.842	+	543.604i	0.113706	+	0.0954106i
$320$	181.205	+	1027.66i	0.0316552	+	0.179525i
$321$	2698.23	+	982.075i	0.469160	+	0.170760i
$322$	501.797			0.0868449
$323$	−2918.16	+	1547.65i	−0.502695	+	0.266605i
$324$	324.000			0.0555556
$325$	5380.62	+	1958.38i	0.918347	+	0.334251i
$326$	−660.376	−	3745.18i	−0.112193	−	0.636277i
$327$	−2230.28	−	1871.43i	−0.377170	−	0.316484i
$328$	−1780.44	+	1493.96i	−0.299720	+	0.251495i
$329$	−1401.16	+	7946.37i	−0.234798	+	1.33160i
$330$	171.716	−	297.421i	0.0286444	−	0.0496136i
$331$	3906.17	+	6765.69i	0.648649	+	1.12349i	0.983446	+	0.181202i	$0.0579988\pi$
$331$	3906.17	+	6765.69i	0.648649	+	1.12349i	−0.334797	+	0.942290i	$0.608668\pi$
$332$	−139.175	+	50.6556i	−0.0230067	+	0.00837375i
$333$	3309.31	−	1204.49i	0.544592	−	0.198215i
$334$	−3979.10	−	6892.00i	−0.651876	−	1.12908i
$335$	1322.92	−	2291.36i	0.215757	−	0.373702i
$336$	−188.487	+	1068.96i	−0.0306036	+	0.173561i
$337$	2468.74	−	2071.52i	0.399053	−	0.334846i	−0.421074	−	0.907026i	$-0.638347\pi$
$337$	2468.74	−	2071.52i	0.399053	−	0.334846i	0.820128	+	0.572181i	$0.193902\pi$
$338$	834.060	+	699.860i	0.134222	+	0.112625i
$339$	548.123	+	3108.56i	0.0878169	+	0.498035i
$340$	2444.35	+	889.672i	0.389893	+	0.141910i
$341$	−870.376			−0.138221
$342$	998.676	−	1106.78i	0.157901	−	0.174994i
$343$	3948.92			0.621637
$344$	3805.56	+	1385.11i	0.596459	+	0.217093i
$345$	94.2410	+	534.467i	0.0147066	+	0.0834051i
$346$	−5192.88	−	4357.34i	−0.806852	−	0.677029i
$347$	905.979	−	760.207i	0.140160	−	0.117608i	−0.570012	−	0.821636i	$-0.693062\pi$
$347$	905.979	−	760.207i	0.140160	−	0.117608i	0.710172	+	0.704028i	$0.248617\pi$
$348$	501.992	−	2846.94i	0.0773264	−	0.438540i
$349$	−612.101	+	1060.19i	−0.0938825	+	0.162609i	−0.909142	−	0.416487i	$-0.863261\pi$
$349$	−612.101	+	1060.19i	−0.0938825	+	0.162609i	0.815259	+	0.579096i	$0.196594\pi$
$350$	−3185.16	−	5516.85i	−0.486440	−	0.842538i
$351$	1031.42	−	375.405i	0.156846	−	0.0570873i
$352$	105.562	−	38.4213i	0.0159842	−	0.00581779i
$353$	1300.52	+	2252.56i	0.196089	+	0.339637i	0.947257	−	0.320475i	$-0.103842\pi$
$353$	1300.52	+	2252.56i	0.196089	+	0.339637i	−0.751168	+	0.660111i	$0.770509\pi$
$354$	538.724	−	933.098i	0.0808838	−	0.140095i
$355$	−1455.35	+	8253.67i	−0.217582	+	1.23397i
$356$	−3863.18	+	3241.59i	−0.575136	+	0.482596i
$357$	2072.73	+	1739.23i	0.307285	+	0.257843i
$358$	−13.3350	−	75.6267i	−0.00196865	−	0.0111648i
$359$	2448.04	+	891.013i	0.359895	+	0.130991i	0.515638	−	0.856806i	$-0.327555\pi$
$359$	2448.04	+	891.013i	0.359895	+	0.130991i	−0.155743	+	0.987798i	$0.549777\pi$
$360$	−1173.96			−0.171869
$361$	−702.495	−	6822.93i	−0.102419	−	0.994741i
$362$	9027.25			1.31067
$363$	3717.45	+	1353.04i	0.537509	+	0.195637i
$364$	638.534	+	3621.31i	0.0919459	+	0.521451i
$365$	−5047.68	−	4235.51i	−0.723857	−	0.607388i
$366$	2425.44	−	2035.19i	0.346393	−	0.290659i
$367$	792.919	−	4496.87i	0.112779	−	0.639604i	−0.875046	−	0.484039i	$-0.839169\pi$
$367$	792.919	−	4496.87i	0.112779	−	0.639604i	0.987826	−	0.155565i	$-0.0497197\pi$
$368$	−88.7603	+	153.737i	−0.0125732	+	0.0217775i
$369$	−1307.36	−	2264.41i	−0.184440	−	0.319460i
$370$	−11990.7	+	4364.26i	−1.68478	+	0.613209i
$371$	5833.56	−	2123.24i	0.816343	−	0.297125i
$372$	1487.61	+	2576.61i	0.207335	+	0.359116i
$373$	−2415.56	+	4183.86i	−0.335316	+	0.580784i	−0.983545	−	0.180661i	$-0.942176\pi$
$373$	−2415.56	+	4183.86i	−0.335316	+	0.580784i	0.648230	+	0.761445i	$0.275510\pi$
$374$	48.6261	−	275.772i	0.00672298	−	0.0381279i
$375$	593.972	−	498.401i	0.0817935	−	0.0686329i
$376$	−2186.71	−	1834.87i	−0.299923	−	0.251666i
$377$	−1700.59	−	9644.53i	−0.232321	−	1.31756i
$378$	−1147.49	−	417.652i	−0.156139	−	0.0568299i
$379$	4412.77			0.598071			0.299036	−	0.954242i	$-0.403335\pi$
$379$	4412.77			0.598071			0.299036	+	0.954242i	$0.403335\pi$
$380$	−3618.53	+	4010.22i	−0.488491	+	0.541369i
$381$	−3478.09			−0.467685
$382$	6186.16	+	2251.58i	0.828564	+	0.301573i
$383$	−1021.56	−	5793.56i	−0.136291	−	0.772943i	−0.973952	−	0.226753i	$-0.927189\pi$
$383$	−1021.56	−	5793.56i	−0.136291	−	0.772943i	0.837661	−	0.546190i	$-0.183922\pi$
$384$	−294.161	−	246.830i	−0.0390920	−	0.0328021i
$385$	−991.546	+	832.006i	−0.131257	+	0.110138i
$386$	179.600	−	1018.56i	0.0236823	−	0.134309i
$387$	−2278.01	+	3945.62i	−0.299219	+	0.518262i
$388$	3283.77	+	5687.66i	0.429661	+	0.744194i
$389$	−8542.06	+	3109.06i	−1.11337	+	0.405232i	−0.832227	−	0.554434i	$-0.812935\pi$
$389$	−8542.06	+	3109.06i	−1.11337	+	0.405232i	−0.281140	+	0.959667i	$0.590712\pi$
$390$	−3737.16	+	1360.21i	−0.485226	+	0.176608i
$391$	221.257	+	383.229i	0.0286176	+	0.0495671i
$392$	673.496	−	1166.53i	0.0867773	−	0.150303i
$393$	−308.865	+	1751.66i	−0.0396443	+	0.224834i
$394$	−2753.70	+	2310.63i	−0.352105	+	0.295451i
$395$	−9121.66	−	7653.98i	−1.16193	−	0.974971i
$396$	21.9454	+	124.458i	0.00278484	+	0.0157936i
$397$	−2667.07	−	970.734i	−0.337170	−	0.122720i	0.167886	−	0.985806i	$-0.446306\pi$
$397$	−2667.07	−	970.734i	−0.337170	−	0.122720i	−0.505056	+	0.863087i	$0.668528\pi$
$398$	4337.33			0.546257
$399$	−4963.64	+	2632.47i	−0.622789	+	0.330296i
$400$	2253.62			0.281703
$401$	10961.9	+	3989.81i	1.36512	+	0.496862i	0.917633	−	0.397430i	$-0.130098\pi$
$401$	10961.9	+	3989.81i	1.36512	+	0.496862i	0.447484	+	0.894292i	$0.352320\pi$
$402$	169.069	+	958.839i	0.0209761	+	0.118962i
$403$	7721.03	+	6478.71i	0.954372	+	0.800813i
$404$	−178.674	+	149.926i	−0.0220034	+	0.0184631i
$405$	229.337	−	1300.64i	0.0281379	−	0.159578i
$406$	−5447.72	+	9435.72i	−0.665925	+	1.15342i
$407$	686.831	+	1189.63i	0.0836485	+	0.144883i
$408$	−899.489	+	327.387i	−0.109145	+	0.0397257i
$409$	5262.33	−	1915.33i	0.636199	−	0.231557i	−0.00372824	−	0.999993i	$-0.501187\pi$
$409$	5262.33	−	1915.33i	0.636199	−	0.231557i	0.639927	+	0.768436i	$0.278965\pi$
$410$	4736.99	+	8204.70i	0.570593	+	0.988296i
$411$	−446.067	+	772.611i	−0.0535350	+	0.0927253i
$412$	31.6477	−	179.483i	0.00378439	−	0.0214623i
$413$	−3110.78	+	2610.25i	−0.370633	+	0.310998i
$414$	−152.987	−	128.372i	−0.0181616	−	0.0152394i
$415$	104.835	+	594.547i	0.0124003	+	0.0703258i
$416$	−1222.42	−	444.924i	−0.144072	−	0.0524380i
$417$	609.627			0.0715913
$418$	492.791	+	308.657i	0.0576632	+	0.0361170i
$419$	3772.52			0.439856			0.219928	−	0.975516i	$-0.429418\pi$
$419$	3772.52			0.439856			0.219928	+	0.975516i	$0.429418\pi$
$420$	4157.73	+	1513.29i	0.483039	+	0.175812i
$421$	−1887.47	−	10704.4i	−0.218503	−	1.23919i	−0.874724	−	0.484621i	$-0.838957\pi$
$421$	−1887.47	−	10704.4i	−0.218503	−	1.23919i	0.656221	−	0.754568i	$-0.272154\pi$
$422$	208.317	+	174.799i	0.0240301	+	0.0201637i
$423$	2460.05	−	2064.23i	0.282771	−	0.237273i
$424$	−381.363	+	2162.82i	−0.0436807	+	0.247726i
$425$	2808.86	−	4865.09i	0.320588	−	0.555274i
$426$	−1542.05	−	2670.90i	−0.175381	−	0.303769i
$427$	−11213.5	+	4081.38i	−1.27086	+	0.462557i
$428$	3597.64	−	1309.43i	0.406305	−	0.147883i
$429$	214.065	+	370.772i	0.0240913	+	0.0417273i
$430$	8253.96	−	14296.3i	0.925677	−	1.60332i
$431$	1948.09	−	11048.2i	0.217717	−	1.23474i	−0.658412	−	0.752658i	$-0.728771\pi$
$431$	1948.09	−	11048.2i	0.217717	−	1.23474i	0.876129	−	0.482077i	$-0.160118\pi$
$432$	330.931	−	277.684i	0.0368563	−	0.0309261i
$433$	3185.83	+	2673.23i	0.353582	+	0.296691i	0.802227	−	0.597020i	$-0.203649\pi$
$433$	3185.83	+	2673.23i	0.353582	+	0.296691i	−0.448645	+	0.893710i	$0.648093\pi$
$434$	−1947.18	−	11043.0i	−0.215363	−	1.22139i
$435$	−11073.2	−	4030.30i	−1.22050	−	0.444226i
$436$	−3881.90			−0.426397
$437$	−910.074	+	126.919i	−0.0996218	+	0.0138932i
$438$	2424.76			0.264520
$439$	8029.72	+	2922.58i	0.872979	+	0.317738i	0.739373	−	0.673296i	$-0.235122\pi$
$439$	8029.72	+	2922.58i	0.872979	+	0.317738i	0.133606	+	0.991035i	$0.457344\pi$
$440$	−79.5151	−	450.953i	−0.00861531	−	0.0488598i
$441$	1160.84	+	974.059i	0.125347	+	0.105179i
$442$	−2484.09	+	2084.40i	−0.267322	+	0.224309i
$443$	−2897.49	+	16432.5i	−0.310754	+	1.76237i	0.284348	+	0.958721i	$0.408223\pi$
$443$	−2897.49	+	16432.5i	−0.310754	+	1.76237i	−0.595102	+	0.803650i	$0.702888\pi$
$444$	2347.80	−	4066.51i	0.250950	−	0.434657i
$445$	10278.3	+	17802.5i	1.09492	+	1.89645i
$446$	2194.69	−	798.800i	0.233008	−	0.0848078i
$447$	703.338	−	255.994i	0.0744223	−	0.0270875i
$448$	723.635	+	1253.37i	0.0763137	+	0.132179i
$449$	2457.73	−	4256.91i	0.258324	−	0.447430i	−0.707469	−	0.706744i	$-0.750163\pi$
$449$	2457.73	−	4256.91i	0.258324	−	0.447430i	0.965793	+	0.259314i	$0.0834966\pi$
$450$	−440.255	+	2496.81i	−0.0461196	+	0.261557i
$451$	781.280	−	655.572i	0.0815721	−	0.0684471i
$452$	3224.04	+	2705.29i	0.335500	+	0.281518i
$453$	−957.522	−	5430.38i	−0.0993119	−	0.563226i
$454$	12562.8	+	4572.47i	1.29868	+	0.472680i
$455$	14989.0			1.54439
$456$	71.4743	−	1986.37i	0.00734011	−	0.203992i
$457$	−14255.0			−1.45913			−0.729565	−	0.683911i	$-0.760278\pi$
$457$	−14255.0			−1.45913			−0.729565	+	0.683911i	$0.760278\pi$
$458$	5869.96	+	2136.49i	0.598876	+	0.217973i
$459$	−186.996	−	1060.51i	−0.0190158	−	0.107844i
$460$	554.322	+	465.132i	0.0561857	+	0.0471454i
$461$	−7823.74	+	6564.90i	−0.790429	+	0.663249i	−0.945852	−	0.324599i	$-0.894771\pi$
$461$	−7823.74	+	6564.90i	−0.790429	+	0.663249i	0.155423	+	0.987848i	$0.450326\pi$
$462$	82.7106	−	469.075i	0.00832910	−	0.0472367i
$463$	−2367.66	+	4100.91i	−0.237656	+	0.411632i	−0.960041	−	0.279859i	$-0.909712\pi$
$463$	−2367.66	+	4100.91i	−0.237656	+	0.411632i	0.722385	+	0.691491i	$0.243046\pi$
$464$	−1927.24	−	3338.07i	−0.192823	−	0.333979i
$465$	11396.3	−	4147.91i	1.13654	−	0.413666i
$466$	7229.00	−	2631.14i	0.718620	−	0.261556i
$467$	163.963	+	283.992i	0.0162469	+	0.0281405i	0.874035	−	0.485864i	$-0.161495\pi$
$467$	163.963	+	283.992i	0.0162469	+	0.0281405i	−0.857788	+	0.514004i	$0.828162\pi$
$468$	731.741	−	1267.41i	0.0722750	−	0.125184i
$469$	637.210	−	3613.80i	0.0627369	−	0.355799i
$470$	−8913.57	+	7479.37i	−0.874792	+	0.734038i
$471$	−7416.06	−	6222.81i	−0.725507	−	0.608773i
$472$	−249.463	−	1414.77i	−0.0243272	−	0.137967i
$473$	−1669.93	−	607.805i	−0.162333	−	0.0590844i
$474$	4381.79			0.424604
$475$	7172.06	+	9199.91i	0.692793	+	0.888675i
$476$	3607.68			0.347390
$477$	−2321.70	−	845.031i	−0.222858	−	0.0811138i
$478$	2338.75	+	13263.7i	0.223791	+	1.26918i
$479$	−4338.77	−	3640.66i	−0.413869	−	0.347278i	0.411956	−	0.911204i	$-0.364846\pi$
$479$	−4338.77	−	3640.66i	−0.413869	−	0.347278i	−0.825825	+	0.563926i	$0.809290\pi$
$480$	−1199.07	+	1006.14i	−0.114020	+	0.0956746i
$481$	2762.26	−	15665.6i	0.261847	−	1.48501i
$482$	1627.05	−	2818.13i	0.153755	−	0.266312i
$483$	376.348	+	651.854i	0.0354543	+	0.0614086i
$484$	4956.60	−	1804.06i	0.465496	−	0.169427i
$485$	25156.4	−	9156.18i	2.35524	−	0.857239i
$486$	243.000	+	420.888i	0.0226805	+	0.0392837i
$487$	−4609.13	+	7983.24i	−0.428869	+	0.742824i	−0.996773	−	0.0802714i	$-0.974421\pi$
$487$	−4609.13	+	7983.24i	−0.428869	+	0.742824i	0.567904	+	0.823095i	$0.307755\pi$
$488$	733.071	−	4157.45i	0.0680012	−	0.385654i
$489$	4369.85	−	3666.74i	0.404113	−	0.339091i
$490$	−4206.09	−	3529.33i	−0.387779	−	0.325386i
$491$	3603.28	+	20435.2i	0.331189	+	1.87827i	0.462031	+	0.886864i	$0.347121\pi$
$491$	3603.28	+	20435.2i	0.331189	+	1.87827i	−0.130842	+	0.991403i	$0.541768\pi$
$492$	−3276.04	−	1192.38i	−0.300194	−	0.109262i
$493$	−9608.24			−0.877755
$494$	−2073.99	−	6406.20i	−0.188894	−	0.583459i
$495$	515.148			0.0467761
$496$	3727.71	+	1356.78i	0.337458	+	0.122825i
$497$	2018.44	+	11447.1i	0.182172	+	1.03315i
$498$	−170.185	−	142.802i	−0.0153136	−	0.0128496i
$499$	−3913.06	+	3283.45i	−0.351047	+	0.294564i	−0.801210	−	0.598383i	$-0.795810\pi$
$499$	−3913.06	+	3283.45i	−0.351047	+	0.294564i	0.450163	+	0.892946i	$0.351366\pi$
$500$	179.523	−	1018.13i	0.0160571	−	0.0910641i
$501$	5968.64	−	10338.0i	0.532254	−	0.921891i
$502$	−4465.46	−	7734.41i	−0.397019	−	0.687656i
$503$	−17369.8	+	6322.08i	−1.53972	+	0.560412i	−0.965978	−	0.258624i	$-0.916731\pi$
$503$	−17369.8	+	6322.08i	−1.53972	+	0.560412i	−0.573742	+	0.819036i	$0.694509\pi$
$504$	−1529.99	+	556.870i	−0.135220	+	0.0492162i
$505$	475.377	+	823.377i	0.0418891	+	0.0725541i
$506$	38.9492	−	67.4621i	0.00342195	−	0.00592698i
$507$	−283.599	+	1608.37i	−0.0248424	+	0.140888i
$508$	−3552.50	+	2980.90i	−0.310269	+	0.260347i
$509$	−14291.2	−	11991.7i	−1.24449	−	1.04425i	−0.997160	−	0.0753171i	$-0.976003\pi$
$509$	−14291.2	−	11991.7i	−1.24449	−	1.04425i	−0.247328	−	0.968932i	$-0.579552\pi$
$510$	677.548	+	3842.56i	0.0588281	+	0.333631i
$511$	−8587.63	−	3125.64i	−0.743433	−	0.270588i
$512$	−512.000			−0.0441942
$513$	2186.76	+	467.233i	0.188202	+	0.0402122i
$514$	6409.55			0.550026
$515$	−698.099	−	254.087i	−0.0597319	−	0.0217406i
$516$	1054.86	+	5982.40i	0.0899952	+	0.510388i
$517$	959.560	+	805.167i	0.0816275	+	0.0684936i
$518$	−13557.0	+	11375.7i	−1.14992	+	0.964899i
$519$	1765.69	−	10013.8i	0.149336	−	0.846927i
$520$	−2651.33	+	4592.24i	−0.223594	+	0.387275i
$521$	−8812.32	−	15263.4i	−0.741026	−	1.28350i	−0.952028	−	0.306010i	$-0.901006\pi$
$521$	−8812.32	−	15263.4i	−0.741026	−	1.28350i	0.211002	−	0.977486i	$-0.432327\pi$
$522$	4074.77	−	1483.10i	0.341663	−	0.124355i
$523$	−19754.1	+	7189.90i	−1.65160	+	0.601133i	−0.989010	−	0.147850i	$-0.952765\pi$
$523$	−19754.1	+	7189.90i	−1.65160	+	0.601133i	−0.662589	+	0.748983i	$0.730542\pi$
$524$	1185.79	+	2053.85i	0.0988577	+	0.171227i
$525$	4777.74	−	8275.28i	0.397176	−	0.687929i
$526$	−2201.49	+	12485.3i	−0.182490	+	1.03495i
$527$	7575.12	−	6356.28i	0.626143	−	0.525396i
$528$	129.082	+	108.313i	0.0106393	+	0.00892746i
$529$	−2091.40	−	11860.9i	−0.171891	−	0.974844i
$530$	8412.28	+	3061.82i	0.689445	+	0.250938i
$531$	1616.17			0.132083
$532$	−2813.67	+	6942.87i	−0.229301	+	0.565812i
$533$	−11810.5			−0.959790
$534$	−7108.34	−	2587.22i	−0.576045	−	0.209663i
$535$	−2709.95	−	15368.9i	−0.218993	−	1.24197i
$536$	994.459	+	834.450i	0.0801382	+	0.0672439i
$537$	88.2407	−	74.0427i	0.00709100	−	0.00595005i
$538$	2804.16	−	15903.2i	0.224713	−	1.27441i
$539$	−295.539	+	511.889i	−0.0236174	+	0.0409066i
$540$	−880.468	−	1525.01i	−0.0701654	−	0.121530i
$541$	−2740.84	+	997.586i	−0.217815	+	0.0792783i	−0.448623	−	0.893721i	$-0.648085\pi$
$541$	−2740.84	+	997.586i	−0.217815	+	0.0792783i	0.230808	+	0.972999i	$0.425863\pi$
$542$	13668.2	−	4974.81i	1.08321	−	0.394255i
$543$	6770.43	+	11726.7i	0.535078	+	0.926782i
$544$	−638.144	+	1105.30i	−0.0502945	+	0.0871126i
$545$	−2747.73	+	15583.1i	−0.215963	+	1.22479i
$546$	−4225.32	+	3545.46i	−0.331185	+	0.277897i
$547$	2518.18	+	2113.00i	0.196837	+	0.165166i	0.735879	−	0.677113i	$-0.236769\pi$
$547$	2518.18	+	2113.00i	0.196837	+	0.165166i	−0.539042	+	0.842279i	$0.681214\pi$
$548$	206.557	+	1171.44i	0.0161016	+	0.0913166i
$549$	4462.87	+	1624.35i	0.346941	+	0.126276i
$550$	−988.921			−0.0766686
$551$	7493.57	−	18490.8i	0.579377	−	1.42964i
$552$	−266.281			−0.0205320
$553$	−15518.7	−	5648.35i	−1.19335	−	0.434344i
$554$	1808.65	+	10257.3i	0.138704	+	0.786629i
$555$	−14662.4	−	12303.2i	−1.12141	−	0.940976i
$556$	622.668	−	522.481i	0.0474946	−	0.0398527i
$557$	−3011.88	+	17081.2i	−0.229116	+	1.29938i	0.625542	+	0.780190i	$0.284878\pi$
$557$	−3011.88	+	17081.2i	−0.229116	+	1.29938i	−0.854658	+	0.519191i	$0.826233\pi$
$558$	−2231.41	+	3864.91i	−0.169289	+	0.293217i
$559$	10289.6	+	17822.1i	0.778537	+	1.34847i
$560$	5543.64	−	2017.72i	0.418324	−	0.152257i
$561$	394.708	−	143.662i	0.0297051	−	0.0108118i
$562$	1396.48	+	2418.77i	0.104817	+	0.181548i
$563$	−7310.85	+	12662.8i	−0.547275	+	0.947907i	0.451185	+	0.892430i	$0.351001\pi$
$563$	−7310.85	+	12662.8i	−0.547275	+	0.947907i	−0.998460	+	0.0554772i	$0.982332\pi$
$564$	743.532	−	4216.78i	0.0555113	−	0.314820i
$565$	13142.0	−	11027.4i	0.978560	−	0.821109i
$566$	−12686.3	−	10645.1i	−0.942129	−	0.790540i
$567$	−318.071	−	1803.87i	−0.0235586	−	0.133608i
$568$	−3864.13	−	1406.43i	−0.285450	−	0.103895i
$569$	−15937.5			−1.17423			−0.587113	−	0.809505i	$-0.699735\pi$
$569$	−15937.5			−1.17423			−0.587113	+	0.809505i	$0.699735\pi$
$570$	−7923.33	−	1692.94i	−0.582231	−	0.124402i
$571$	5889.36			0.431632			0.215816	−	0.976434i	$-0.430759\pi$
$571$	5889.36			0.431632			0.215816	+	0.976434i	$0.430759\pi$
$572$	536.414	+	195.239i	0.0392109	+	0.0142716i
$573$	1714.73	+	9724.74i	0.125016	+	0.709000i
$574$	10065.5	+	8445.97i	0.731927	+	0.614160i
$575$	1197.14	−	1004.52i	0.0868246	−	0.0728545i
$576$	100.021	−	567.249i	0.00723534	−	0.0410337i
$577$	7671.85	−	13288.0i	0.553524	−	0.958732i	−0.444493	−	0.895782i	$-0.646616\pi$
$577$	7671.85	−	13288.0i	0.553524	−	0.958732i	0.998017	−	0.0629492i	$-0.0200506\pi$
$578$	−3322.27	−	5754.33i	−0.239080	−	0.414098i
$579$	1457.85	−	530.613i	0.104639	−	0.0380856i
$580$	−14764.2	+	5373.74i	−1.05698	+	0.384711i
$581$	418.654	+	725.129i	0.0298945	+	0.0517787i
$582$	−4925.66	+	8531.49i	−0.350816	+	0.607632i
$583$	167.347	−	949.074i	0.0118882	−	0.0674213i
$584$	2476.64	−	2078.14i	0.175486	−	0.147250i
$585$	−4569.84	−	3834.55i	−0.322973	−	0.271007i
$586$	1705.40	+	9671.82i	0.120221	+	0.681808i
$587$	10990.0	+	4000.05i	0.772756	+	0.281260i	0.698149	−	0.715953i	$-0.254007\pi$
$587$	10990.0	+	4000.05i	0.772756	+	0.281260i	0.0746073	+	0.997213i	$0.476230\pi$
$588$	2020.49			0.141707
$589$	6324.55	+	19535.4i	0.442443	+	1.36663i
$590$	−5855.92			−0.408618
$591$	−5066.87	−	1844.19i	−0.352662	−	0.128358i
$592$	−1087.18	−	6165.68i	−0.0754775	−	0.428054i
$593$	−8132.51	−	6823.98i	−0.563174	−	0.472559i	0.316199	−	0.948693i	$-0.397593\pi$
$593$	−8132.51	−	6823.98i	−0.563174	−	0.472559i	−0.879373	+	0.476134i	$0.842038\pi$
$594$	−145.217	+	121.852i	−0.0100309	+	0.00841689i
$595$	2553.63	−	14482.4i	0.175947	−	0.997847i
$596$	498.985	−	864.267i	0.0342940	−	0.0593989i
$597$	3252.99	+	5634.35i	0.223009	+	0.386262i
$598$	−847.675	+	308.528i	−0.0579666	+	0.0210981i
$599$	174.512	−	63.5173i	0.0119038	−	0.00433263i	−0.336061	−	0.941840i	$-0.609095\pi$
$599$	174.512	−	63.5173i	0.0119038	−	0.00433263i	0.347965	+	0.937507i	$0.386873\pi$
$600$	1690.22	+	2927.54i	0.115005	+	0.199194i
$601$	−10596.7	+	18354.0i	−0.719213	+	1.24571i	0.242100	+	0.970251i	$0.422164\pi$
$601$	−10596.7	+	18354.0i	−0.719213	+	1.24571i	−0.961312	+	0.275461i	$0.911169\pi$
$602$	3975.69	−	22547.2i	0.269164	−	1.52651i
$603$	−1118.77	+	938.756i	−0.0755550	+	0.0633982i
$604$	−5632.11	−	4725.90i	−0.379416	−	0.318368i
$605$	−3733.60	−	21174.3i	−0.250897	−	1.42291i
$606$	−328.765	−	119.661i	−0.0220382	−	0.00802126i
$607$	−2847.55			−0.190410			−0.0952048	−	0.995458i	$-0.530351\pi$
$607$	−2847.55			−0.190410			−0.0952048	+	0.995458i	$0.530351\pi$
$608$	−1629.42	−	2090.12i	−0.108687	−	0.139417i
$609$	−16343.1			−1.08745
$610$	−16170.4	−	5885.55i	−1.07331	−	0.390654i
$611$	−2518.85	−	14285.1i	−0.166779	−	0.945850i
$612$	−1099.91	−	922.930i	−0.0726487	−	0.0609595i
$613$	−3568.61	+	2994.42i	−0.235130	+	0.197297i	−0.752738	−	0.658321i	$-0.771267\pi$
$613$	−3568.61	+	2994.42i	−0.235130	+	0.197297i	0.517608	+	0.855618i	$0.326823\pi$
$614$	2135.53	−	12111.2i	0.140363	−	0.796040i
$615$	−7105.48	+	12307.1i	−0.465887	+	0.806940i
$616$	−317.541	−	549.997i	−0.0207696	−	0.0359740i
$617$	13853.3	−	5042.18i	0.903909	−	0.328996i	0.152091	−	0.988367i	$-0.451399\pi$
$617$	13853.3	−	5042.18i	0.903909	−	0.328996i	0.751818	+	0.659371i	$0.229177\pi$
$618$	256.891	−	93.5006i	0.0167211	−	0.00608600i
$619$	−2411.42	−	4176.70i	−0.156580	−	0.271205i	0.777053	−	0.629435i	$-0.216714\pi$
$619$	−2411.42	−	4176.70i	−0.156580	−	0.271205i	−0.933633	+	0.358230i	$0.883380\pi$
$620$	8085.12	−	14003.8i	0.523720	−	0.907109i
$621$	52.0191	−	295.015i	0.00336144	−	0.0190637i
$622$	11658.7	−	9782.85i	0.751565	−	0.630638i
$623$	21840.1	+	18326.0i	1.40450	+	1.17852i
$624$	−338.841	−	1921.66i	−0.0217380	−	0.123282i
$625$	12584.6	+	4580.43i	0.805417	+	0.293148i
$626$	−13862.9			−0.885098
$627$	−31.3639	+	871.647i	−0.00199769	+	0.0555187i
$628$	−12908.0			−0.820197
$629$	−14665.4	−	5337.77i	−0.929647	−	0.338364i
$630$	1152.48	+	6536.01i	0.0728821	+	0.413335i
$631$	−12413.7	−	10416.3i	−0.783171	−	0.657159i	0.160874	−	0.986975i	$-0.448569\pi$
$631$	−12413.7	−	10416.3i	−0.783171	−	0.657159i	−0.944045	+	0.329816i	$0.893013\pi$
$632$	4475.53	−	3755.41i	0.281688	−	0.236364i
$633$	−70.8325	+	401.711i	−0.00444761	+	0.0252237i
$634$	658.133	−	1139.92i	0.0412268	−	0.0714069i
$635$	9451.69	+	16370.8i	0.590675	+	1.02308i
$636$	−3095.60	+	1126.71i	−0.193001	+	0.0702466i
$637$	6432.00	−	2341.06i	0.400071	−	0.145614i
$638$	845.698	+	1464.79i	0.0524788	+	0.0908960i
$639$	2313.07	−	4006.35i	0.143198	−	0.248026i
$640$	−362.410	+	2055.33i	−0.0223836	+	0.126944i
$641$	−7914.88	+	6641.38i	−0.487705	+	0.409233i	−0.853203	−	0.521579i	$-0.825343\pi$
$641$	−7914.88	+	6641.38i	−0.487705	+	0.409233i	0.365498	+	0.930812i	$0.380899\pi$
$642$	4399.23	+	3691.39i	0.270442	+	0.226928i
$643$	1357.02	+	7696.03i	0.0832279	+	0.472009i	0.997725	+	0.0674164i	$0.0214756\pi$
$643$	1357.02	+	7696.03i	0.0832279	+	0.472009i	−0.914497	+	0.404593i	$0.867413\pi$
$644$	943.070	+	343.249i	0.0577052	+	0.0210030i
$645$	24761.9			1.51162
$646$	−6542.99	+	912.485i	−0.398499	+	0.0555747i
$647$	−18199.1			−1.10584			−0.552921	−	0.833234i	$-0.686487\pi$
$647$	−18199.1			−1.10584			−0.552921	+	0.833234i	$0.686487\pi$
$648$	608.921	+	221.629i	0.0369146	+	0.0134358i
$649$	109.468	+	620.822i	0.00662093	+	0.0375491i
$650$	8772.64	+	7361.12i	0.529371	+	0.444195i
$651$	12884.9	−	10811.7i	0.775729	−	0.650914i
$652$	1320.75	−	7490.36i	0.0793323	−	0.449916i
$653$	−6370.64	+	11034.3i	−0.381780	+	0.661263i	−0.991317	−	0.131495i	$-0.958022\pi$
$653$	−6370.64	+	11034.3i	−0.381780	+	0.661263i	0.609537	+	0.792758i	$0.291355\pi$
$654$	−2911.42	−	5042.73i	−0.174076	−	0.301508i
$655$	9084.12	−	3306.35i	0.541902	−	0.197236i
$656$	−4368.06	+	1589.84i	−0.259976	+	0.0946234i
$657$	1818.57	+	3149.86i	0.107990	+	0.187044i
$658$	−8068.96	+	13975.8i	−0.478056	+	0.828017i
$659$	1140.86	−	6470.12i	0.0674377	−	0.382458i	−0.932344	−	0.361572i	$-0.882240\pi$
$659$	1140.86	−	6470.12i	0.0674377	−	0.382458i	0.999782	−	0.0208862i	$-0.00664875\pi$
$660$	526.169	−	441.508i	0.0310319	−	0.0260389i
$661$	24165.3	+	20277.1i	1.42197	+	1.19318i	0.950274	+	0.311414i	$0.100803\pi$
$661$	24165.3	+	20277.1i	1.42197	+	1.19318i	0.471696	+	0.881761i	$0.343642\pi$
$662$	2713.20	+	15387.3i	0.159292	+	0.903391i
$663$	−4570.78	−	1663.63i	−0.267744	−	0.0974510i
$664$	−296.214			−0.0173122
$665$	25879.3	+	16209.3i	1.50910	+	0.945219i
$666$	7043.40			0.409799
$667$	−2511.65	−	914.167i	−0.145805	−	0.0530685i
$668$	−2763.85	−	15674.6i	−0.160085	−	0.907886i
$669$	2683.69	+	2251.88i	0.155093	+	0.130139i
$670$	4053.65	−	3401.42i	0.233741	−	0.196132i
$671$	−321.682	+	1824.35i	−0.0185073	+	0.104960i
$672$	−1085.45	+	1880.06i	−0.0623098	+	0.107924i
$673$	4657.31	+	8066.70i	0.266755	+	0.462033i	0.968022	−	0.250866i	$-0.0807152\pi$
$673$	4657.31	+	8066.70i	0.266755	+	0.462033i	−0.701267	+	0.712899i	$0.747382\pi$
$674$	6056.72	−	2204.47i	0.346137	−	0.125984i
$675$	−3573.64	+	1300.70i	−0.203777	+	0.0741688i
$676$	1088.79	+	1885.84i	0.0619475	+	0.107296i
$677$	−15413.2	+	26696.5i	−0.875006	+	1.51555i	−0.0182488	+	0.999833i	$0.505809\pi$
$677$	−15413.2	+	26696.5i	−0.875006	+	1.51555i	−0.856757	+	0.515721i	$0.827524\pi$
$678$	−1096.25	+	6217.12i	−0.0620960	+	0.352164i
$679$	28442.4	−	23866.0i	1.60754	−	1.34889i
$680$	3985.31	+	3344.07i	0.224750	+	0.188587i
$681$	3482.26	+	19748.9i	0.195948	+	1.11127i
$682$	−1635.77	−	595.372i	−0.0918430	−	0.0334281i
$683$	24554.7			1.37564			0.687819	−	0.725882i	$-0.258568\pi$
$683$	24554.7			1.37564			0.687819	+	0.725882i	$0.258568\pi$
$684$	2633.98	−	1396.93i	0.147241	−	0.0780892i
$685$	4848.74			0.270454
$686$	7421.54	+	2701.22i	0.413055	+	0.150340i
$687$	1627.09	+	9227.67i	0.0903599	+	0.512456i
$688$	6204.64	+	5206.31i	0.343822	+	0.288501i
$689$	−8549.03	+	7173.49i	−0.472703	+	0.396645i
$690$	−188.482	+	1068.93i	−0.0103991	+	0.0589763i
$691$	13740.6	−	23799.5i	0.756467	−	1.31024i	−0.188175	−	0.982136i	$-0.560257\pi$
$691$	13740.6	−	23799.5i	0.756467	−	1.31024i	0.944642	−	0.328104i	$-0.106409\pi$
$692$	−6778.82	−	11741.3i	−0.372387	−	0.644994i
$693$	671.379	−	244.362i	0.0368017	−	0.0133947i
$694$	2222.70	−	808.995i	0.121574	−	0.0442493i
$695$	−1656.66	−	2869.41i	−0.0904181	−	0.156609i
$696$	2890.86	−	5007.11i	0.157439	−	0.272692i
$697$	−2012.11	+	11411.2i	−0.109346	+	0.620131i
$698$	−1875.59	+	1573.80i	−0.101708	+	0.0853429i
$699$	8839.70	+	7417.39i	0.478323	+	0.401361i
$700$	−2212.39	−	12547.1i	−0.119458	−	0.677478i
$701$	15492.5	+	5638.82i	0.834729	+	0.303816i	0.723798	−	0.690012i	$-0.242395\pi$
$701$	15492.5	+	5638.82i	0.834729	+	0.303816i	0.110930	+	0.993828i	$0.464617\pi$
$702$	2195.22			0.118025
$703$	21710.1	−	24060.2i	1.16474	−	1.29082i
$704$	224.673			0.0120279
$705$	−16401.2	−	5969.54i	−0.876176	−	0.318902i
$706$	903.330	+	5123.04i	0.0481548	+	0.273099i
$707$	1010.12	+	847.589i	0.0537332	+	0.0450875i
$708$	1650.75	−	1385.14i	0.0876256	−	0.0735266i
$709$	2360.19	−	13385.3i	0.125020	−	0.709022i	−0.856277	−	0.516518i	$-0.827228\pi$
$709$	2360.19	−	13385.3i	0.125020	−	0.709022i	0.981296	−	0.192504i	$-0.0616609\pi$
$710$	−8381.00	+	14516.3i	−0.443005	+	0.767306i
$711$	3286.34	+	5692.11i	0.173344	+	0.300240i
$712$	−9477.79	+	3449.63i	−0.498870	+	0.181574i
$713$	2584.95	−	940.843i	0.135774	−	0.0494177i
$714$	2705.76	+	4686.52i	0.141822	+	0.245642i
$715$	1163.44	−	2015.14i	0.0608535	−	0.105401i
$716$	26.6701	−	151.253i	0.00139205	−	0.00789470i
$717$	−15476.0	+	12985.9i	−0.806084	+	0.676385i
$718$	3991.32	+	3349.11i	0.207458	+	0.174078i
$719$	−2810.42	−	15938.7i	−0.145773	−	0.826720i	−0.966743	−	0.255749i	$-0.917678\pi$
$719$	−2810.42	−	15938.7i	−0.145773	−	0.826720i	0.820970	−	0.570971i	$-0.193433\pi$
$720$	−2206.32	−	803.034i	−0.114201	−	0.0415657i
$721$	−1030.34			−0.0532204
$722$	3346.90	−	13303.4i	0.172519	−	0.685738i
$723$	4881.15			0.251082
$724$	16965.7	+	6175.00i	0.870890	+	0.316978i
$725$	5892.19	+	33416.3i	0.301835	+	1.71179i
$726$	6060.99	+	5085.77i	0.309841	+	0.259987i
$727$	−3383.05	+	2838.71i	−0.172586	+	0.144817i	−0.724989	−	0.688760i	$-0.758155\pi$
$727$	−3383.05	+	2838.71i	−0.172586	+	0.144817i	0.552403	+	0.833577i	$0.313711\pi$
$728$	−1277.07	+	7242.62i	−0.0650155	+	0.368721i
$729$	−364.500	+	631.333i	−0.0185185	+	0.0320750i
$730$	−6589.28	−	11413.0i	−0.334082	−	0.578648i
$731$	18972.6	−	6905.47i	0.959956	−	0.349395i
$732$	5950.49	−	2165.80i	0.300460	−	0.109358i
$733$	−13497.2	−	23377.8i	−0.680122	−	1.17801i	−0.974943	−	0.222454i	$-0.928593\pi$
$733$	−13497.2	−	23377.8i	−0.680122	−	1.17801i	0.294821	−	0.955552i	$-0.404740\pi$
$734$	4566.24	−	7908.96i	0.229623	−	0.397718i
$735$	1430.17	−	8110.87i	0.0717721	−	0.407040i
$736$	−271.977	+	228.216i	−0.0136212	+	0.0114296i
$737$	−436.382	−	366.168i	−0.0218105	−	0.0183012i
$738$	−908.082	−	5149.99i	−0.0452940	−	0.256875i
$739$	4034.19	+	1468.33i	0.200812	+	0.0730896i	0.440468	−	0.897768i	$-0.354812\pi$
$739$	4034.19	+	1468.33i	0.200812	+	0.0730896i	−0.239656	+	0.970858i	$0.577035\pi$
$740$	−25520.5			−1.26777
$741$	6766.41	−	7498.85i	0.335452	−	0.371764i
$742$	12415.9			0.614288
$743$	−11238.6	−	4090.53i	−0.554920	−	0.201974i	0.0493110	−	0.998783i	$-0.484297\pi$
$743$	−11238.6	−	4090.53i	−0.554920	−	0.201974i	−0.604231	+	0.796809i	$0.706520\pi$
$744$	1033.28	+	5860.02i	0.0509165	+	0.288762i
$745$	−3116.24	−	2614.83i	−0.153249	−	0.128591i
$746$	−7401.69	+	6210.76i	−0.363264	+	0.304815i
$747$	57.8666	−	328.178i	0.00283431	−	0.0160742i
$748$	280.026	−	485.020i	0.0136882	−	0.0237087i
$749$	−10822.1	−	18744.4i	−0.527945	−	0.914427i
$750$	1457.23	−	530.388i	0.0709473	−	0.0258227i
$751$	−25394.2	+	9242.73i	−1.23388	+	0.449097i	−0.874926	−	0.484256i	$-0.839090\pi$
$751$	−25394.2	+	9242.73i	−1.23388	+	0.449097i	−0.358958	+	0.933354i	$0.616868\pi$
$752$	−2854.55	−	4944.23i	−0.138424	−	0.239757i
$753$	6698.19	−	11601.6i	0.324164	−	0.561469i
$754$	3401.18	−	19289.1i	0.164276	−	0.931653i
$755$	−22957.8	+	19263.9i	−1.10665	+	0.928590i
$756$	−1870.88	−	1569.86i	−0.0900045	−	0.0755228i
$757$	−2430.92	−	13786.4i	−0.116715	−	0.661924i	−0.985887	−	0.167413i	$-0.946459\pi$
$757$	−2430.92	−	13786.4i	−0.116715	−	0.661924i	0.869172	−	0.494510i	$-0.164653\pi$
$758$	8293.30	+	3018.52i	0.397396	+	0.144640i
$759$	116.848			0.00558801
$760$	−9543.76	+	5061.53i	−0.455511	+	0.241580i
$761$	17713.5			0.843775			0.421888	−	0.906648i	$-0.361368\pi$
$761$	17713.5			0.843775			0.421888	+	0.906648i	$0.361368\pi$
$762$	−6536.68	−	2379.16i	−0.310760	−	0.113107i
$763$	3810.87	+	21612.5i	0.180816	+	1.02546i
$764$	10086.0	+	8463.16i	0.477616	+	0.400768i
$765$	−4483.48	+	3762.08i	−0.211896	+	0.177802i
$766$	2043.12	−	11587.1i	0.0963721	−	0.546553i
$767$	3650.06	−	6322.09i	0.171833	−	0.297624i
$768$	−384.000	−	665.108i	−0.0180422	−	0.0312500i
$769$	3109.13	−	1131.63i	0.145797	−	0.0530658i	−0.268091	−	0.963394i	$-0.586393\pi$
$769$	3109.13	−	1131.63i	0.145797	−	0.0530658i	0.413888	+	0.910328i	$0.364171\pi$
$770$	−2432.62	+	885.402i	−0.113851	+	0.0414386i
$771$	4807.16	+	8326.25i	0.224547	+	0.388927i
$772$	1034.27	−	1791.41i	0.0482180	−	0.0835161i
$773$	1396.78	−	7921.51i	0.0649917	−	0.368586i	−0.934914	−	0.354874i	$-0.884524\pi$
$773$	1396.78	−	7921.51i	0.0649917	−	0.368586i	0.999906	−	0.0137125i	$-0.00436498\pi$
$774$	−6980.22	+	5857.10i	−0.324159	+	0.272001i
$775$	−26751.8	−	22447.4i	−1.23994	−	1.04043i
$776$	2280.89	+	12935.5i	0.105514	+	0.598401i
$777$	−24945.1	−	9079.29i	−1.15174	−	0.419199i
$778$	−18180.5			−0.837795
$779$	−20391.3	−	12772.0i	−0.937862	−	0.587425i
$780$	−7954.00			−0.365127
$781$	1695.63	+	617.160i	0.0776883	+	0.0282762i
$782$	153.684	+	871.584i	0.00702777	+	0.0398565i
$783$	4982.68	+	4180.96i	0.227416	+	0.190824i
$784$	2063.71	−	1731.66i	0.0940102	−	0.0788840i
$785$	−9136.66	+	51816.6i	−0.415416	+	2.35594i
$786$	−1778.68	+	3080.77i	−0.0807170	+	0.139806i
$787$	−14750.4	−	25548.4i	−0.668099	−	1.15718i	−0.978435	−	0.206554i	$-0.933775\pi$
$787$	−14750.4	−	25548.4i	−0.668099	−	1.15718i	0.310337	−	0.950627i	$-0.399558\pi$
$788$	−6755.83	+	2458.92i	−0.305414	+	0.111162i
$789$	−17870.0	+	6504.14i	−0.806323	+	0.293477i
$790$	−11907.5	−	20624.4i	−0.536265	−	0.928838i
$791$	11896.7	−	20605.7i	0.534763	−	0.926236i
$792$	−43.8907	+	248.917i	−0.00196918	+	0.0111678i
$793$	16433.3	−	13789.2i	0.735893	−	0.617488i
$794$	−4348.43	−	3648.77i	−0.194358	−	0.163085i
$795$	2331.79	+	13224.2i	0.104025	+	0.589956i
$796$	8151.50	+	2966.91i	0.362968	+	0.132110i
$797$	29002.5			1.28898			0.644492	−	0.764611i	$-0.277069\pi$
$797$	29002.5			1.28898			0.644492	+	0.764611i	$0.277069\pi$
$798$	−11129.3	+	1552.09i	−0.493701	+	0.0688514i
$799$	−14231.4			−0.630125
$800$	4235.43	+	1541.57i	0.187181	+	0.0681284i
$801$	−1970.35	−	11174.4i	−0.0869151	−	0.492920i
$802$	17872.5	+	14996.8i	0.786906	+	0.660293i
$803$	−1086.78	+	911.918i	−0.0477605	+	0.0400758i
$804$	−338.138	+	1917.68i	−0.0148324	+	0.0841185i
$805$	2045.45	−	3542.81i	0.0895559	−	0.155115i
$806$	10079.1	+	17457.5i	0.440472	+	0.762921i
$807$	22761.9	−	8284.67i	0.992885	−	0.361380i
$808$	−438.353	+	159.548i	−0.0190857	+	0.00694661i
$809$	437.736	+	758.181i	0.0190235	+	0.0329496i	0.875380	−	0.483435i	$-0.160611\pi$
$809$	437.736	+	758.181i	0.0190235	+	0.0329496i	−0.856357	+	0.516384i	$0.827278\pi$
$810$	1320.70	−	2287.52i	0.0572898	−	0.0992288i
$811$	1093.83	−	6203.40i	0.0473606	−	0.268595i	−0.951927	−	0.306324i	$-0.900901\pi$
$811$	1093.83	−	6203.40i	0.0473606	−	0.268595i	0.999288	+	0.0377282i	$0.0120121\pi$
$812$	−16692.8	+	14006.9i	−0.721430	+	0.605352i
$813$	16713.6	+	14024.4i	0.720998	+	0.604989i
$814$	477.068	+	2705.58i	0.0205420	+	0.116500i
$815$	−29133.8	−	10603.8i	−1.25216	−	0.455749i
$816$	−1914.43			−0.0821306
$817$	−1507.58	+	41897.9i	−0.0645577	+	1.79415i
$818$	11200.1			0.478732
$819$	−7774.68	−	2829.75i	−0.331708	−	0.120732i
$820$	3290.28	+	18660.1i	0.140124	+	0.794681i
$821$	5205.73	+	4368.13i	0.221293	+	0.185687i	0.746693	−	0.665168i	$-0.231640\pi$
$821$	5205.73	+	4368.13i	0.221293	+	0.185687i	−0.525401	+	0.850855i	$0.676085\pi$
$822$	−1366.83	+	1146.91i	−0.0579972	+	0.0486654i
$823$	−7316.60	+	41494.5i	−0.309891	+	1.75748i	0.289646	+	0.957134i	$0.406462\pi$
$823$	−7316.60	+	41494.5i	−0.309891	+	1.75748i	−0.599537	+	0.800347i	$0.704649\pi$
$824$	182.252	−	315.669i	0.00770514	−	0.0133457i
$825$	−741.691	−	1284.65i	−0.0312998	−	0.0542129i
$826$	−7631.86	+	2777.77i	−0.321485	+	0.117011i
$827$	−7978.42	+	2903.91i	−0.335474	+	0.122102i	−0.504264	−	0.863550i	$-0.668236\pi$
$827$	−7978.42	+	2903.91i	−0.335474	+	0.122102i	0.168790	+	0.985652i	$0.446014\pi$
$828$	−199.711	−	345.909i	−0.00838216	−	0.0145183i
$829$	1686.59	−	2921.27i	0.0706608	−	0.122388i	−0.828530	−	0.559944i	$-0.810823\pi$
$829$	1686.59	−	2921.27i	0.0706608	−	0.122388i	0.899191	+	0.437556i	$0.144156\pi$
$830$	−209.670	+	1189.09i	−0.00876836	+	0.0497278i
$831$	−11968.2	+	10042.5i	−0.499605	+	0.419219i
$832$	−1993.05	−	1672.37i	−0.0830488	−	0.0696863i
$833$	−1166.12	−	6613.41i	−0.0485039	−	0.275079i
$834$	1145.72	+	417.009i	0.0475697	+	0.0173140i
$835$	−64879.0			−2.68890
$836$	715.011	+	917.174i	0.0295803	+	0.0379439i
$837$	−6694.23			−0.276447
$838$	7090.03	+	2580.56i	0.292268	+	0.106377i
$839$	−2139.47	−	12133.5i	−0.0880365	−	0.499280i	−0.996660	−	0.0816635i	$-0.973977\pi$
$839$	−2139.47	−	12133.5i	−0.0880365	−	0.499280i	0.908623	−	0.417616i	$-0.137134\pi$
$840$	6778.82	+	5688.11i	0.278442	+	0.233641i
$841$	25774.4	−	21627.3i	1.05680	−	0.886763i
$842$	3774.94	−	21408.7i	0.154505	−	0.876240i
$843$	−2094.72	+	3628.16i	−0.0855824	+	0.148233i
$844$	271.939	+	471.012i	0.0110907	+	0.0192096i
$845$	8341.02	−	3035.88i	0.339574	−	0.123595i
$846$	6035.41	−	2196.71i	0.245274	−	0.0892723i
$847$	−14910.0	−	25824.9i	−0.604857	−	1.04764i
$848$	−2196.18	+	3803.90i	−0.0889354	+	0.154041i
$849$	4313.62	−	24463.8i	0.174374	−	0.988922i
$850$	8606.85	−	7222.01i	0.347309	−	0.291427i
$851$	−3325.77	−	2790.65i	−0.133967	−	0.112412i
$852$	−1071.09	−	6074.48i	−0.0430693	−	0.244258i
$853$	1097.60	+	399.493i	0.0440575	+	0.0160356i	0.363955	−	0.931417i	$-0.381426\pi$
$853$	1097.60	+	399.493i	0.0440575	+	0.0160356i	−0.319897	+	0.947452i	$0.603648\pi$
$854$	−23866.3			−0.956310
$855$	−3743.30	−	11562.4i	−0.149729	−	0.462486i
$856$	7657.05			0.305739
$857$	−11451.3	−	4167.92i	−0.456438	−	0.166130i	0.103561	−	0.994623i	$-0.466976\pi$
$857$	−11451.3	−	4167.92i	−0.456438	−	0.166130i	−0.559999	+	0.828493i	$0.689199\pi$
$858$	148.688	+	843.252i	0.00591623	+	0.0335526i
$859$	18287.8	+	15345.3i	0.726395	+	0.609518i	0.929146	−	0.369713i	$-0.120544\pi$
$859$	18287.8	+	15345.3i	0.726395	+	0.609518i	−0.202751	+	0.979230i	$0.564988\pi$
$860$	25291.6	−	21222.2i	1.00283	−	0.841476i
$861$	−3422.50	+	19410.0i	−0.135469	+	0.768281i
$862$	11218.6	−	19431.2i	0.443279	−	0.767782i
$863$	−15664.1	−	27131.1i	−0.617860	−	1.07017i	−0.989875	−	0.141939i	$-0.954666\pi$
$863$	−15664.1	−	27131.1i	−0.617860	−	1.07017i	0.372015	−	0.928227i	$-0.378667\pi$
$864$	811.894	−	295.505i	0.0319690	−	0.0116358i
$865$	−51931.3	+	18901.5i	−2.04129	+	0.742970i
$866$	4158.80	+	7203.25i	0.163189	+	0.282652i
$867$	4983.40	−	8631.50i	0.195208	−	0.338110i
$868$	3894.36	−	22086.0i	0.152285	−	0.863650i
$869$	−1963.92	+	1647.93i	−0.0766646	+	0.0643292i
$870$	−18053.9	−	15149.0i	−0.703544	−	0.590343i
$871$	1145.51	+	6496.49i	0.0445626	+	0.252727i
$872$	−7295.58	−	2655.37i	−0.283325	−	0.103122i
$873$	−14777.0			−0.572881
$874$	−1797.20	−	383.998i	−0.0695550	−	0.0148615i
$875$	−5844.67			−0.225812
$876$	4557.07	+	1658.64i	0.175764	+	0.0639727i
$877$	−5468.89	−	31015.6i	−0.210571	−	1.19421i	−0.888428	−	0.459016i	$-0.848202\pi$
$877$	−5468.89	−	31015.6i	−0.210571	−	1.19421i	0.677856	−	0.735194i	$-0.262909\pi$
$878$	13091.8	+	10985.3i	0.503219	+	0.422251i
$879$	−11285.0	+	9469.25i	−0.433031	+	0.363356i
$880$	159.030	−	901.906i	0.00609194	−	0.0345491i
$881$	5842.01	−	10118.7i	0.223408	−	0.386953i	−0.732433	−	0.680839i	$-0.761615\pi$
$881$	5842.01	−	10118.7i	0.223408	−	0.386953i	0.955841	+	0.293886i	$0.0949485\pi$
$882$	1515.37	+	2624.69i	0.0578515	+	0.100202i
$883$	−12534.6	+	4562.22i	−0.477715	+	0.173874i	−0.569644	−	0.821891i	$-0.692919\pi$
$883$	−12534.6	+	4562.22i	−0.477715	+	0.173874i	0.0919289	+	0.995766i	$0.470697\pi$
$884$	−6094.38	+	2218.17i	−0.231873	+	0.0843950i
$885$	−4391.94	−	7607.06i	−0.166817	−	0.288936i
$886$	−16686.0	+	28901.0i	−0.632705	+	1.09588i
$887$	−1516.25	+	8599.10i	−0.0573966	+	0.325512i	−0.999964	−	0.00850412i	$-0.997293\pi$
$887$	−1516.25	+	8599.10i	−0.0573966	+	0.325512i	0.942567	+	0.334017i	$0.108404\pi$
$888$	7194.07	−	6036.54i	0.271866	−	0.228123i
$889$	20083.7	+	16852.2i	0.757688	+	0.635776i
$890$	7139.22	+	40488.6i	0.268885	+	1.52492i
$891$	−267.203	−	97.2538i	−0.0100467	−	0.00365671i
$892$	4671.07			0.175335
$893$	11099.2	−	27387.9i	0.415925	−	1.02632i
$894$	1496.95			0.0560018
$895$	−588.300	−	214.124i	−0.0219717	−	0.00799706i
$896$	502.631	+	2850.56i	0.0187408	+	0.106284i
$897$	−1036.55	−	869.766i	−0.0385834	−	0.0323753i
$898$	7530.91	−	6319.19i	0.279855	−	0.234826i
$899$	−10371.8	+	58821.1i	−0.384780	+	2.18220i
$900$	−2535.33	+	4391.32i	−0.0939010	+	0.162641i
$901$	5474.53	+	9482.17i	0.202423	+	0.350607i
$902$	1916.76	−	697.645i	0.0707552	−	0.0257528i
$903$	32271.5	−	11745.9i	1.18929	−	0.432866i
$904$	4208.68	+	7289.66i	0.154844	+	0.268197i
$905$	36797.2	−	63734.6i	1.35158	−	2.34101i
$906$	1915.04	−	10860.8i	0.0702241	−	0.398261i
$907$	−15899.9	+	13341.6i	−0.582079	+	0.488423i	−0.885629	−	0.464393i	$-0.846273\pi$
$907$	−15899.9	+	13341.6i	−0.582079	+	0.488423i	0.303550	+	0.952816i	$0.401828\pi$
$908$	20482.5	+	17186.9i	0.748608	+	0.628157i
$909$	−91.1300	−	516.824i	−0.00332518	−	0.0188580i
$910$	28170.2	+	10253.1i	1.02619	+	0.373502i
$911$	14277.3			0.519239			0.259619	−	0.965711i	$-0.416403\pi$
$911$	14277.3			0.519239			0.259619	+	0.965711i	$0.416403\pi$
$912$	1493.09	−	3684.27i	0.0542117	−	0.133770i
$913$	129.983			0.00471172
$914$	−26790.7	−	9751.02i	−0.969538	−	0.352883i
$915$	−4482.26	−	25420.2i	−0.161944	−	0.918431i
$916$	9570.47	+	8030.58i	0.345215	+	0.289670i
$917$	10270.7	−	8618.16i	0.369868	−	0.310356i
$918$	373.992	−	2121.02i	0.0134462	−	0.0762571i
$919$	13508.7	−	23397.8i	0.484887	−	0.839848i	−0.514963	−	0.857213i	$-0.672194\pi$
$919$	13508.7	−	23397.8i	0.484887	−	0.839848i	0.999849	+	0.0173643i	$0.00552750\pi$
$920$	723.616	+	1253.34i	0.0259314	+	0.0449146i
$921$	17334.6	−	6309.27i	0.620188	−	0.225730i
$922$	−19194.5	+	6986.22i	−0.685614	+	0.249543i
$923$	−10447.9	−	18096.4i	−0.372587	−	0.645340i
$924$	476.311	−	824.995i	0.0169583	−	0.0293727i
$925$	−9570.65	+	54277.8i	−0.340196	+	1.92935i
$926$	−7254.94	+	6087.62i	−0.257465	+	0.216038i
$927$	314.129	+	263.586i	0.0111298	+	0.00933903i
$928$	−1338.64	−	7591.83i	−0.0473526	−	0.268550i
$929$	−33799.5	−	12302.0i	−1.19368	−	0.434463i	−0.332664	−	0.943045i	$-0.607948\pi$
$929$	−33799.5	−	12302.0i	−1.19368	−	0.434463i	−0.861013	+	0.508582i	$0.830170\pi$
$930$	24255.3			0.855230
$931$	13636.8	+	2913.70i	0.480051	+	0.102570i
$932$	15385.9			0.540752
$933$	21452.4	+	7808.02i	0.752753	+	0.273980i
$934$	113.888	+	645.888i	0.00398984	+	0.0226275i
$935$	−1748.81	−	1467.43i	−0.0611681	−	0.0513261i
$936$	2242.18	−	1881.42i	0.0782992	−	0.0657008i
$937$	−4604.51	+	26113.5i	−0.160537	+	0.910448i	0.793011	+	0.609207i	$0.208512\pi$
$937$	−4604.51	+	26113.5i	−0.160537	+	0.910448i	−0.953548	+	0.301241i	$0.902599\pi$
$938$	3669.54	−	6355.84i	0.127734	−	0.221243i
$939$	−10397.1	−	18008.4i	−0.361340	−	0.625859i
$940$	−21868.2	+	7959.38i	−0.758790	+	0.276177i
$941$	−31782.9	+	11568.0i	−1.10106	+	0.400752i	−0.827706	−	0.561163i	$-0.810354\pi$
$941$	−31782.9	+	11568.0i	−1.10106	+	0.400752i	−0.273351	+	0.961914i	$0.588132\pi$
$942$	−9680.98	−	16767.9i	−0.334844	−	0.579967i
$943$	−1611.69	+	2791.53i	−0.0556562	+	0.0963994i
$944$	498.925	−	2829.55i	0.0172019	−	0.0975571i
$945$	−7626.17	+	6399.12i	−0.262518	+	0.220279i
$946$	−2722.68	−	2284.60i	−0.0935750	−	0.0785188i
$947$	1381.11	+	7832.69i	0.0473919	+	0.268773i	0.999291	−	0.0376373i	$-0.0119831\pi$
$947$	1381.11	+	7832.69i	0.0473919	+	0.268773i	−0.951900	+	0.306410i	$0.900872\pi$
$948$	8235.07	+	2997.32i	0.282134	+	0.102688i
$949$	16428.7			0.561958
$950$	7185.96	+	22196.1i	0.245414	+	0.758040i
$951$	1974.40			0.0673231
$952$	6780.22	+	2467.80i	0.230828	+	0.0840145i
$953$	5413.19	+	30699.7i	0.183998	+	1.04351i	0.927236	+	0.374478i	$0.122178\pi$
$953$	5413.19	+	30699.7i	0.183998	+	1.04351i	−0.743237	+	0.669028i	$0.766711\pi$
$954$	−3785.34	−	3176.28i	−0.128464	−	0.107794i
$955$	41113.0	−	34497.9i	1.39307	−	1.16893i
$956$	−4677.50	+	26527.4i	−0.158244	+	0.897447i
$957$	−1268.55	+	2197.19i	−0.0428488	+	0.0742163i
$958$	−5663.86	−	9810.10i	−0.191014	−	0.330845i
$959$	6319.23	−	2300.01i	0.212783	−	0.0774466i
$960$	−2941.76	+	1070.71i	−0.0989008	+	0.0359969i
$961$	−15840.2	−	27436.1i	−0.531712	−	0.920952i
$962$	15907.2	−	27552.1i	0.533128	−	0.923405i
$963$	−1495.84	+	8483.32i	−0.0500547	+	0.283874i
$964$	4985.57	−	4183.39i	0.166571	−	0.139770i
$965$	−6459.20	−	5419.91i	−0.215471	−	0.180801i
$966$	261.409	+	1482.52i	0.00870671	+	0.0493782i
$967$	43436.3	+	15809.5i	1.44448	+	0.525749i	0.941045	−	0.338281i	$-0.109845\pi$
$967$	43436.3	+	15809.5i	1.44448	+	0.525749i	0.503440	+	0.864030i	$0.332068\pi$
$968$	10549.4			0.350280
$969$	−6092.60	−	7815.23i	−0.201984	−	0.259093i
$970$	53541.8			1.77229
$971$	−11257.0	−	4097.21i	−0.372043	−	0.135413i	0.149230	−	0.988803i	$-0.452321\pi$
$971$	−11257.0	−	4097.21i	−0.372043	−	0.135413i	−0.521273	+	0.853390i	$0.674543\pi$
$972$	168.786	+	957.233i	0.00556977	+	0.0315877i
$973$	−3520.19	−	2953.79i	−0.115984	−	0.0973219i
$974$	−14123.2	+	11850.8i	−0.464616	+	0.389859i
$975$	−2982.89	+	16916.8i	−0.0979785	+	0.555664i
$976$	4221.59	−	7312.01i	0.138453	−	0.239807i
$977$	9190.30	+	15918.1i	0.300946	+	0.521253i	0.976350	−	0.216194i	$-0.0693644\pi$
$977$	9190.30	+	15918.1i	0.300946	+	0.521253i	−0.675405	+	0.737447i	$0.736031\pi$
$978$	10720.8	−	3902.06i	0.350526	−	0.127581i
$979$	4158.98	−	1513.75i	0.135773	−	0.0494173i
$980$	−5490.66	−	9510.11i	−0.178972	−	0.309989i
$981$	4367.14	−	7564.10i	0.142132	−	0.246181i
$982$	−7206.57	+	40870.5i	−0.234186	+	1.32814i
$983$	21175.2	−	17768.1i	0.687064	−	0.576515i	−0.230997	−	0.972954i	$-0.574199\pi$
$983$	21175.2	−	17768.1i	0.687064	−	0.576515i	0.918061	+	0.396440i	$0.129754\pi$
$984$	−5341.31	−	4481.89i	−0.173043	−	0.145201i
$985$	5088.89	+	28860.5i	0.164615	+	0.933576i
$986$	−18057.6	−	6572.42i	−0.583236	−	0.212281i
$987$	−24206.9			−0.780662
$988$	484.265	−	13458.4i	0.0155937	−	0.433370i
$989$	5616.57			0.180583
$990$	968.162	+	352.382i	0.0310810	+	0.0113126i
$991$	−492.543	−	2793.35i	−0.0157883	−	0.0895396i	0.975895	−	0.218238i	$-0.0700311\pi$
$991$	−492.543	−	2793.35i	−0.0157883	−	0.0895396i	−0.991684	+	0.128699i	$0.958920\pi$
$992$	6077.72	+	5099.81i	0.194524	+	0.163225i
$993$	−17953.8	+	15065.0i	−0.573763	+	0.481445i
$994$	−4036.88	+	22894.3i	−0.128815	+	0.730546i
$995$	17680.0	−	30622.6i	0.563309	−	0.975680i
$996$	−222.160	−	384.793i	−0.00706769	−	0.0122416i
$997$	−27286.4	+	9931.44i	−0.866769	+	0.315478i	−0.736858	−	0.676047i	$-0.763691\pi$
$997$	−27286.4	+	9931.44i	−0.866769	+	0.315478i	−0.129911	+	0.991526i	$0.541469\pi$
$998$	−9600.16	+	3494.17i	−0.304497	+	0.110828i
$999$	5282.55	+	9149.64i	0.167300	+	0.289772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.i.c.61.3	yes	18
19.5	even	9	inner	114.4.i.c.43.3	✓	18
19.9	even	9		2166.4.a.bk.1.9		9
19.10	odd	18		2166.4.a.bl.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.i.c.43.3	✓	18	19.5	even	9	inner
114.4.i.c.61.3	yes	18	1.1	even	1	trivial
2166.4.a.bk.1.9		9	19.9	even	9
2166.4.a.bl.1.9		9	19.10	odd	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.87939 + 0.684040i) q^{2} +(0.520945 + 2.95442i) q^{3} +(3.06418 + 2.57115i) q^{4} +(12.4903 - 10.4806i) q^{5} +(-1.04189 + 5.90885i) q^{6} +(11.3068 - 19.5839i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-8.45723 + 3.07818i) q^{9} +O(q^{10})\)	\(q+(1.87939 + 0.684040i) q^{2} +(0.520945 + 2.95442i) q^{3} +(3.06418 + 2.57115i) q^{4} +(12.4903 - 10.4806i) q^{5} +(-1.04189 + 5.90885i) q^{6} +(11.3068 - 19.5839i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-8.45723 + 3.07818i) q^{9} +(30.6433 - 11.1532i) q^{10} +(-1.75525 - 3.04019i) q^{11} +(-6.00000 + 10.3923i) q^{12} +(-7.05919 + 40.0347i) q^{13} +(34.6460 - 29.0715i) q^{14} +(37.4710 + 31.4419i) q^{15} +(2.77837 + 15.7569i) q^{16} +(37.4787 + 13.6411i) q^{17} -18.0000 q^{18} +(-55.4820 + 61.4878i) q^{19} +65.2198 q^{20} +(63.7494 + 23.2029i) q^{21} +(-1.21919 - 6.91435i) q^{22} +(8.49929 + 7.13175i) q^{23} +(-18.3851 + 15.4269i) q^{24} +(24.4586 - 138.712i) q^{25} +(-40.6523 + 70.4118i) q^{26} +(-13.5000 - 23.3827i) q^{27} +(84.9993 - 30.9372i) q^{28} +(-226.376 + 82.3942i) q^{29} +(48.9149 + 84.7230i) q^{30} +(123.967 - 214.717i) q^{31} +(-5.55674 + 31.5138i) q^{32} +(8.06762 - 6.76953i) q^{33} +(61.1058 + 51.2739i) q^{34} +(-64.0264 - 363.112i) q^{35} +(-33.8289 - 12.3127i) q^{36} -391.300 q^{37} +(-146.332 + 77.6073i) q^{38} -121.957 q^{39} +(122.573 + 44.6130i) q^{40} +(50.4490 + 286.111i) q^{41} +(103.938 + 87.2144i) q^{42} +(387.790 - 325.394i) q^{43} +(2.43837 - 13.8287i) q^{44} +(-73.3723 + 127.085i) q^{45} +(11.0950 + 19.2172i) q^{46} +(-335.300 + 122.039i) q^{47} +(-45.1052 + 16.4170i) q^{48} +(-84.1871 - 145.816i) q^{49} +(140.852 - 243.962i) q^{50} +(-20.7774 + 117.834i) q^{51} +(-124.566 + 104.523i) q^{52} +(210.297 + 176.460i) q^{53} +(-9.37700 - 53.1796i) q^{54} +(-53.7868 - 19.5768i) q^{55} +180.909 q^{56} +(-210.564 - 131.886i) q^{57} -481.809 q^{58} +(-168.745 - 61.4182i) q^{59} +(33.9759 + 192.687i) q^{60} +(-404.241 - 339.198i) q^{61} +(379.857 - 318.738i) q^{62} +(-35.3413 + 200.430i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(331.417 + 574.030i) q^{65} +(19.7928 - 7.20399i) q^{66} +(152.486 - 55.5002i) q^{67} +(79.7680 + 138.162i) q^{68} +(-16.6426 + 28.8258i) q^{69} +(128.053 - 726.224i) q^{70} +(-393.759 + 330.403i) q^{71} +(-55.1552 - 46.2807i) q^{72} +(-70.1760 - 397.988i) q^{73} +(-735.403 - 267.665i) q^{74} +422.555 q^{75} +(-328.101 + 45.7569i) q^{76} -79.3852 q^{77} +(-229.204 - 83.4233i) q^{78} +(-126.815 - 719.203i) q^{79} +(199.845 + 167.690i) q^{80} +(62.0496 - 52.0658i) q^{81} +(-100.898 + 572.221i) q^{82} +(-18.5134 + 32.0661i) q^{83} +(135.681 + 235.007i) q^{84} +(611.089 - 222.418i) q^{85} +(951.390 - 346.277i) q^{86} +(-361.357 - 625.889i) q^{87} +(14.0420 - 24.3215i) q^{88} +(-218.928 + 1241.60i) q^{89} +(-224.826 + 188.651i) q^{90} +(704.219 + 590.910i) q^{91} +(7.70653 + 43.7059i) q^{92} +(698.946 + 254.396i) q^{93} -713.638 q^{94} +(-48.5577 + 1349.49i) q^{95} -96.0000 q^{96} +(1542.87 + 561.558i) q^{97} +(-58.4757 - 331.632i) q^{98} +(24.2029 + 20.3086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 9 q^{5} - 30 q^{7} + 72 q^{8}+O(q^{10}) \) 18 * q + 9 * q^5 - 30 * q^7 + 72 * q^8	\( 18 q + 9 q^{5} - 30 q^{7} + 72 q^{8} + 18 q^{10} + 57 q^{11} - 108 q^{12} - 228 q^{13} + 6 q^{14} + 27 q^{15} + 27 q^{17} - 324 q^{18} + 105 q^{19} - 24 q^{20} + 45 q^{21} + 222 q^{22} - 576 q^{23} - 243 q^{25} - 186 q^{26} - 243 q^{27} + 60 q^{28} - 339 q^{29} - 18 q^{30} + 429 q^{31} + 288 q^{33} - 450 q^{34} + 1680 q^{35} - 318 q^{37} + 114 q^{38} - 558 q^{39} + 72 q^{40} + 531 q^{41} + 18 q^{42} + 2172 q^{43} - 444 q^{44} + 27 q^{45} - 48 q^{46} - 816 q^{47} - 249 q^{49} + 780 q^{50} - 756 q^{51} + 276 q^{52} - 744 q^{53} + 2862 q^{55} - 480 q^{56} - 171 q^{57} + 900 q^{58} - 2307 q^{59} + 168 q^{61} + 1770 q^{62} - 108 q^{63} - 576 q^{64} + 1209 q^{65} - 90 q^{66} + 1944 q^{67} + 588 q^{68} + 72 q^{69} - 3360 q^{70} - 1011 q^{71} + 4152 q^{73} + 1854 q^{74} + 2340 q^{75} - 276 q^{76} - 7686 q^{77} - 954 q^{78} - 4929 q^{79} + 144 q^{80} - 1062 q^{82} + 156 q^{83} - 360 q^{84} - 2049 q^{85} + 2064 q^{86} + 675 q^{87} - 456 q^{88} - 4785 q^{89} - 162 q^{90} + 5166 q^{91} + 3852 q^{92} + 315 q^{93} + 1368 q^{94} - 1350 q^{95} - 1728 q^{96} + 2247 q^{97} - 2538 q^{98} + 864 q^{99}+O(q^{100}) \) 18 * q + 9 * q^5 - 30 * q^7 + 72 * q^8 + 18 * q^10 + 57 * q^11 - 108 * q^12 - 228 * q^13 + 6 * q^14 + 27 * q^15 + 27 * q^17 - 324 * q^18 + 105 * q^19 - 24 * q^20 + 45 * q^21 + 222 * q^22 - 576 * q^23 - 243 * q^25 - 186 * q^26 - 243 * q^27 + 60 * q^28 - 339 * q^29 - 18 * q^30 + 429 * q^31 + 288 * q^33 - 450 * q^34 + 1680 * q^35 - 318 * q^37 + 114 * q^38 - 558 * q^39 + 72 * q^40 + 531 * q^41 + 18 * q^42 + 2172 * q^43 - 444 * q^44 + 27 * q^45 - 48 * q^46 - 816 * q^47 - 249 * q^49 + 780 * q^50 - 756 * q^51 + 276 * q^52 - 744 * q^53 + 2862 * q^55 - 480 * q^56 - 171 * q^57 + 900 * q^58 - 2307 * q^59 + 168 * q^61 + 1770 * q^62 - 108 * q^63 - 576 * q^64 + 1209 * q^65 - 90 * q^66 + 1944 * q^67 + 588 * q^68 + 72 * q^69 - 3360 * q^70 - 1011 * q^71 + 4152 * q^73 + 1854 * q^74 + 2340 * q^75 - 276 * q^76 - 7686 * q^77 - 954 * q^78 - 4929 * q^79 + 144 * q^80 - 1062 * q^82 + 156 * q^83 - 360 * q^84 - 2049 * q^85 + 2064 * q^86 + 675 * q^87 - 456 * q^88 - 4785 * q^89 - 162 * q^90 + 5166 * q^91 + 3852 * q^92 + 315 * q^93 + 1368 * q^94 - 1350 * q^95 - 1728 * q^96 + 2247 * q^97 - 2538 * q^98 + 864 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more