LMFDB - Embedded newform 114.4.i.c.55.2

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			55.2
Root			$-2.92272 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	114.55
Dual form			114.4.i.c.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.347296 + 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(-1.70026 + 0.618843i) q^{5} +(-4.59627 + 3.85673i) q^{6} +(8.26871 + 14.3218i) q^{7} +(4.00000 - 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +O(q^{10})$	\(q+(-0.347296 + 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(-1.70026 + 0.618843i) q^{5} +(-4.59627 + 3.85673i) q^{6} +(8.26871 + 14.3218i) q^{7} +(4.00000 - 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +(-0.628389 - 3.56377i) q^{10} +(-21.4412 + 37.1373i) q^{11} +(-6.00000 - 10.3923i) q^{12} +(-53.5798 + 44.9588i) q^{13} +(-31.0802 + 11.3123i) q^{14} +(-5.10077 - 1.85653i) q^{15} +(12.2567 + 10.2846i) q^{16} +(11.6356 - 65.9886i) q^{17} -18.0000 q^{18} +(80.9274 + 17.6000i) q^{19} +7.23750 q^{20} +(-8.61508 + 48.8586i) q^{21} +(-65.6997 - 55.1286i) q^{22} +(-91.5870 - 33.3349i) q^{23} +(22.5526 - 8.20848i) q^{24} +(-93.2476 + 78.2441i) q^{25} +(-69.9435 - 121.146i) q^{26} +(-13.5000 + 23.3827i) q^{27} +(-11.4868 - 65.1447i) q^{28} +(-7.92735 - 44.9582i) q^{29} +(5.42813 - 9.40179i) q^{30} +(91.8990 + 159.174i) q^{31} +(-24.5134 + 20.5692i) q^{32} +(-120.889 + 44.0000i) q^{33} +(125.931 + 45.8352i) q^{34} +(-22.9219 - 19.2338i) q^{35} +(6.25133 - 35.4531i) q^{36} +313.863 q^{37} +(-62.7710 + 153.283i) q^{38} -209.831 q^{39} +(-2.51356 + 14.2551i) q^{40} +(24.0251 + 20.1595i) q^{41} +(-93.2406 - 33.9368i) q^{42} +(442.885 - 161.197i) q^{43} +(131.399 - 110.257i) q^{44} +(-8.14219 - 14.1027i) q^{45} +(97.4649 - 168.814i) q^{46} +(52.3506 + 296.895i) q^{47} +(8.33511 + 47.2708i) q^{48} +(34.7568 - 60.2005i) q^{49} +(-121.726 - 210.836i) q^{50} +(153.990 - 129.213i) q^{51} +(262.902 - 95.6884i) q^{52} +(85.6761 + 31.1836i) q^{53} +(-41.3664 - 34.7105i) q^{54} +(13.4734 - 76.4117i) q^{55} +132.299 q^{56} +(152.043 + 196.504i) q^{57} +91.3036 q^{58} +(111.469 - 632.173i) q^{59} +(16.6327 + 13.9565i) q^{60} +(224.482 + 81.7047i) q^{61} +(-345.427 + 125.725i) q^{62} +(-114.016 + 95.6705i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(63.2770 - 109.599i) q^{65} +(-44.6788 - 253.386i) q^{66} +(80.3728 + 455.817i) q^{67} +(-134.013 + 232.118i) q^{68} +(-146.197 - 253.221i) q^{69} +(45.8438 - 38.4675i) q^{70} +(596.270 - 217.025i) q^{71} +(67.6579 + 24.6255i) q^{72} +(524.338 + 439.972i) q^{73} +(-109.003 + 618.189i) q^{74} -365.178 q^{75} +(-280.109 - 176.870i) q^{76} -709.165 q^{77} +(72.8734 - 413.285i) q^{78} +(-746.628 - 626.495i) q^{79} +(-27.2041 - 9.90148i) q^{80} +(-76.1151 + 27.7036i) q^{81} +(-48.0503 + 40.3190i) q^{82} +(-247.560 - 428.787i) q^{83} +(99.2246 - 171.862i) q^{84} +(21.0531 + 119.398i) q^{85} +(163.684 + 928.296i) q^{86} +(68.4777 - 118.607i) q^{87} +(171.530 + 297.098i) q^{88} +(-898.776 + 754.163i) q^{89} +(30.6046 - 11.1392i) q^{90} +(-1086.93 - 395.610i) q^{91} +(298.650 + 250.597i) q^{92} +(-95.7485 + 543.017i) q^{93} -602.950 q^{94} +(-148.489 + 20.1568i) q^{95} -96.0000 q^{96} +(-71.4232 + 405.061i) q^{97} +(106.501 + 89.3649i) q^{98} +(-362.667 - 132.000i) 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 $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.347296	+	1.96962i	−0.122788	+	0.696364i
$2$	−0.347296	+	1.96962i	−0.122788	+	0.696364i
$3$	2.29813	+	1.92836i	0.442276	+	0.371114i
$3$	2.29813	+	1.92836i	0.442276	+	0.371114i
$4$	−3.75877	−	1.36808i	−0.469846	−	0.171010i
$5$	−1.70026	+	0.618843i	−0.152076	+	0.0553510i	−0.416936	−	0.908936i	$-0.636896\pi$
$5$	−1.70026	+	0.618843i	−0.152076	+	0.0553510i	0.264861	+	0.964287i	$0.414674\pi$
$6$	−4.59627	+	3.85673i	−0.312736	+	0.262417i
$7$	8.26871	+	14.3218i	0.446469	+	0.773306i	0.998153	−	0.0607466i	$-0.0193481\pi$
$7$	8.26871	+	14.3218i	0.446469	+	0.773306i	−0.551685	+	0.834053i	$0.686015\pi$
$8$	4.00000	−	6.92820i	0.176777	−	0.306186i
$9$	1.56283	+	8.86327i	0.0578827	+	0.328269i
$10$	−0.628389	−	3.56377i	−0.0198714	−	0.112696i
$11$	−21.4412	+	37.1373i	−0.587707	+	1.01794i	0.406825	+	0.913506i	$0.366636\pi$
$11$	−21.4412	+	37.1373i	−0.587707	+	1.01794i	−0.994532	+	0.104432i	$0.966698\pi$
$12$	−6.00000	−	10.3923i	−0.144338	−	0.250000i
$13$	−53.5798	+	44.9588i	−1.14311	+	0.959179i	−0.999536	−	0.0304608i	$-0.990303\pi$
$13$	−53.5798	+	44.9588i	−1.14311	+	0.959179i	−0.143570	+	0.989640i	$0.545858\pi$
$14$	−31.0802	+	11.3123i	−0.593324	+	0.215952i
$15$	−5.10077	−	1.85653i	−0.0878009	−	0.0319569i
$16$	12.2567	+	10.2846i	0.191511	+	0.160697i
$17$	11.6356	−	65.9886i	0.166002	−	0.941446i	−0.782023	−	0.623250i	$-0.785812\pi$
$17$	11.6356	−	65.9886i	0.166002	−	0.941446i	0.948025	−	0.318196i	$-0.103077\pi$
$18$	−18.0000			−0.235702
$19$	80.9274	+	17.6000i	0.977159	+	0.212511i
$19$	80.9274	+	17.6000i	0.977159	+	0.212511i
$20$	7.23750			0.0809177
$21$	−8.61508	+	48.8586i	−0.0895221	+	0.507705i
$22$	−65.6997	−	55.1286i	−0.636692	−	0.534248i
$23$	−91.5870	−	33.3349i	−0.830314	−	0.302209i	−0.108326	−	0.994115i	$-0.534549\pi$
$23$	−91.5870	−	33.3349i	−0.830314	−	0.302209i	−0.721988	+	0.691906i	$0.756771\pi$
$24$	22.5526	−	8.20848i	0.191814	−	0.0698146i
$25$	−93.2476	+	78.2441i	−0.745981	+	0.625953i
$26$	−69.9435	−	121.146i	−0.527579	−	0.913793i
$27$	−13.5000	+	23.3827i	−0.0962250	+	0.166667i
$28$	−11.4868	−	65.1447i	−0.0775284	−	0.439686i
$29$	−7.92735	−	44.9582i	−0.0507611	−	0.287881i	0.948851	−	0.315724i	$-0.102247\pi$
$29$	−7.92735	−	44.9582i	−0.0507611	−	0.287881i	−0.999612	+	0.0278431i	$0.991136\pi$
$30$	5.42813	−	9.40179i	0.0330345	−	0.0572175i
$31$	91.8990	+	159.174i	0.532437	+	0.922207i	0.999283	+	0.0378688i	$0.0120569\pi$
$31$	91.8990	+	159.174i	0.532437	+	0.922207i	−0.466846	+	0.884339i	$0.654610\pi$
$32$	−24.5134	+	20.5692i	−0.135419	+	0.113630i
$33$	−120.889	+	44.0000i	−0.637699	+	0.232103i
$34$	125.931	+	45.8352i	0.635206	+	0.231196i
$35$	−22.9219	−	19.2338i	−0.110700	−	0.0928885i
$36$	6.25133	−	35.4531i	0.0289414	−	0.164135i
$37$	313.863			1.39456			0.697280	−	0.716798i	$-0.254393\pi$
$37$	313.863			1.39456			0.697280	+	0.716798i	$0.254393\pi$
$38$	−62.7710	+	153.283i	−0.267969	+	0.654364i
$39$	−209.831			−0.861533
$40$	−2.51356	+	14.2551i	−0.00993571	+	0.0563482i
$41$	24.0251	+	20.1595i	0.0915145	+	0.0767898i	0.687397	−	0.726282i	$-0.258753\pi$
$41$	24.0251	+	20.1595i	0.0915145	+	0.0767898i	−0.595883	+	0.803072i	$0.703198\pi$
$42$	−93.2406	−	33.9368i	−0.342556	−	0.124680i
$43$	442.885	−	161.197i	1.57068	−	0.571682i	0.597531	−	0.801846i	$-0.296149\pi$
$43$	442.885	−	161.197i	1.57068	−	0.571682i	0.973152	+	0.230165i	$0.0739264\pi$
$44$	131.399	−	110.257i	0.450209	−	0.377771i
$45$	−8.14219	−	14.1027i	−0.0269726	−	0.0467179i
$46$	97.4649	−	168.814i	0.312400	−	0.541093i
$47$	52.3506	+	296.895i	0.162471	+	0.921417i	0.951634	+	0.307233i	$0.0994033\pi$
$47$	52.3506	+	296.895i	0.162471	+	0.921417i	−0.789164	+	0.614183i	$0.789486\pi$
$48$	8.33511	+	47.2708i	0.0250640	+	0.142145i
$49$	34.7568	−	60.2005i	0.101332	−	0.175512i
$50$	−121.726	−	210.836i	−0.344294	−	0.596334i
$51$	153.990	−	129.213i	0.422802	−	0.354773i
$52$	262.902	−	95.6884i	0.701113	−	0.255184i
$53$	85.6761	+	31.1836i	0.222048	+	0.0808187i	0.450648	−	0.892702i	$-0.351193\pi$
$53$	85.6761	+	31.1836i	0.222048	+	0.0808187i	−0.228601	+	0.973520i	$0.573415\pi$
$54$	−41.3664	−	34.7105i	−0.104245	−	0.0874723i
$55$	13.4734	−	76.4117i	0.0330320	−	0.187334i
$56$	132.299			0.315701
$57$	152.043	+	196.504i	0.353308	+	0.456626i
$58$	91.3036			0.206703
$59$	111.469	−	632.173i	0.245967	−	1.39495i	−0.572269	−	0.820066i	$-0.693937\pi$
$59$	111.469	−	632.173i	0.245967	−	1.39495i	0.818236	−	0.574882i	$-0.194952\pi$
$60$	16.6327	+	13.9565i	0.0357880	+	0.0300297i
$61$	224.482	+	81.7047i	0.471180	+	0.171495i	0.566687	−	0.823933i	$-0.308225\pi$
$61$	224.482	+	81.7047i	0.471180	+	0.171495i	−0.0955070	+	0.995429i	$0.530447\pi$
$62$	−345.427	+	125.725i	−0.707569	+	0.257534i
$63$	−114.016	+	95.6705i	−0.228010	+	0.191323i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	63.2770	−	109.599i	0.120747	−	0.209140i
$66$	−44.6788	−	253.386i	−0.0833269	−	0.472570i
$67$	80.3728	+	455.817i	0.146554	+	0.831148i	0.966107	+	0.258144i	$0.0831108\pi$
$67$	80.3728	+	455.817i	0.146554	+	0.831148i	−0.819553	+	0.573004i	$0.805778\pi$
$68$	−134.013	+	232.118i	−0.238992	+	0.413947i
$69$	−146.197	−	253.221i	−0.255074	−	0.441801i
$70$	45.8438	−	38.4675i	0.0782769	−	0.0656821i
$71$	596.270	−	217.025i	0.996679	−	0.362762i	0.208376	−	0.978049i	$-0.433182\pi$
$71$	596.270	−	217.025i	0.996679	−	0.362762i	0.788303	+	0.615287i	$0.210960\pi$
$72$	67.6579	+	24.6255i	0.110744	+	0.0403075i
$73$	524.338	+	439.972i	0.840674	+	0.705409i	0.957715	−	0.287718i	$-0.0928966\pi$
$73$	524.338	+	439.972i	0.840674	+	0.705409i	−0.117042	+	0.993127i	$0.537341\pi$
$74$	−109.003	+	618.189i	−0.171235	+	0.971122i
$75$	−365.178			−0.562229
$76$	−280.109	−	176.870i	−0.422773	−	0.266952i
$77$	−709.165			−1.04957
$78$	72.8734	−	413.285i	0.105786	−	0.599941i
$79$	−746.628	−	626.495i	−1.06332	−	0.892231i	−0.0688889	−	0.997624i	$-0.521945\pi$
$79$	−746.628	−	626.495i	−1.06332	−	0.892231i	−0.994431	+	0.105393i	$0.966390\pi$
$80$	−27.2041	−	9.90148i	−0.0380189	−	0.0138377i
$81$	−76.1151	+	27.7036i	−0.104410	+	0.0380022i
$82$	−48.0503	+	40.3190i	−0.0647105	+	0.0542986i
$83$	−247.560	−	428.787i	−0.327389	−	0.567054i	0.654604	−	0.755972i	$-0.272835\pi$
$83$	−247.560	−	428.787i	−0.327389	−	0.567054i	−0.981993	+	0.188918i	$0.939502\pi$
$84$	99.2246	−	171.862i	0.128884	−	0.223234i
$85$	21.0531	+	119.398i	0.0268651	+	0.152359i
$86$	163.684	+	928.296i	0.205238	+	1.16396i
$87$	68.4777	−	118.607i	0.0843860	−	0.146161i
$88$	171.530	+	297.098i	0.207786	+	0.359895i
$89$	−898.776	+	754.163i	−1.07045	+	0.898215i	−0.995093	−	0.0989421i	$-0.968454\pi$
$89$	−898.776	+	754.163i	−1.07045	+	0.898215i	−0.0753572	+	0.997157i	$0.524010\pi$
$90$	30.6046	−	11.1392i	0.0358446	−	0.0130464i
$91$	−1086.93	−	395.610i	−1.25210	−	0.455727i
$92$	298.650	+	250.597i	0.338439	+	0.283984i
$93$	−95.7485	+	543.017i	−0.106760	+	0.605465i
$94$	−602.950			−0.661591
$95$	−148.489	+	20.1568i	−0.160365	+	0.0217689i
$96$	−96.0000			−0.102062
$97$	−71.4232	+	405.061i	−0.0747621	+	0.423997i	0.924338	+	0.381575i	$0.124618\pi$
$97$	−71.4232	+	405.061i	−0.0747621	+	0.423997i	−0.999100	+	0.0424215i	$0.986493\pi$
$98$	106.501	+	89.3649i	0.109778	+	0.0921145i
$99$	−362.667	−	132.000i	−0.368176	−	0.134005i
$100$	457.541	−	166.531i	0.457541	−	0.166531i
$101$	440.606	−	369.712i	0.434078	−	0.364235i	−0.399410	−	0.916773i	$-0.630785\pi$
$101$	440.606	−	369.712i	0.434078	−	0.364235i	0.833488	+	0.552538i	$0.186340\pi$
$102$	201.020	+	348.176i	0.195136	+	0.337986i
$103$	613.098	−	1061.92i	0.586508	−	1.01586i	−0.408177	−	0.912903i	$-0.633836\pi$
$103$	613.098	−	1061.92i	0.586508	−	1.01586i	0.994686	−	0.102959i	$-0.0328311\pi$
$104$	97.1645	+	551.047i	0.0916131	+	0.519564i
$105$	−15.5879	−	88.4035i	−0.0144879	−	0.0821647i
$106$	−91.1746	+	157.919i	−0.0835440	+	0.144702i
$107$	−261.323	−	452.624i	−0.236103	−	0.408943i	0.723490	−	0.690335i	$-0.242537\pi$
$107$	−261.323	−	452.624i	−0.236103	−	0.408943i	−0.959593	+	0.281393i	$0.909204\pi$
$108$	82.7328	−	69.4211i	0.0737127	−	0.0618523i
$109$	−959.386	+	349.188i	−0.843051	+	0.306845i	−0.727204	−	0.686422i	$-0.759180\pi$
$109$	−959.386	+	349.188i	−0.843051	+	0.306845i	−0.115847	+	0.993267i	$0.536958\pi$
$110$	145.822	+	53.0750i	0.126397	+	0.0460046i
$111$	721.299	+	605.242i	0.616781	+	0.517540i
$112$	−45.9471	+	260.579i	−0.0387642	+	0.219843i
$113$	−889.874			−0.740817			−0.370409	−	0.928869i	$-0.620782\pi$
$113$	−889.874			−0.740817			−0.370409	+	0.928869i	$0.620782\pi$
$114$	−439.842	+	231.220i	−0.361360	+	0.189963i
$115$	176.350			0.142998
$116$	−31.7094	+	179.833i	−0.0253806	+	0.143940i
$117$	−482.219	−	404.629i	−0.381035	−	0.319726i
$118$	1206.43	+	439.103i	0.941190	+	0.342565i
$119$	1041.29	−	378.998i	0.802141	−	0.291955i
$120$	−33.2655	+	27.9131i	−0.0253059	+	0.0212342i
$121$	−253.952	−	439.859i	−0.190798	−	0.330472i
$122$	−238.889	+	413.767i	−0.177278	+	0.307055i
$123$	16.3382	+	92.6583i	0.0119769	+	0.0679246i
$124$	−127.665	−	724.022i	−0.0924567	−	0.524348i
$125$	223.210	−	386.611i	0.159716	−	0.276636i
$126$	−148.837	−	257.793i	−0.105234	−	0.182270i
$127$	−1075.84	+	902.737i	−0.751696	+	0.630748i	−0.935951	−	0.352131i	$-0.885457\pi$
$127$	−1075.84	+	902.737i	−0.751696	+	0.630748i	0.184255	+	0.982878i	$0.441013\pi$
$128$	120.281	−	43.7786i	0.0830579	−	0.0302306i
$129$	1328.66	+	483.591i	0.906834	+	0.330061i
$130$	193.892	+	162.695i	0.130811	+	0.109764i
$131$	233.490	−	1324.19i	0.155726	−	0.883166i	−0.802393	−	0.596796i	$-0.796440\pi$
$131$	233.490	−	1324.19i	0.155726	−	0.883166i	0.958119	−	0.286370i	$-0.0924486\pi$
$132$	514.589			0.339313
$133$	417.101	+	1304.56i	0.271934	+	0.850522i
$134$	−925.697			−0.596776
$135$	8.48326	−	48.1109i	0.00540832	−	0.0306721i
$136$	−410.640	−	344.568i	−0.258912	−	0.217253i
$137$	1703.49	+	620.021i	1.06233	+	0.386657i	0.813304	−	0.581840i	$-0.197667\pi$
$137$	1703.49	+	620.021i	1.06233	+	0.386657i	0.249028	+	0.968496i	$0.419889\pi$
$138$	549.522	−	200.010i	0.338974	−	0.123376i
$139$	−1138.40	+	955.232i	−0.694662	+	0.582890i	−0.920249	−	0.391333i	$-0.872014\pi$
$139$	−1138.40	+	955.232i	−0.694662	+	0.582890i	0.225588	+	0.974223i	$0.427570\pi$
$140$	59.8448	+	103.654i	0.0361272	+	0.0625742i
$141$	−452.213	+	783.255i	−0.270093	+	0.467815i
$142$	220.373	+	1249.79i	0.130234	+	0.738595i
$143$	−520.832	−	2953.78i	−0.304574	−	1.72733i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	41.3006	+	71.5348i	0.0236540	+	0.0409699i
$146$	−1048.68	+	879.944i	−0.594446	+	0.498799i
$147$	195.964	−	71.3251i	0.109951	−	0.0400190i
$148$	−1179.74	−	429.390i	−0.655229	−	0.238484i
$149$	2483.05	+	2083.53i	1.36523	+	1.14557i	0.974328	+	0.225134i	$0.0722819\pi$
$149$	2483.05	+	2083.53i	1.36523	+	1.14557i	0.390904	+	0.920432i	$0.372163\pi$
$150$	126.825	−	719.261i	0.0690349	−	0.391516i
$151$	−1397.07			−0.752924			−0.376462	−	0.926432i	$-0.622860\pi$
$151$	−1397.07			−0.752924			−0.376462	+	0.926432i	$0.622860\pi$
$152$	445.646	−	490.281i	0.237807	−	0.261625i
$153$	603.059			0.318656
$154$	246.291	−	1396.78i	0.128874	−	0.730883i
$155$	−254.755	−	213.765i	−0.132016	−	0.110774i
$156$	788.705	+	287.065i	0.404788	+	0.147331i
$157$	−1152.86	+	419.606i	−0.586039	+	0.213301i	−0.617986	−	0.786189i	$-0.712051\pi$
$157$	−1152.86	+	419.606i	−0.586039	+	0.213301i	0.0319475	+	0.999490i	$0.489829\pi$
$158$	1493.26	−	1252.99i	0.751880	−	0.630903i
$159$	136.762	+	236.879i	0.0682134	+	0.118149i
$160$	28.9500	−	50.1429i	0.0143044	−	0.0247759i
$161$	−279.889	−	1587.33i	−0.137008	−	0.777014i
$162$	−28.1310	−	159.539i	−0.0136431	−	0.0773738i
$163$	1644.41	−	2848.21i	0.790186	−	1.36864i	−0.135665	−	0.990755i	$-0.543317\pi$
$163$	1644.41	−	2848.21i	0.790186	−	1.36864i	0.925851	−	0.377888i	$-0.123350\pi$
$164$	−62.7252	−	108.643i	−0.0298659	−	0.0517293i
$165$	178.313	−	149.623i	0.0841313	−	0.0705945i
$166$	930.523	−	338.683i	0.435076	−	0.158355i
$167$	2270.09	+	826.247i	1.05189	+	0.382856i	0.809375	−	0.587293i	$-0.199806\pi$
$167$	2270.09	+	826.247i	1.05189	+	0.382856i	0.242512	+	0.970148i	$0.422028\pi$
$168$	304.042	+	255.121i	0.139627	+	0.117161i
$169$	467.998	−	2654.15i	0.213017	−	1.20808i
$170$	−242.480			−0.109396
$171$	−29.5175	+	744.787i	−0.0132004	+	0.333072i
$172$	−1885.23			−0.835743
$173$	−304.600	+	1727.47i	−0.133863	+	0.759176i	0.841781	+	0.539819i	$0.181507\pi$
$173$	−304.600	+	1727.47i	−0.133863	+	0.759176i	−0.975645	+	0.219357i	$0.929604\pi$
$174$	209.828	+	176.066i	0.0914196	+	0.0767101i
$175$	−1891.64	−	688.499i	−0.817110	−	0.297404i
$176$	−644.741	+	234.667i	−0.276132	+	0.100504i
$177$	1475.23	−	1237.87i	0.626470	−	0.525670i
$178$	−1173.27	−	2032.16i	−0.494046	−	0.855713i
$179$	2212.57	−	3832.29i	0.923885	−	1.60022i	0.130540	−	0.991443i	$-0.458329\pi$
$179$	2212.57	−	3832.29i	0.923885	−	1.60022i	0.793345	−	0.608773i	$-0.208338\pi$
$180$	11.3110	+	64.1479i	0.00468374	+	0.0265628i
$181$	374.909	+	2126.21i	0.153960	+	0.873151i	0.959730	+	0.280923i	$0.0906404\pi$
$181$	374.909	+	2126.21i	0.153960	+	0.873151i	−0.805770	+	0.592228i	$0.798248\pi$
$182$	1156.69	−	2003.44i	0.471095	−	0.815960i
$183$	358.333	+	620.651i	0.144747	+	0.250709i
$184$	−597.299	+	501.194i	−0.239312	+	0.200807i
$185$	−533.648	+	194.232i	−0.212079	+	0.0771903i
$186$	−1036.28	−	377.176i	−0.408515	−	0.148687i
$187$	2201.16	+	1846.99i	0.860773	+	0.722274i
$188$	209.402	−	1187.58i	0.0812353	−	0.460708i
$189$	−446.510			−0.171846
$190$	11.8685	−	299.466i	0.00453175	−	0.114345i
$191$	−2689.49			−1.01887			−0.509436	−	0.860508i	$-0.670146\pi$
$191$	−2689.49			−1.01887			−0.509436	+	0.860508i	$0.670146\pi$
$192$	33.3405	−	189.083i	0.0125320	−	0.0710724i
$193$	−54.3505	−	45.6055i	−0.0202707	−	0.0170091i	0.632596	−	0.774482i	$-0.281989\pi$
$193$	−54.3505	−	45.6055i	−0.0202707	−	0.0170091i	−0.652867	+	0.757473i	$0.726434\pi$
$194$	−773.009	−	281.352i	−0.286076	−	0.104123i
$195$	356.766	−	129.852i	0.131018	−	0.0476867i
$196$	−213.002	+	178.730i	−0.0776246	+	0.0651348i
$197$	1277.47	+	2212.64i	0.462009	+	0.800222i	0.999061	−	0.0433265i	$-0.0137956\pi$
$197$	1277.47	+	2212.64i	0.462009	+	0.800222i	−0.537052	+	0.843549i	$0.680462\pi$
$198$	385.942	−	668.471i	0.138524	−	0.239930i
$199$	345.291	+	1958.24i	0.123000	+	0.697569i	0.982476	+	0.186392i	$0.0596794\pi$
$199$	345.291	+	1958.24i	0.123000	+	0.697569i	−0.859475	+	0.511177i	$0.829210\pi$
$200$	169.100	+	959.015i	0.0597860	+	0.339063i
$201$	−694.273	+	1202.52i	−0.243633	+	0.421985i
$202$	575.170	+	996.224i	0.200341	+	0.347000i
$203$	578.335	−	485.281i	0.199957	−	0.167783i
$204$	−755.587	+	275.011i	−0.259322	+	0.0943854i
$205$	−53.3244	−	19.4085i	−0.0181675	−	0.00661243i
$206$	1878.64	+	1576.37i	0.635394	+	0.533159i
$207$	152.321	−	863.857i	0.0511452	−	0.290059i
$208$	−1119.10			−0.373055
$209$	−2388.80	+	2628.06i	−0.790606	+	0.869792i
$210$	179.534			0.0589955
$211$	226.860	−	1286.59i	0.0740174	−	0.419773i	−0.925173	−	0.379545i	$-0.876080\pi$
$211$	226.860	−	1286.59i	0.0740174	−	0.419773i	0.999191	−	0.0402281i	$-0.0128085\pi$
$212$	−279.375	−	234.424i	−0.0905074	−	0.0759447i
$213$	1788.81	+	651.074i	0.575433	+	0.209441i
$214$	982.253	−	357.511i	0.313764	−	0.114201i
$215$	−653.263	+	548.152i	−0.207219	+	0.173878i
$216$	108.000	+	187.061i	0.0340207	+	0.0589256i
$217$	−1519.77	+	2632.32i	−0.475432	+	0.823473i
$218$	−354.575	−	2010.89i	−0.110160	−	0.624747i
$219$	356.574	+	2022.23i	0.110023	+	0.623971i
$220$	−155.181	+	268.781i	−0.0475559	+	0.0823692i
$221$	2343.34	+	4058.78i	0.713258	+	1.23540i
$222$	−1442.60	+	1210.48i	−0.436130	+	0.365956i
$223$	1651.33	−	601.034i	0.495879	−	0.180485i	−0.0819603	−	0.996636i	$-0.526118\pi$
$223$	1651.33	−	601.034i	0.495879	−	0.180485i	0.577840	+	0.816150i	$0.303896\pi$
$224$	−497.283	−	180.996i	−0.148331	−	0.0539880i
$225$	−839.229	−	704.197i	−0.248660	−	0.208651i
$226$	309.050	−	1752.71i	0.0909633	−	0.515879i
$227$	−2527.35			−0.738970			−0.369485	−	0.929237i	$-0.620466\pi$
$227$	−2527.35			−0.738970			−0.369485	+	0.929237i	$0.620466\pi$
$228$	−302.660	−	946.622i	−0.0879128	−	0.274963i
$229$	−3324.12			−0.959233			−0.479616	−	0.877478i	$-0.659224\pi$
$229$	−3324.12			−0.959233			−0.479616	+	0.877478i	$0.659224\pi$
$230$	−61.2459	+	347.343i	−0.0175584	+	0.0995787i
$231$	−1629.76	−	1367.53i	−0.464200	−	0.389510i
$232$	−343.189	−	124.911i	−0.0971184	−	0.0353482i
$233$	−532.044	+	193.648i	−0.149594	+	0.0544477i	−0.415732	−	0.909487i	$-0.636475\pi$
$233$	−532.044	+	193.648i	−0.149594	+	0.0544477i	0.266138	+	0.963935i	$0.414252\pi$
$234$	964.437	−	809.259i	0.269433	−	0.226081i
$235$	−272.741	−	472.401i	−0.0757091	−	0.131132i
$236$	−1283.85	+	2223.70i	−0.354117	+	0.613348i
$237$	−507.741	−	2879.54i	−0.139162	−	0.789225i
$238$	384.845	+	2182.56i	0.104814	+	0.594431i
$239$	−3066.87	+	5311.97i	−0.830038	+	1.43767i	0.0679695	+	0.997687i	$0.478348\pi$
$239$	−3066.87	+	5311.97i	−0.830038	+	1.43767i	−0.898007	+	0.439980i	$0.854985\pi$
$240$	−43.4250	−	75.2143i	−0.0116795	−	0.0202294i
$241$	852.232	−	715.107i	0.227789	−	0.191137i	−0.521749	−	0.853099i	$-0.674720\pi$
$241$	852.232	−	715.107i	0.227789	−	0.191137i	0.749538	+	0.661962i	$0.230276\pi$
$242$	954.549	−	347.427i	0.253557	−	0.0922871i
$243$	−228.345	−	83.1109i	−0.0602813	−	0.0219406i
$244$	−731.997	−	614.219i	−0.192055	−	0.161153i
$245$	−21.8408	+	123.865i	−0.00569533	+	0.0322998i
$246$	−188.175			−0.0487708
$247$	−5127.35	+	2695.39i	−1.32083	+	0.694347i
$248$	1470.38			0.376490
$249$	257.930	−	1462.80i	0.0656453	−	0.372293i
$250$	683.955	+	573.907i	0.173029	+	0.145188i
$251$	372.707	+	135.654i	0.0937254	+	0.0341133i	0.388457	−	0.921467i	$-0.373008\pi$
$251$	372.707	+	135.654i	0.0937254	+	0.0341133i	−0.294732	+	0.955580i	$0.595230\pi$
$252$	559.443	−	203.621i	0.139848	−	0.0509004i
$253$	3201.71	−	2686.55i	0.795611	−	0.667597i
$254$	−1404.41	−	2432.51i	−0.346931	−	0.600902i
$255$	−181.860	+	314.991i	−0.0446609	+	0.0773549i
$256$	44.4539	+	252.111i	0.0108530	+	0.0615505i
$257$	539.277	+	3058.39i	0.130892	+	0.742324i	0.977633	+	0.210319i	$0.0674502\pi$
$257$	539.277	+	3058.39i	0.130892	+	0.742324i	−0.846741	+	0.532005i	$0.821439\pi$
$258$	−1413.93	+	2448.99i	−0.341190	+	0.590959i
$259$	2595.24	+	4495.09i	0.622627	+	1.07842i
$260$	−387.784	+	325.389i	−0.0924975	+	0.0776146i
$261$	386.088	−	140.524i	0.0915641	−	0.0333266i
$262$	2527.05	+	919.770i	0.595884	+	0.216884i
$263$	4384.02	+	3678.63i	1.02787	+	0.862487i	0.990596	−	0.136818i	$-0.0436875\pi$
$263$	4384.02	+	3678.63i	1.02787	+	0.862487i	0.0372760	+	0.999305i	$0.488132\pi$
$264$	−178.715	+	1013.54i	−0.0416634	+	0.236285i
$265$	−164.969			−0.0382414
$266$	−2714.33	+	368.460i	−0.625664	+	0.0849314i
$267$	−3519.81			−0.806774
$268$	321.491	−	1823.27i	0.0732769	−	0.415574i
$269$	−5915.83	−	4963.97i	−1.34087	−	1.12512i	−0.981401	−	0.191968i	$-0.938513\pi$
$269$	−5915.83	−	4963.97i	−1.34087	−	1.12512i	−0.359470	−	0.933157i	$-0.617043\pi$
$270$	91.8139	+	33.4175i	0.0206949	+	0.00753231i
$271$	3119.39	−	1135.36i	0.699223	−	0.254496i	0.0321436	−	0.999483i	$-0.489767\pi$
$271$	3119.39	−	1135.36i	0.699223	−	0.254496i	0.667079	+	0.744987i	$0.267544\pi$
$272$	821.280	−	689.136i	0.183079	−	0.153621i
$273$	−1735.03	−	3005.16i	−0.384647	−	0.666229i
$274$	−1812.82	+	3139.90i	−0.399695	+	0.692293i
$275$	−906.429	−	5140.61i	−0.198763	−	1.12724i
$276$	203.095	+	1151.81i	0.0442931	+	0.251199i
$277$	3645.50	−	6314.19i	0.790747	−	1.36961i	−0.134758	−	0.990878i	$-0.543026\pi$
$277$	3645.50	−	6314.19i	0.790747	−	1.36961i	0.925505	−	0.378735i	$-0.123641\pi$
$278$	−1486.08	−	2573.96i	−0.320608	−	0.555309i
$279$	−1267.18	+	1063.29i	−0.271913	+	0.228162i
$280$	−224.943	+	81.8725i	−0.0480104	+	0.0174744i
$281$	−7762.76	−	2825.41i	−1.64800	−	0.599822i	−0.659587	−	0.751628i	$-0.729269\pi$
$281$	−7762.76	−	2825.41i	−1.64800	−	0.599822i	−0.988410	+	0.151806i	$0.951491\pi$
$282$	−1385.66	−	1162.71i	−0.292606	−	0.245525i
$283$	1194.69	−	6775.44i	0.250944	−	1.42317i	−0.555330	−	0.831630i	$-0.687408\pi$
$283$	1194.69	−	6775.44i	0.250944	−	1.42317i	0.806273	−	0.591543i	$-0.201481\pi$
$284$	−2538.15			−0.530322
$285$	−380.117	−	240.018i	−0.0790042	−	0.0498857i
$286$	5998.70			1.24025
$287$	−90.0637	+	510.777i	−0.0185237	+	0.105053i
$288$	−220.621	−	185.123i	−0.0451396	−	0.0378766i
$289$	397.603	+	144.716i	0.0809287	+	0.0294556i
$290$	−155.240	+	56.5026i	−0.0314344	+	0.0114412i
$291$	−945.245	+	793.154i	−0.190417	+	0.159778i
$292$	−1368.95	−	2371.09i	−0.274355	−	0.475197i
$293$	−2277.44	+	3944.64i	−0.454094	+	0.786513i	−0.998636	−	0.0522204i	$-0.983370\pi$
$293$	−2277.44	+	3944.64i	−0.454094	+	0.786513i	0.544542	+	0.838734i	$0.316704\pi$
$294$	72.4254	+	410.745i	0.0143671	+	0.0814800i
$295$	201.690	+	1143.84i	0.0398062	+	0.225752i
$296$	1255.45	−	2174.51i	0.246526	−	0.426995i
$297$	−578.913	−	1002.71i	−0.113104	−	0.195902i
$298$	−4966.10	+	4167.06i	−0.965365	+	0.810037i
$299$	6405.92	−	2331.56i	1.23901	−	0.450962i
$300$	1372.62	+	499.594i	0.264161	+	0.0961468i
$301$	5970.73	+	5010.03i	1.14335	+	0.959380i
$302$	485.196	−	2751.68i	0.0924499	−	0.524310i
$303$	1725.51			0.327155
$304$	810.894	+	1048.02i	0.152987	+	0.197725i
$305$	−432.239			−0.0811474
$306$	−209.440	+	1187.79i	−0.0391271	+	0.221901i
$307$	834.531	+	700.255i	0.155144	+	0.130181i	0.717055	−	0.697016i	$-0.245489\pi$
$307$	834.531	+	700.255i	0.155144	+	0.130181i	−0.561911	+	0.827197i	$0.689934\pi$
$308$	2665.59	+	970.195i	0.493137	+	0.179487i
$309$	3456.74	−	1258.15i	0.636399	−	0.231630i
$310$	509.511	−	427.530i	0.0933492	−	0.0783293i
$311$	4955.01	+	8582.33i	0.903450	+	1.56482i	0.822984	+	0.568064i	$0.192307\pi$
$311$	4955.01	+	8582.33i	0.903450	+	1.56482i	0.0804658	+	0.996757i	$0.474359\pi$
$312$	−839.322	+	1453.75i	−0.152299	+	0.263789i
$313$	−1318.44	−	7477.26i	−0.238092	−	1.35029i	−0.836003	−	0.548725i	$-0.815114\pi$
$313$	−1318.44	−	7477.26i	−0.238092	−	1.35029i	0.597911	−	0.801562i	$-0.295998\pi$
$314$	−426.079	−	2416.42i	−0.0765766	−	0.434287i
$315$	134.651	−	233.222i	0.0240848	−	0.0417161i
$316$	1949.31	+	3376.30i	0.347016	+	0.601050i
$317$	−435.419	+	365.360i	−0.0771469	+	0.0647339i	−0.680546	−	0.732706i	$-0.738257\pi$
$317$	−435.419	+	365.360i	−0.0771469	+	0.0647339i	0.603399	+	0.797440i	$0.293813\pi$
$318$	−514.057	+	187.101i	−0.0906505	+	0.0329941i
$319$	1839.60	+	669.559i	0.322877	+	0.117518i
$320$	88.7080	+	74.4348i	0.0154966	+	0.0130032i
$321$	272.269	−	1544.12i	0.0473414	−	0.268487i
$322$	3223.64			0.557907
$323$	2103.04	−	5135.50i	0.362279	−	0.884665i
$324$	324.000			0.0555556
$325$	1478.43	−	8384.61i	0.252334	−	1.43106i
$326$	5038.77	+	4228.03i	0.856049	+	0.718310i
$327$	−2878.16	−	1047.56i	−0.486735	−	0.177157i
$328$	235.769	−	85.8131i	0.0396896	−	0.0144458i
$329$	−3819.21	+	3204.70i	−0.639999	+	0.537023i
$330$	232.771	+	403.172i	0.0388292	+	0.0672542i
$331$	−1697.55	+	2940.24i	−0.281890	+	0.488248i	−0.971850	−	0.235599i	$-0.924295\pi$
$331$	−1697.55	+	2940.24i	−0.281890	+	0.488248i	0.689960	+	0.723847i	$0.257628\pi$
$332$	343.907	+	1950.39i	0.0568505	+	0.322415i
$333$	490.516	+	2781.85i	0.0807210	+	0.457791i
$334$	−2415.78	+	4184.26i	−0.395766	+	0.685487i
$335$	−418.733	−	725.267i	−0.0682921	−	0.118285i
$336$	−608.083	+	510.243i	−0.0987311	+	0.0828453i
$337$	−830.772	+	302.376i	−0.134288	+	0.0488768i	−0.408290	−	0.912852i	$-0.633875\pi$
$337$	−830.772	+	302.376i	−0.134288	+	0.0488768i	0.274002	+	0.961729i	$0.411653\pi$
$338$	5065.12	+	1843.55i	0.815107	+	0.296675i
$339$	−2045.05	−	1716.00i	−0.327646	−	0.274927i
$340$	84.2124	−	477.592i	0.0134325	−	0.0761797i
$341$	−7881.71			−1.25167
$342$	−1456.69	−	316.800i	−0.230318	−	0.0500894i
$343$	6821.91			1.07390
$344$	654.735	−	3713.19i	0.102619	−	0.581981i
$345$	405.277	+	340.068i	0.0632446	+	0.0530685i
$346$	−3296.67	−	1199.89i	−0.512226	−	0.186435i
$347$	−33.4958	+	12.1915i	−0.00518199	+	0.00188609i	−0.344610	−	0.938746i	$-0.611989\pi$
$347$	−33.4958	+	12.1915i	−0.00518199	+	0.00188609i	0.339428	+	0.940632i	$0.389767\pi$
$348$	−419.656	+	352.133i	−0.0646434	+	0.0542423i
$349$	317.606	+	550.109i	0.0487136	+	0.0843744i	0.889354	−	0.457219i	$-0.151155\pi$
$349$	317.606	+	550.109i	0.0487136	+	0.0843744i	−0.840640	+	0.541594i	$0.817821\pi$
$350$	2013.04	−	3486.68i	0.307432	−	0.532489i
$351$	−327.930	−	1859.78i	−0.0498679	−	0.282815i
$352$	−238.287	−	1351.39i	−0.0360816	−	0.204629i
$353$	6424.65	−	11127.8i	0.968696	−	1.67783i	0.269359	−	0.963040i	$-0.413188\pi$
$353$	6424.65	−	11127.8i	0.968696	−	1.67783i	0.699338	−	0.714791i	$-0.253478\pi$
$354$	1925.78	+	3335.54i	0.289135	+	0.500797i
$355$	−879.508	+	737.995i	−0.131491	+	0.110334i
$356$	4410.05	−	1605.13i	0.656551	−	0.238965i
$357$	3123.87	+	1136.99i	0.463116	+	0.168561i
$358$	6779.71	+	5688.86i	1.00089	+	0.839847i
$359$	1375.81	−	7802.59i	0.202263	−	1.14709i	−0.699427	−	0.714704i	$-0.746561\pi$
$359$	1375.81	−	7802.59i	0.202263	−	1.14709i	0.901689	−	0.432385i	$-0.142328\pi$
$360$	−130.275			−0.0190725
$361$	6239.48	+	2848.64i	0.909678	+	0.415315i
$362$	−4318.03			−0.626935
$363$	264.590	−	1500.57i	0.0382573	−	0.216968i
$364$	3544.29	+	2974.01i	0.510361	+	0.428243i
$365$	−1163.78	−	423.583i	−0.166891	−	0.0607433i
$366$	−1346.89	+	490.228i	−0.192358	+	0.0700127i
$367$	−2677.56	+	2246.74i	−0.380837	+	0.319561i	−0.813031	−	0.582220i	$-0.802184\pi$
$367$	−2677.56	+	2246.74i	−0.380837	+	0.319561i	0.432194	+	0.901781i	$0.357740\pi$
$368$	−779.719	−	1350.51i	−0.110450	−	0.191305i
$369$	−141.132	+	244.447i	−0.0199106	+	0.0344862i
$370$	−197.228	−	1118.54i	−0.0277119	−	0.157162i
$371$	261.826	+	1484.89i	0.0366396	+	0.207794i
$372$	1102.79	−	1910.08i	0.153701	−	0.266218i
$373$	4092.59	+	7088.58i	0.568114	+	0.984002i	0.996753	+	0.0805260i	$0.0256600\pi$
$373$	4092.59	+	7088.58i	0.568114	+	0.984002i	−0.428639	+	0.903476i	$0.641007\pi$
$374$	−4402.31	+	3693.98i	−0.608658	+	0.510725i
$375$	1258.49	−	458.054i	0.173302	−	0.0630768i
$376$	2266.35	+	824.884i	0.310846	+	0.113139i
$377$	2446.02	+	2052.45i	0.334154	+	0.280389i
$378$	155.071	−	879.454i	0.0211006	−	0.119667i
$379$	−6220.60			−0.843089			−0.421544	−	0.906808i	$-0.638512\pi$
$379$	−6220.60			−0.843089			−0.421544	+	0.906808i	$0.638512\pi$
$380$	585.712	+	127.380i	0.0790694	+	0.0171959i
$381$	−4213.23			−0.566536
$382$	934.050	−	5297.26i	0.125105	−	0.709506i
$383$	−5320.54	−	4464.46i	−0.709835	−	0.595623i	0.214718	−	0.976676i	$-0.431117\pi$
$383$	−5320.54	−	4464.46i	−0.709835	−	0.595623i	−0.924553	+	0.381054i	$0.875561\pi$
$384$	360.842	+	131.336i	0.0479535	+	0.0174536i
$385$	1205.76	−	438.862i	0.159614	−	0.0580947i
$386$	108.701	−	91.2110i	0.0143335	−	0.0120273i
$387$	2120.89	+	3673.49i	0.278581	+	0.482516i
$388$	822.619	−	1424.82i	0.107634	−	0.186428i
$389$	−767.691	−	4353.79i	−0.100060	−	0.567470i	−0.993079	−	0.117450i	$-0.962528\pi$
$389$	−767.691	−	4353.79i	−0.100060	−	0.567470i	0.893018	−	0.450020i	$-0.148583\pi$
$390$	131.855	+	747.788i	0.0171199	+	0.0970916i
$391$	−3265.39	+	5655.83i	−0.422348	+	0.731528i
$392$	−278.054	−	481.604i	−0.0358262	−	0.0620527i
$393$	3090.10	−	2592.90i	0.396629	−	0.332811i
$394$	−4801.70	+	1747.68i	−0.613975	+	0.223469i
$395$	1657.16	+	603.158i	0.211091	+	0.0768308i
$396$	1182.60	+	992.315i	0.150070	+	0.125924i
$397$	637.577	−	3615.88i	0.0806022	−	0.457118i	−0.917617	−	0.397466i	$-0.869890\pi$
$397$	637.577	−	3615.88i	0.0806022	−	0.457118i	0.998219	−	0.0596521i	$-0.0189991\pi$
$398$	−3976.91			−0.500865
$399$	−1557.11	+	3802.37i	−0.195371	+	0.477084i
$400$	−1947.62			−0.243452
$401$	−1026.35	+	5820.71i	−0.127814	+	0.724869i	0.851783	+	0.523895i	$0.175522\pi$
$401$	−1026.35	+	5820.71i	−0.127814	+	0.724869i	−0.979597	+	0.200974i	$0.935589\pi$
$402$	−2127.38	−	1785.08i	−0.263940	−	0.221472i
$403$	−12080.2	−	4396.83i	−1.49319	−	0.543478i
$404$	−2161.93	+	786.879i	−0.266238	+	0.0969027i
$405$	112.271	−	94.2066i	0.0137748	−	0.0115584i
$406$	754.963	+	1307.63i	0.0922862	+	0.159844i
$407$	−6729.61	+	11656.0i	−0.819593	+	1.41958i
$408$	−279.254	−	1583.73i	−0.0338851	−	0.192172i
$409$	−2286.96	−	12970.0i	−0.276486	−	1.56803i	−0.734202	−	0.678931i	$-0.762444\pi$
$409$	−2286.96	−	12970.0i	−0.276486	−	1.56803i	0.457716	−	0.889098i	$-0.348668\pi$
$410$	56.7467	−	98.2881i	0.00683541	−	0.0118393i
$411$	2719.23	+	4709.85i	0.326350	+	0.565255i
$412$	−3757.28	+	3152.73i	−0.449291	+	0.377000i
$413$	9975.59	−	3630.82i	1.18854	−	0.432593i
$414$	1648.57	+	600.029i	0.195707	+	0.0712314i
$415$	686.268	+	575.847i	0.0811749	+	0.0681138i
$416$	388.658	−	2204.19i	0.0458066	−	0.259782i
$417$	−4458.23			−0.523551
$418$	−4346.64	−	5617.73i	−0.508615	−	0.657350i
$419$	−3493.10			−0.407277			−0.203638	−	0.979046i	$-0.565277\pi$
$419$	−3493.10			−0.407277			−0.203638	+	0.979046i	$0.565277\pi$
$420$	−62.3517	+	353.614i	−0.00724393	+	0.0410824i
$421$	−10925.9	−	9167.94i	−1.26484	−	1.06133i	−0.995149	−	0.0983777i	$-0.968635\pi$
$421$	−10925.9	−	9167.94i	−1.26484	−	1.06133i	−0.269689	−	0.962947i	$-0.586921\pi$
$422$	2455.29	+	893.653i	0.283227	+	0.103086i
$423$	−2549.64	+	927.995i	−0.293068	+	0.106668i
$424$	558.751	−	468.847i	0.0639984	−	0.0537010i
$425$	4078.23	+	7063.69i	0.465466	+	0.806211i
$426$	−1903.61	+	3297.15i	−0.216503	+	0.374994i
$427$	686.015	+	3890.58i	0.0777485	+	0.440933i
$428$	363.026	+	2058.82i	0.0409989	+	0.232516i
$429$	4499.02	−	7792.54i	0.506328	−	0.876987i
$430$	−852.774	−	1477.05i	−0.0956381	−	0.165650i
$431$	−7927.48	+	6651.94i	−0.885970	+	0.743417i	−0.967398	−	0.253262i	$-0.918497\pi$
$431$	−7927.48	+	6651.94i	−0.885970	+	0.743417i	0.0814276	+	0.996679i	$0.474052\pi$
$432$	−405.947	+	147.753i	−0.0452110	+	0.0164555i
$433$	5978.31	+	2175.93i	0.663509	+	0.241498i	0.651751	−	0.758433i	$-0.274035\pi$
$433$	5978.31	+	2175.93i	0.663509	+	0.241498i	0.0117584	+	0.999931i	$0.496257\pi$
$434$	−4656.85	−	3907.56i	−0.515060	−	0.432187i
$435$	−43.0307	+	244.039i	−0.00474290	+	0.0268983i
$436$	4083.83			0.448578
$437$	−6825.20	−	4309.64i	−0.747125	−	0.471758i
$438$	−4106.85			−0.448020
$439$	−1873.37	+	10624.4i	−0.203670	+	1.15507i	0.695848	+	0.718189i	$0.255029\pi$
$439$	−1873.37	+	10624.4i	−0.203670	+	1.15507i	−0.899518	+	0.436883i	$0.856082\pi$
$440$	−475.502	−	398.993i	−0.0515197	−	0.0432301i
$441$	587.892	+	213.975i	0.0634804	+	0.0231050i
$442$	−8808.07	+	3205.87i	−0.947866	+	0.344995i
$443$	3271.27	−	2744.92i	0.350842	−	0.294391i	−0.450286	−	0.892884i	$-0.648678\pi$
$443$	3271.27	−	2744.92i	0.350842	−	0.294391i	0.801128	+	0.598493i	$0.204234\pi$
$444$	−1883.18	−	3261.76i	−0.201288	−	0.348640i
$445$	1061.44	−	1838.47i	0.113072	−	0.195847i
$446$	610.306	+	3461.22i	0.0647956	+	0.367474i
$447$	1688.59	+	9576.45i	0.178674	+	1.01331i
$448$	529.198	−	916.597i	0.0558086	−	0.0966633i
$449$	1617.03	+	2800.78i	0.169961	+	0.294381i	0.938406	−	0.345535i	$-0.112302\pi$
$449$	1617.03	+	2800.78i	0.169961	+	0.294381i	−0.768445	+	0.639916i	$0.778969\pi$
$450$	1678.46	−	1408.39i	0.175829	−	0.147538i
$451$	−1263.80	+	459.984i	−0.131951	+	0.0480262i
$452$	3344.83	+	1217.42i	0.348070	+	0.126687i
$453$	−3210.64	−	2694.05i	−0.333000	−	0.279420i
$454$	877.740	−	4977.91i	0.0907365	−	0.514592i
$455$	2092.88			0.215639
$456$	1969.59	−	267.365i	0.202269	−	0.0274572i
$457$	9512.93			0.973734			0.486867	−	0.873476i	$-0.338140\pi$
$457$	9512.93			0.973734			0.486867	+	0.873476i	$0.338140\pi$
$458$	1154.46	−	6547.25i	0.117782	−	0.667976i
$459$	1385.91	+	1162.92i	0.140934	+	0.118258i
$460$	−662.861	−	241.262i	−0.0671871	−	0.0244541i
$461$	−15017.3	+	5465.85i	−1.51719	+	0.552213i	−0.960445	−	0.278470i	$-0.910173\pi$
$461$	−15017.3	+	5465.85i	−1.51719	+	0.552213i	−0.556747	+	0.830682i	$0.687951\pi$
$462$	3259.51	−	2735.06i	0.328239	−	0.275425i
$463$	1794.15	+	3107.57i	0.180090	+	0.311924i	0.941911	−	0.335863i	$-0.109028\pi$
$463$	1794.15	+	3107.57i	0.180090	+	0.311924i	−0.761821	+	0.647787i	$0.775695\pi$
$464$	365.214	−	632.570i	0.0365402	−	0.0632895i
$465$	−173.245	−	982.521i	−0.0172775	−	0.0979856i
$466$	−196.636	−	1115.18i	−0.0195471	−	0.110857i
$467$	5703.66	−	9879.03i	0.565169	−	0.978901i	−0.431865	−	0.901938i	$-0.642144\pi$
$467$	5703.66	−	9879.03i	0.565169	−	0.978901i	0.997034	−	0.0769632i	$-0.0245224\pi$
$468$	1258.98	+	2180.62i	0.124352	+	0.215383i
$469$	−5863.55	+	4920.10i	−0.577300	+	0.484412i
$470$	1025.17	−	373.131i	0.100612	−	0.0366197i
$471$	−3458.57	−	1258.82i	−0.338350	−	0.123149i
$472$	−3933.95	−	3300.97i	−0.383633	−	0.321906i
$473$	−3509.58	+	19903.8i	−0.341164	+	1.93484i
$474$	5847.92			0.566675
$475$	−8923.38	+	4690.93i	−0.861964	+	0.453125i
$476$	−4432.46			−0.426810
$477$	−142.491	+	808.105i	−0.0136776	+	0.0775694i
$478$	−9397.42	−	7885.37i	−0.899222	−	0.754537i
$479$	15356.0	+	5589.11i	1.46478	+	0.533138i	0.946679	−	0.322178i	$-0.104415\pi$
$479$	15356.0	+	5589.11i	1.46478	+	0.533138i	0.518106	+	0.855317i	$0.326637\pi$
$480$	163.225	−	59.4089i	0.0155211	−	0.00564924i
$481$	−16816.7	+	14110.9i	−1.59413	+	1.33763i
$482$	1112.51	+	1926.92i	0.105132	+	0.182093i
$483$	2417.73	−	4187.63i	0.227765	−	0.394500i
$484$	352.787	+	2000.75i	0.0331318	+	0.187900i
$485$	−129.231	−	732.907i	−0.0120992	−	0.0686177i
$486$	243.000	−	420.888i	0.0226805	−	0.0392837i
$487$	−40.6948	−	70.4855i	−0.00378657	−	0.00655852i	0.864126	−	0.503276i	$-0.167872\pi$
$487$	−40.6948	−	70.4855i	−0.00378657	−	0.00655852i	−0.867912	+	0.496717i	$0.834539\pi$
$488$	1463.99	−	1228.44i	0.135803	−	0.113952i
$489$	9271.46	−	3374.53i	0.857402	−	0.312069i
$490$	−236.382	−	86.0359i	−0.0217931	−	0.00793205i
$491$	12688.7	+	10647.1i	1.16626	+	0.978610i	0.999972	−	0.00746649i	$-0.00237668\pi$
$491$	12688.7	+	10647.1i	1.16626	+	0.978610i	0.166290	+	0.986077i	$0.446821\pi$
$492$	65.3526	−	370.633i	0.00598847	−	0.0339623i
$493$	−3058.97			−0.279450
$494$	−3528.18	−	11035.0i	−0.321337	−	1.00504i
$495$	698.314			0.0634078
$496$	−510.659	+	2896.09i	−0.0462283	+	0.262174i
$497$	8038.57	+	6745.17i	0.725512	+	0.608777i
$498$	2791.57	+	1016.05i	0.251191	+	0.0914261i
$499$	17971.6	−	6541.11i	1.61226	−	0.586814i	0.630374	−	0.776292i	$-0.282902\pi$
$499$	17971.6	−	6541.11i	1.61226	−	0.586814i	0.981885	+	0.189477i	$0.0606793\pi$
$500$	−1367.91	+	1147.81i	−0.122350	+	0.102664i
$501$	3623.68	+	6276.39i	0.323141	+	0.559697i
$502$	−396.627	+	686.978i	−0.0352636	+	0.0610783i
$503$	−1870.46	−	10607.9i	−0.165805	−	0.940327i	−0.948231	−	0.317583i	$-0.897129\pi$
$503$	−1870.46	−	10607.9i	−0.165805	−	0.940327i	0.782426	−	0.622744i	$-0.213982\pi$
$504$	206.762	+	1172.61i	0.0182736	+	0.103635i
$505$	−520.349	+	901.272i	−0.0458520	+	0.0794179i
$506$	4179.53	+	7239.16i	0.367199	+	0.636008i
$507$	6193.69	−	5197.12i	0.542547	−	0.455251i
$508$	5278.85	−	1921.35i	0.461046	−	0.167807i
$509$	9566.61	+	3481.96i	0.833070	+	0.303213i	0.723118	−	0.690724i	$-0.242708\pi$
$509$	9566.61	+	3481.96i	0.833070	+	0.303213i	0.109952	+	0.993937i	$0.464930\pi$
$510$	−557.251	−	467.589i	−0.0483834	−	0.0405985i
$511$	−1965.60	+	11147.5i	−0.170163	+	0.965041i
$512$	−512.000			−0.0441942
$513$	−1504.05	+	1654.70i	−0.129446	+	0.142411i
$514$	−6211.15			−0.533000
$515$	−385.264	+	2184.94i	−0.0329646	+	0.186952i
$516$	−4332.52	−	3635.41i	−0.369629	−	0.310155i
$517$	−12148.3	−	4421.63i	−1.03343	−	0.376138i
$518$	−9754.92	+	3550.50i	−0.827426	+	0.301158i
$519$	−4031.21	+	3382.59i	−0.340945	+	0.286087i
$520$	−506.216	−	876.792i	−0.0426905	−	0.0739421i
$521$	9319.63	−	16142.1i	0.783686	−	1.35738i	−0.146096	−	0.989270i	$-0.546671\pi$
$521$	9319.63	−	16142.1i	0.783686	−	1.35738i	0.929781	−	0.368113i	$-0.119996\pi$
$522$	142.692	+	809.248i	0.0119645	+	0.0678541i
$523$	−3540.39	−	20078.6i	−0.296005	−	1.67873i	−0.663090	−	0.748540i	$-0.730755\pi$
$523$	−3540.39	−	20078.6i	−0.296005	−	1.67873i	0.367085	−	0.930187i	$-0.380356\pi$
$524$	−2689.23	+	4657.88i	−0.224197	+	0.388321i
$525$	−3019.56	−	5230.02i	−0.251018	−	0.434775i
$526$	−8768.05	+	7357.26i	−0.726815	+	0.609871i
$527$	11572.9	−	4212.21i	0.956594	−	0.348172i
$528$	−1934.22	−	704.000i	−0.159425	−	0.0580259i
$529$	−2043.50	−	1714.70i	−0.167954	−	0.140930i
$530$	57.2932	−	324.926i	0.00469558	−	0.0266299i
$531$	5777.33			0.472156
$532$	216.953	−	5474.16i	0.0176806	−	0.446118i
$533$	−2193.61			−0.178266
$534$	1222.42	−	6932.67i	0.0990620	−	0.561809i
$535$	724.419	+	607.860i	0.0585409	+	0.0491216i
$536$	3479.48	+	1266.43i	0.280393	+	0.102055i
$537$	12474.8	−	4540.47i	1.00247	−	0.364871i
$538$	11831.7	−	9927.94i	0.948139	−	0.795583i
$539$	1490.46	+	2581.55i	0.119107	+	0.206299i
$540$	−97.7063	+	169.232i	−0.00778631	+	0.0134863i
$541$	−1659.79	−	9413.16i	−0.131904	−	0.748065i	−0.976966	−	0.213396i	$-0.931547\pi$
$541$	−1659.79	−	9413.16i	−0.131904	−	0.748065i	0.845062	−	0.534669i	$-0.179564\pi$
$542$	1152.88	+	6538.30i	0.0913660	+	0.518163i
$543$	−3238.52	+	5609.28i	−0.255945	+	0.443310i
$544$	1072.11	+	1856.94i	0.0844966	+	0.146352i
$545$	1415.11	−	1187.42i	0.111223	−	0.0933273i
$546$	6521.57	−	2373.66i	0.511168	−	0.186050i
$547$	−7664.50	−	2789.65i	−0.599105	−	0.218056i	0.0246243	−	0.999697i	$-0.492161\pi$
$547$	−7664.50	−	2789.65i	−0.599105	−	0.218056i	−0.623729	+	0.781640i	$0.714383\pi$
$548$	−5554.81	−	4661.04i	−0.433010	−	0.363339i
$549$	−373.343	+	2117.33i	−0.0290235	+	0.164600i
$550$	10439.8			0.809375
$551$	149.725	−	3777.87i	0.0115763	−	0.292092i
$552$	−2339.16			−0.180364
$553$	2798.91	−	15873.4i	0.215229	−	1.22062i
$554$	11170.5	+	9373.13i	0.856656	+	0.718820i
$555$	−1600.94	−	582.695i	−0.122444	−	0.0445658i
$556$	5585.82	−	2033.07i	0.426064	−	0.155075i
$557$	8817.28	−	7398.57i	0.670736	−	0.562814i	−0.242547	−	0.970140i	$-0.577983\pi$
$557$	8817.28	−	7398.57i	0.670736	−	0.562814i	0.913283	+	0.407325i	$0.133538\pi$
$558$	−1654.18	−	2865.13i	−0.125497	−	0.217366i
$559$	−16482.5	+	28548.5i	−1.24711	+	2.16006i
$560$	−83.1355	−	471.485i	−0.00627343	−	0.0355784i
$561$	1496.89	+	8489.26i	0.112653	+	0.638889i
$562$	8260.96	−	14308.4i	0.620049	−	1.07396i
$563$	−6422.43	−	11124.0i	−0.480770	−	0.832718i	0.518987	−	0.854782i	$-0.326309\pi$
$563$	−6422.43	−	11124.0i	−0.480770	−	0.832718i	−0.999757	+	0.0220646i	$0.992976\pi$
$564$	2771.32	−	2325.41i	0.206904	−	0.173613i
$565$	1513.01	−	550.692i	0.112660	−	0.0410050i
$566$	12930.1	+	4706.17i	0.960234	+	0.349497i
$567$	−1026.14	−	861.034i	−0.0760033	−	0.0637743i
$568$	881.490	−	4999.18i	0.0651171	−	0.369297i
$569$	−3092.39			−0.227838			−0.113919	−	0.993490i	$-0.536340\pi$
$569$	−3092.39			−0.227838			−0.113919	+	0.993490i	$0.536340\pi$
$570$	604.755	−	665.327i	0.0444393	−	0.0488903i
$571$	21101.9			1.54657			0.773283	−	0.634062i	$-0.218613\pi$
$571$	21101.9			1.54657			0.773283	+	0.634062i	$0.218613\pi$
$572$	−2083.33	+	11815.1i	−0.152287	+	0.863663i
$573$	−6180.81	−	5186.31i	−0.450623	−	0.378117i
$574$	−974.755	−	354.782i	−0.0708806	−	0.0257984i
$575$	11148.5	−	4057.73i	0.808567	−	0.294294i
$576$	441.242	−	370.246i	0.0319185	−	0.0267828i
$577$	2577.81	+	4464.90i	0.185989	+	0.322142i	0.943909	−	0.330205i	$-0.107118\pi$
$577$	2577.81	+	4464.90i	0.185989	+	0.322142i	−0.757920	+	0.652347i	$0.773784\pi$
$578$	−423.120	+	732.865i	−0.0304489	+	0.0527391i
$579$	−36.9608	−	209.615i	−0.00265292	−	0.0150454i
$580$	−57.3742	−	325.385i	−0.00410747	−	0.0232946i
$581$	4094.01	−	7091.04i	0.292338	−	0.506344i
$582$	−1233.93	−	2137.23i	−0.0878832	−	0.152218i
$583$	−2995.07	+	2513.17i	−0.212767	+	0.178533i
$584$	5145.57	−	1872.83i	0.364598	−	0.132703i
$585$	1070.30	+	389.556i	0.0756433	+	0.0275319i
$586$	−6978.48	−	5855.64i	−0.491943	−	0.412789i
$587$	435.650	−	2470.69i	0.0306324	−	0.173725i	−0.965653	−	0.259834i	$-0.916332\pi$
$587$	435.650	−	2470.69i	0.0306324	−	0.173725i	0.996286	+	0.0861090i	$0.0274433\pi$
$588$	−834.163			−0.0585039
$589$	4635.68	+	14498.9i	0.324295	+	1.01429i
$590$	−2322.97			−0.162093
$591$	−1330.98	+	7548.35i	−0.0926381	+	0.525377i
$592$	3846.93	+	3227.96i	0.267074	+	0.224102i
$593$	−26277.0	−	9564.04i	−1.81967	−	0.662307i	−0.995365	−	0.0961660i	$-0.969342\pi$
$593$	−26277.0	−	9564.04i	−1.81967	−	0.662307i	−0.824308	−	0.566141i	$-0.808436\pi$
$594$	2176.00	−	792.000i	0.150307	−	0.0547073i
$595$	−1535.92	+	1288.79i	−0.105826	+	0.0887986i
$596$	−6482.79	−	11228.5i	−0.445546	−	0.771708i
$597$	−2982.68	+	5166.15i	−0.204477	+	0.354165i
$598$	2367.53	+	13426.9i	0.161899	+	0.918174i
$599$	−1890.04	−	10718.9i	−0.128923	−	0.731158i	−0.978900	−	0.204339i	$-0.934496\pi$
$599$	−1890.04	−	10718.9i	−0.128923	−	0.731158i	0.849977	−	0.526819i	$-0.176615\pi$
$600$	−1460.71	+	2530.03i	−0.0993890	+	0.172147i
$601$	−7977.50	−	13817.4i	−0.541446	−	0.937812i	−0.998821	−	0.0485384i	$-0.984544\pi$
$601$	−7977.50	−	13817.4i	−0.541446	−	0.937812i	0.457375	−	0.889274i	$-0.348790\pi$
$602$	−11941.5	+	10020.1i	−0.808467	+	0.678384i
$603$	−3914.42	+	1424.73i	−0.264357	+	0.0962182i
$604$	5251.25	+	1911.30i	0.353759	+	0.128758i
$605$	703.988	+	590.716i	0.0473077	+	0.0396959i
$606$	−599.264	+	3398.59i	−0.0401707	+	0.227819i
$607$	−2302.78			−0.153982			−0.0769908	−	0.997032i	$-0.524531\pi$
$607$	−2302.78			−0.153982			−0.0769908	+	0.997032i	$0.524531\pi$
$608$	−2345.82	+	1233.18i	−0.156473	+	0.0822564i
$609$	2264.89			0.150703
$610$	150.115	−	851.345i	0.00996391	−	0.0565081i
$611$	−16153.0	−	13554.0i	−1.06952	−	0.897438i
$612$	−2266.76	−	825.033i	−0.149720	−	0.0544935i
$613$	25222.4	−	9180.22i	1.66187	−	0.604871i	0.671213	−	0.741264i	$-0.265773\pi$
$613$	25222.4	−	9180.22i	1.66187	−	0.604871i	0.990655	+	0.136394i	$0.0435512\pi$
$614$	−1669.06	+	1400.51i	−0.109703	+	0.0920521i
$615$	−85.1200	−	147.432i	−0.00558109	−	0.00966673i
$616$	−2836.66	+	4913.24i	−0.185540	+	0.321364i
$617$	4114.56	+	23334.8i	0.268470	+	1.52257i	0.758969	+	0.651127i	$0.225703\pi$
$617$	4114.56	+	23334.8i	0.268470	+	1.52257i	−0.490499	+	0.871442i	$0.663186\pi$
$618$	1277.56	+	7245.40i	0.0831570	+	0.471607i
$619$	3761.98	−	6515.94i	0.244276	−	0.423098i	−0.717652	−	0.696402i	$-0.754783\pi$
$619$	3761.98	−	6515.94i	0.244276	−	0.423098i	0.961928	+	0.273304i	$0.0881165\pi$
$620$	665.119	+	1152.02i	0.0430836	+	0.0746229i
$621$	2015.89	−	1691.53i	0.130265	−	0.109305i
$622$	−18624.8	+	6778.86i	−1.20062	+	0.436989i
$623$	−18232.7	−	6636.16i	−1.17252	−	0.426761i
$624$	−2571.83	−	2158.02i	−0.164993	−	0.138446i
$625$	2501.93	−	14189.1i	0.160123	−	0.908105i
$626$	15185.2			0.969527
$627$	−10557.6	+	1433.16i	−0.672458	+	0.0912836i
$628$	4907.38			0.311825
$629$	3651.97	−	20711.4i	0.231500	−	1.31290i
$630$	412.594	+	346.208i	0.0260923	+	0.0218940i
$631$	−2402.26	−	874.351i	−0.151557	−	0.0551622i	0.265128	−	0.964213i	$-0.414586\pi$
$631$	−2402.26	−	874.351i	−0.151557	−	0.0551622i	−0.416685	+	0.909051i	$0.636808\pi$
$632$	−7327.00	+	2666.81i	−0.461159	+	0.167848i
$633$	3002.36	−	2519.28i	0.188520	−	0.158187i
$634$	−568.399	−	984.496i	−0.0356057	−	0.0616709i
$635$	1270.55	−	2200.66i	0.0794021	−	0.137528i
$636$	−189.988	−	1077.47i	−0.0118451	−	0.0671771i
$637$	844.281	+	4788.16i	0.0525143	+	0.297824i
$638$	−1957.66	+	3390.77i	−0.121480	+	0.210410i
$639$	2855.42	+	4945.73i	0.176774	+	0.306182i
$640$	−177.416	+	148.870i	−0.0109578	+	0.00919467i
$641$	−21343.7	+	7768.47i	−1.31517	+	0.478683i	−0.901908	−	0.431928i	$-0.857833\pi$
$641$	−21343.7	+	7768.47i	−1.31517	+	0.478683i	−0.413264	+	0.910611i	$0.635611\pi$
$642$	2946.76	+	1072.53i	0.181151	+	0.0659338i
$643$	9986.03	+	8379.27i	0.612458	+	0.513913i	0.895423	−	0.445217i	$-0.146873\pi$
$643$	9986.03	+	8379.27i	0.612458	+	0.513913i	−0.282965	+	0.959130i	$0.591318\pi$
$644$	−1119.56	+	6349.32i	−0.0685042	+	0.388507i
$645$	−2558.32			−0.156176
$646$	9384.58	+	5925.71i	0.571565	+	0.360904i
$647$	−4416.85			−0.268384			−0.134192	−	0.990955i	$-0.542844\pi$
$647$	−4416.85			−0.268384			−0.134192	+	0.990955i	$0.542844\pi$
$648$	−112.524	+	638.155i	−0.00682154	+	0.0386869i
$649$	21087.2	+	17694.2i	1.27541	+	1.07020i
$650$	16001.0	+	5823.89i	0.965555	+	0.351433i
$651$	−8568.71	+	3118.76i	−0.515874	+	0.187763i
$652$	−10077.5	+	8456.07i	−0.605318	+	0.507922i
$653$	59.1634	+	102.474i	0.00354555	+	0.00614107i	0.867793	−	0.496926i	$-0.165538\pi$
$653$	59.1634	+	102.474i	0.00354555	+	0.00614107i	−0.864247	+	0.503067i	$0.832205\pi$
$654$	3062.87	−	5305.05i	0.183131	−	0.317192i
$655$	422.471	+	2395.95i	0.0252020	+	0.142927i
$656$	87.1369	+	494.178i	0.00518616	+	0.0294122i
$657$	−3080.14	+	5334.96i	−0.182904	+	0.316798i
$658$	−4985.62	−	8635.35i	−0.295380	−	0.511612i
$659$	23611.1	−	19812.1i	1.39569	−	1.17112i	0.432716	−	0.901530i	$-0.357555\pi$
$659$	23611.1	−	19812.1i	1.39569	−	1.17112i	0.962974	−	0.269593i	$-0.0868890\pi$
$660$	−874.934	+	318.450i	−0.0516012	+	0.0187813i
$661$	−5175.58	−	1883.76i	−0.304549	−	0.110847i	0.185225	−	0.982696i	$-0.440699\pi$
$661$	−5175.58	−	1883.76i	−0.304549	−	0.110847i	−0.489774	+	0.871849i	$0.662921\pi$
$662$	−5201.58	−	4364.65i	−0.305386	−	0.256249i
$663$	−2441.50	+	13846.4i	−0.143016	+	0.811087i
$664$	−3960.97			−0.231499
$665$	−1516.49	−	1959.96i	−0.0884318	−	0.114292i
$666$	−5649.53			−0.328701
$667$	−772.638	+	4381.85i	−0.0448526	+	0.254372i
$668$	−7402.39	−	6211.34i	−0.428753	−	0.359767i
$669$	4953.99	+	1803.10i	0.286296	+	0.104203i
$670$	1573.92	−	572.861i	0.0907551	−	0.0330322i
$671$	−7847.46	+	6584.80i	−0.451487	+	0.378843i
$672$	−793.796	−	1374.90i	−0.0455675	−	0.0789252i
$673$	−11511.6	+	19938.8i	−0.659348	+	1.14202i	0.321436	+	0.946931i	$0.395834\pi$
$673$	−11511.6	+	19938.8i	−0.659348	+	1.14202i	−0.980785	+	0.195094i	$0.937499\pi$
$674$	−307.041	−	1741.32i	−0.0175471	−	0.0995148i
$675$	−570.713	−	3236.68i	−0.0325434	−	0.184563i
$676$	−5390.19	+	9336.08i	−0.306679	+	0.531183i
$677$	5794.17	+	10035.8i	0.328933	+	0.569729i	0.982301	−	0.187312i	$-0.0599775\pi$
$677$	5794.17	+	10035.8i	0.328933	+	0.569729i	−0.653367	+	0.757041i	$0.726644\pi$
$678$	4090.10	−	3432.00i	0.231680	−	0.194403i
$679$	−6391.79	+	2326.42i	−0.361258	+	0.131487i
$680$	911.427	+	331.732i	0.0513994	+	0.0187079i
$681$	−5808.19	−	4873.65i	−0.326829	−	0.274242i
$682$	2737.29	−	15523.9i	0.153689	−	0.871616i
$683$	12617.6			0.706881			0.353441	−	0.935457i	$-0.385012\pi$
$683$	12617.6			0.706881			0.353441	+	0.935457i	$0.385012\pi$
$684$	1129.88	−	2759.10i	0.0631608	−	0.154235i
$685$	−3280.07			−0.182956
$686$	−2369.23	+	13436.5i	−0.131862	+	0.747827i
$687$	−7639.28	−	6410.12i	−0.424246	−	0.355984i
$688$	7086.16	+	2579.15i	0.392671	+	0.142920i
$689$	−5992.49	+	2181.09i	−0.331343	+	0.120599i
$690$	−810.554	+	680.135i	−0.0447207	+	0.0375251i
$691$	−14161.9	−	24529.1i	−0.779658	−	1.35041i	−0.932139	−	0.362101i	$-0.882059\pi$
$691$	−14161.9	−	24529.1i	−0.779658	−	1.35041i	0.152480	−	0.988306i	$-0.451274\pi$
$692$	3508.25	−	6076.46i	0.192722	−	0.333804i
$693$	−1108.31	−	6285.52i	−0.0607520	−	0.344542i
$694$	−12.3796	−	70.2080i	−0.000677120	−	0.00384014i
$695$	1344.44	−	2328.63i	0.0733775	−	0.127094i
$696$	−547.822	−	948.855i	−0.0298349	−	0.0516756i
$697$	1609.84	−	1350.82i	0.0874851	−	0.0734087i
$698$	−1193.81	+	434.510i	−0.0647368	+	0.0235623i
$699$	−1596.13	−	580.945i	−0.0863681	−	0.0314354i
$700$	6168.30	+	5175.82i	0.333057	+	0.279468i
$701$	−4953.70	+	28093.8i	−0.266902	+	1.51368i	0.496661	+	0.867945i	$0.334559\pi$
$701$	−4953.70	+	28093.8i	−0.266902	+	1.51368i	−0.763563	+	0.645733i	$0.776552\pi$
$702$	3776.95			0.203065
$703$	25400.1	+	5523.99i	1.36271	+	0.296360i
$704$	2744.48			0.146927
$705$	284.166	−	1611.58i	0.0151806	−	0.0860932i
$706$	19686.3	+	16518.8i	1.04944	+	0.880583i
$707$	8938.20	+	3253.24i	0.475468	+	0.173056i
$708$	−7238.55	+	2634.62i	−0.384239	+	0.139852i
$709$	−21544.9	+	18078.4i	−1.14124	+	0.957612i	−0.999479	−	0.0322895i	$-0.989720\pi$
$709$	−21544.9	+	18078.4i	−1.14124	+	0.957612i	−0.141759	+	0.989901i	$0.545276\pi$
$710$	−1148.12	−	1988.60i	−0.0606874	−	0.105114i
$711$	4385.94	−	7596.68i	0.231344	−	0.400700i
$712$	1629.89	+	9243.55i	0.0857902	+	0.486541i
$713$	−3110.70	−	17641.7i	−0.163390	−	0.926629i
$714$	−3324.35	+	5757.94i	−0.174245	+	0.301800i
$715$	2713.47	+	4699.87i	0.141928	+	0.245826i
$716$	−13559.4	+	11377.7i	−0.707737	+	0.593862i
$717$	−17291.5	+	6293.58i	−0.900644	+	0.327808i
$718$	14890.3	+	5419.62i	0.773956	+	0.281697i
$719$	−18472.9	−	15500.6i	−0.958169	−	0.803999i	0.0224856	−	0.999747i	$-0.492842\pi$
$719$	−18472.9	−	15500.6i	−0.958169	−	0.803999i	−0.980654	+	0.195748i	$0.937286\pi$
$720$	45.2440	−	256.592i	0.00234187	−	0.0132814i
$721$	20278.1			1.04743
$722$	−7777.68	+	11300.1i	−0.400908	+	0.582471i
$723$	3337.53			0.171679
$724$	1499.64	−	8504.86i	0.0769800	−	0.436575i
$725$	4256.92	+	3571.98i	0.218066	+	0.182979i
$726$	2863.65	+	1042.28i	0.146391	+	0.0532820i
$727$	−5870.59	+	2136.72i	−0.299489	+	0.109005i	−0.487394	−	0.873182i	$-0.662052\pi$
$727$	−5870.59	+	2136.72i	−0.299489	+	0.109005i	0.187905	+	0.982187i	$0.439830\pi$
$728$	−7088.58	+	5948.03i	−0.360879	+	0.302814i
$729$	−364.500	−	631.333i	−0.0185185	−	0.0320750i
$730$	1238.47	−	2145.10i	0.0627917	−	0.108758i
$731$	−5483.94	−	31101.0i	−0.277470	−	1.57361i
$732$	−497.791	−	2823.11i	−0.0251351	−	0.142548i
$733$	5216.78	−	9035.72i	0.262873	−	0.455310i	−0.704131	−	0.710070i	$-0.748663\pi$
$733$	5216.78	−	9035.72i	0.262873	−	0.455310i	0.967004	+	0.254760i	$0.0819966\pi$
$734$	−3495.30	−	6054.04i	−0.175768	−	0.304440i
$735$	−289.050	+	242.542i	−0.0145058	+	0.0121718i
$736$	2930.78	−	1066.72i	0.146780	−	0.0534236i
$737$	−18651.1	−	6788.44i	−0.932187	−	0.339288i
$738$	−432.452	−	362.871i	−0.0215702	−	0.0180995i
$739$	−195.449	+	1108.44i	−0.00972895	+	0.0551756i	−0.989286	−	0.145992i	$-0.953363\pi$
$739$	−195.449	+	1108.44i	−0.00972895	+	0.0551756i	0.979557	+	0.201168i	$0.0644737\pi$
$740$	2271.58			0.112845
$741$	−16981.0	−	3693.02i	−0.841854	−	0.183086i
$742$	−3015.59			−0.149199
$743$	−3731.27	+	21161.1i	−0.184236	+	1.04485i	0.742698	+	0.669627i	$0.233546\pi$
$743$	−3731.27	+	21161.1i	−0.184236	+	1.04485i	−0.926934	+	0.375226i	$0.877565\pi$
$744$	3379.14	+	2835.43i	0.166512	+	0.139720i
$745$	−5511.20	−	2005.91i	−0.271027	−	0.0986456i
$746$	−15383.1	+	5599.00i	−0.754981	+	0.274791i
$747$	3413.56	−	2864.32i	0.167196	−	0.140294i
$748$	−5746.81	−	9953.77i	−0.280915	−	0.486559i
$749$	4321.61	−	7485.24i	0.210825	−	0.365160i
$750$	465.120	+	2637.83i	0.0226451	+	0.128427i
$751$	−1797.99	−	10196.9i	−0.0873628	−	0.495459i	−0.996822	−	0.0796653i	$-0.974615\pi$
$751$	−1797.99	−	10196.9i	−0.0873628	−	0.495459i	0.909459	−	0.415794i	$-0.136496\pi$
$752$	−2411.80	+	4177.36i	−0.116954	+	0.202570i
$753$	594.940	+	1030.47i	0.0287926	+	0.0498702i
$754$	−4892.03	+	4104.90i	−0.236283	+	0.198265i
$755$	2375.37	−	864.564i	0.114501	−	0.0416751i
$756$	1678.33	+	610.862i	0.0807411	+	0.0293874i
$757$	12242.1	+	10272.4i	0.587778	+	0.493205i	0.887491	−	0.460825i	$-0.152446\pi$
$757$	12242.1	+	10272.4i	0.587778	+	0.493205i	−0.299713	+	0.954029i	$0.596891\pi$
$758$	2160.39	−	12252.2i	0.103521	−	0.587097i
$759$	12538.6			0.599634
$760$	−454.305	+	1109.39i	−0.0216834	+	0.0529497i
$761$	−24519.5			−1.16798			−0.583989	−	0.811761i	$-0.698509\pi$
$761$	−24519.5			−1.16798			−0.583989	+	0.811761i	$0.698509\pi$
$762$	1463.24	−	8298.44i	0.0695637	−	0.394515i
$763$	−12933.9	−	10852.8i	−0.613681	−	0.514939i
$764$	10109.2	+	3679.44i	0.478713	+	0.174237i
$765$	−1025.36	+	373.199i	−0.0484599	+	0.0176379i
$766$	10641.1	−	8928.93i	0.501929	−	0.421169i
$767$	22449.3	+	38883.3i	1.05684	+	1.83050i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	2514.23	+	14258.9i	0.117901	+	0.668647i	0.985273	+	0.170988i	$0.0546959\pi$
$769$	2514.23	+	14258.9i	0.117901	+	0.668647i	−0.867373	+	0.497659i	$0.834193\pi$
$770$	445.632	+	2527.30i	0.0208564	+	0.118283i
$771$	−4658.36	+	8068.52i	−0.217596	+	0.376888i
$772$	141.899	+	245.777i	0.00661537	+	0.0114582i
$773$	25870.2	−	21707.6i	1.20373	−	1.01005i	0.204216	−	0.978926i	$-0.434535\pi$
$773$	25870.2	−	21707.6i	1.20373	−	1.01005i	0.999515	−	0.0311253i	$-0.00990909\pi$
$774$	−7971.93	+	2901.55i	−0.370213	+	0.134747i
$775$	−21023.8	−	7652.02i	−0.974446	−	0.354669i
$776$	2520.65	+	2115.08i	0.116606	+	0.0978439i
$777$	−2703.95	+	15334.9i	−0.124844	+	0.708026i
$778$	8841.91			0.407452
$779$	1589.48	+	2054.30i	0.0731055	+	0.0944837i
$780$	−1518.65			−0.0697133
$781$	−4725.06	+	26797.1i	−0.216486	+	1.22776i
$782$	−10005.7	−	8395.82i	−0.457551	−	0.383931i
$783$	1158.26	+	421.573i	0.0528646	+	0.0192411i
$784$	1045.14	−	380.401i	0.0476103	−	0.0173287i
$785$	1700.48	−	1426.88i	0.0773158	−	0.0648757i
$786$	4033.84	+	6986.82i	0.183056	+	0.317063i
$787$	19896.5	−	34461.8i	0.901189	−	1.56090i	0.0752352	−	0.997166i	$-0.476029\pi$
$787$	19896.5	−	34461.8i	0.901189	−	1.56090i	0.825953	−	0.563739i	$-0.190637\pi$
$788$	−1774.64	−	10064.5i	−0.0802270	−	0.454990i
$789$	2981.33	+	16908.0i	0.134522	+	0.762915i
$790$	−1763.51	+	3054.50i	−0.0794216	+	0.137562i
$791$	−7358.12	−	12744.6i	−0.330752	−	0.572879i
$792$	−2365.19	+	1984.63i	−0.106115	+	0.0890414i
$793$	−15701.1	+	5714.72i	−0.703103	+	0.255909i
$794$	6900.46	+	2511.56i	0.308424	+	0.112257i
$795$	−379.121	−	318.120i	−0.0169133	−	0.0141919i
$796$	1381.17	−	7832.98i	0.0615001	−	0.348785i
$797$	−4320.31			−0.192011			−0.0960057	−	0.995381i	$-0.530607\pi$
$797$	−4320.31			−0.192011			−0.0960057	+	0.995381i	$0.530607\pi$
$798$	−6948.43	−	4387.45i	−0.308235	−	0.194629i
$799$	20200.8			0.894435
$800$	676.401	−	3836.06i	0.0298930	−	0.169531i
$801$	−8088.99	−	6787.46i	−0.356817	−	0.299405i
$802$	−11108.1	−	4043.02i	−0.489079	−	0.178010i
$803$	−27581.8	+	10039.0i	−1.21213	+	0.441180i
$804$	4254.75	−	3570.16i	0.186634	−	0.156604i
$805$	1458.19	+	2525.66i	0.0638441	+	0.110581i
$806$	12855.5	−	22266.3i	0.561805	−	0.973074i
$807$	−4023.03	−	22815.7i	−0.175486	−	0.995231i
$808$	−799.018	−	4531.46i	−0.0347888	−	0.197297i
$809$	−10811.1	+	18725.3i	−0.469835	+	0.813779i	−0.999405	−	0.0344876i	$-0.989020\pi$
$809$	−10811.1	+	18725.3i	−0.469835	+	0.813779i	0.529570	+	0.848266i	$0.322353\pi$
$810$	146.559	+	253.848i	0.00635750	+	0.0110115i
$811$	13790.0	−	11571.2i	0.597080	−	0.501009i	−0.293426	−	0.955982i	$-0.594795\pi$
$811$	13790.0	−	11571.2i	0.597080	−	0.501009i	0.890505	+	0.454973i	$0.150351\pi$
$812$	−2837.73	+	1032.85i	−0.122642	+	0.0446379i
$813$	9358.16	+	3406.09i	0.403696	+	0.146933i
$814$	−20620.7	−	17302.8i	−0.887906	−	0.745042i
$815$	−1033.33	+	5860.32i	−0.0444123	+	0.251875i
$816$	3216.32			0.137982
$817$	38678.6	−	5250.47i	1.65629	−	0.224836i
$818$	26340.1			1.12587
$819$	1807.71	−	10252.0i	0.0771262	−	0.437405i
$820$	173.882	+	145.904i	0.00740514	+	0.00621365i
$821$	30718.1	+	11180.5i	1.30581	+	0.475275i	0.898884	−	0.438187i	$-0.144379\pi$
$821$	30718.1	+	11180.5i	1.30581	+	0.475275i	0.406924	+	0.913462i	$0.366601\pi$
$822$	−10221.0	+	3720.13i	−0.433695	+	0.157852i
$823$	14957.4	−	12550.7i	0.633513	−	0.531580i	−0.268506	−	0.963278i	$-0.586530\pi$
$823$	14957.4	−	12550.7i	0.633513	−	0.531580i	0.902018	+	0.431698i	$0.142085\pi$
$824$	−4904.78	−	8495.33i	−0.207362	−	0.359161i
$825$	7829.87	−	13561.7i	0.330426	−	0.572314i
$826$	3686.83	+	20909.0i	0.155304	+	0.880773i
$827$	5595.15	+	31731.7i	0.235263	+	1.33424i	0.842059	+	0.539385i	$0.181343\pi$
$827$	5595.15	+	31731.7i	0.235263	+	1.33424i	−0.606796	+	0.794857i	$0.707546\pi$
$828$	−1754.37	+	3038.65i	−0.0736334	+	0.127537i
$829$	−15162.7	−	26262.6i	−0.635252	−	1.10029i	−0.986462	−	0.163992i	$-0.947563\pi$
$829$	−15162.7	−	26262.6i	−0.635252	−	1.10029i	0.351210	−	0.936297i	$-0.385770\pi$
$830$	−1372.54	+	1151.69i	−0.0573993	+	0.0481637i
$831$	20553.9	−	7481.01i	0.858011	−	0.312290i
$832$	4206.43	+	1531.01i	0.175278	+	0.0637961i
$833$	−3568.13	−	2994.02i	−0.148413	−	0.124534i
$834$	1548.33	−	8781.00i	0.0642856	−	0.364582i
$835$	−4371.06			−0.181158
$836$	12574.3	−	6610.20i	0.520207	−	0.273467i
$837$	−4962.54			−0.204935
$838$	1213.14	−	6880.05i	0.0500086	−	0.283613i
$839$	6017.89	+	5049.61i	0.247629	+	0.207785i	0.758150	−	0.652080i	$-0.226103\pi$
$839$	6017.89	+	5049.61i	0.247629	+	0.207785i	−0.510522	+	0.859865i	$0.670548\pi$
$840$	−674.829	−	245.618i	−0.0277188	−	0.0100888i
$841$	20959.8	−	7628.73i	0.859394	−	0.312794i
$842$	21851.8	−	18335.9i	0.894376	−	0.750470i
$843$	−12391.4	−	21462.6i	−0.506268	−	0.876881i
$844$	−2612.87	+	4525.62i	−0.106562	+	0.184571i
$845$	846.784	+	4802.35i	0.0344737	+	0.195510i
$846$	−942.311	−	5344.11i	−0.0382947	−	0.217180i
$847$	4199.72	−	7274.13i	0.170371	−	0.295091i
$848$	729.397	+	1263.35i	0.0295373	+	0.0511600i
$849$	15811.1	−	13267.1i	0.639145	−	0.536307i
$850$	−15329.1	+	5579.34i	−0.618570	+	0.225141i
$851$	−28745.8	−	10462.6i	−1.15792	−	0.421449i
$852$	−5833.01	−	4894.47i	−0.234549	−	0.196810i
$853$	−1496.87	+	8489.19i	−0.0600843	+	0.340755i	−1.00000		0.000652100i	$-0.999792\pi$
$853$	−1496.87	+	8489.19i	−0.0600843	+	0.340755i	0.939915	+	0.341407i	$0.110904\pi$
$854$	−7901.21			−0.316597
$855$	−410.719	−	1284.60i	−0.0164284	−	0.0513827i
$856$	−4181.17			−0.166950
$857$	−2398.24	+	13601.1i	−0.0955920	+	0.542129i	0.898972	+	0.438005i	$0.144315\pi$
$857$	−2398.24	+	13601.1i	−0.0955920	+	0.542129i	−0.994564	+	0.104124i	$0.966796\pi$
$858$	13785.8	+	11567.7i	0.548531	+	0.460272i
$859$	20488.9	+	7457.34i	0.813820	+	0.296206i	0.715201	−	0.698919i	$-0.246335\pi$
$859$	20488.9	+	7457.34i	0.813820	+	0.296206i	0.0986194	+	0.995125i	$0.468557\pi$
$860$	3205.38	−	1166.66i	0.127096	−	0.0462592i
$861$	−1191.94	+	1000.16i	−0.0471792	+	0.0395880i
$862$	−10348.6	−	17924.3i	−0.408903	−	0.708241i
$863$	827.836	−	1433.85i	0.0326534	−	0.0565573i	−0.849237	−	0.528012i	$-0.822938\pi$
$863$	827.836	−	1433.85i	0.0326534	−	0.0565573i	0.881890	+	0.471455i	$0.156271\pi$
$864$	−150.032	−	850.874i	−0.00590763	−	0.0335038i
$865$	−551.136	−	3125.65i	−0.0216638	−	0.122862i
$866$	−6361.99	+	11019.3i	−0.249641	+	0.432391i
$867$	634.680	+	1099.30i	0.0248614	+	0.0430613i
$868$	9313.70	−	7815.13i	0.364202	−	0.305602i
$869$	39275.0	−	14294.9i	1.53316	−	0.558023i
$870$	−465.719	−	169.508i	−0.0181487	−	0.00660557i
$871$	−24799.3	−	20809.1i	−0.964746	−	0.809518i
$872$	−1418.30	+	8043.57i	−0.0550799	+	0.312374i
$873$	−3701.79			−0.143513
$874$	10858.7	−	11946.3i	0.420253	−	0.462345i
$875$	7382.64			0.285233
$876$	1426.29	−	8088.92i	0.0550114	−	0.311985i
$877$	34846.2	+	29239.4i	1.34170	+	1.12582i	0.981185	+	0.193068i	$0.0618438\pi$
$877$	34846.2	+	29239.4i	1.34170	+	1.12582i	0.360516	+	0.932753i	$0.382601\pi$
$878$	−20275.4	−	7379.65i	−0.779342	−	0.283657i
$879$	−12840.6	+	4673.58i	−0.492720	+	0.179336i
$880$	951.004	−	797.987i	0.0364299	−	0.0305683i
$881$	3829.92	+	6633.61i	0.146462	+	0.253680i	0.929917	−	0.367768i	$-0.119878\pi$
$881$	3829.92	+	6633.61i	0.146462	+	0.253680i	−0.783455	+	0.621448i	$0.786545\pi$
$882$	−625.622	+	1083.61i	−0.0238841	+	0.0413685i
$883$	6502.84	+	36879.5i	0.247835	+	1.40554i	0.813816	+	0.581123i	$0.197386\pi$
$883$	6502.84	+	36879.5i	0.247835	+	1.40554i	−0.565981	+	0.824418i	$0.691502\pi$
$884$	−3255.33	−	18461.9i	−0.123856	−	0.702422i
$885$	−1742.23	+	3017.62i	−0.0661743	+	0.114617i
$886$	4270.34	+	7396.45i	0.161924	+	0.280461i
$887$	36603.4	−	30713.9i	1.38559	−	1.16265i	0.418504	−	0.908215i	$-0.362554\pi$
$887$	36603.4	−	30713.9i	1.38559	−	1.16265i	0.967089	−	0.254437i	$-0.0818900\pi$
$888$	7078.43	−	2576.34i	0.267496	−	0.0973607i
$889$	−21824.7	−	7943.53i	−0.823369	−	0.299682i
$890$	3252.45	+	2729.13i	0.122497	+	0.102787i
$891$	603.163	−	3420.71i	0.0226787	−	0.128617i
$892$	−7029.23			−0.263852
$893$	−988.756	+	24948.3i	−0.0370520	+	0.934897i
$894$	−19448.4			−0.727573
$895$	−1390.36	+	7885.11i	−0.0519268	+	0.294492i
$896$	1621.56	+	1360.65i	0.0604602	+	0.0507322i
$897$	19217.7	+	6994.69i	0.715342	+	0.260363i
$898$	−6078.06	+	2212.23i	−0.225866	+	0.0822084i
$899$	6427.65	−	5393.44i	0.238459	−	0.200090i
$900$	2191.07	+	3795.05i	0.0811508	+	0.140557i
$901$	3054.65	−	5290.81i	0.112947	−	0.195630i
$902$	−467.080	−	2648.94i	−0.0172418	−	0.0977829i
$903$	4060.36	+	23027.4i	0.149635	+	0.848622i
$904$	−3559.50	+	6165.23i	−0.130959	+	0.226828i
$905$	−1953.23	−	3383.10i	−0.0717433	−	0.124263i
$906$	6421.29	−	5388.10i	0.235467	−	0.197580i
$907$	−28672.9	+	10436.1i	−1.04969	+	0.382055i	−0.808545	−	0.588434i	$-0.799744\pi$
$907$	−28672.9	+	10436.1i	−1.04969	+	0.382055i	−0.241143	+	0.970490i	$0.577522\pi$
$908$	9499.73	+	3457.62i	0.347202	+	0.126371i
$909$	3965.45	+	3327.41i	0.144693	+	0.121412i
$910$	−726.849	+	4122.17i	−0.0264778	+	0.150163i
$911$	−29112.6			−1.05877			−0.529386	−	0.848381i	$-0.677578\pi$
$911$	−29112.6			−1.05877			−0.529386	+	0.848381i	$0.677578\pi$
$912$	−157.427	+	3972.20i	−0.00571593	+	0.144224i
$913$	21232.0			0.769635
$914$	−3303.81	+	18736.8i	−0.119563	+	0.678073i
$915$	−993.343	−	833.514i	−0.0358895	−	0.0301149i
$916$	12494.6	+	4547.67i	0.450692	+	0.164038i
$917$	20895.4	−	7605.31i	0.752484	−	0.273882i
$918$	−2771.82	+	2325.83i	−0.0996555	+	0.0836209i
$919$	1046.46	+	1812.52i	0.0375620	+	0.0650592i	0.884195	−	0.467118i	$-0.154708\pi$
$919$	1046.46	+	1812.52i	0.0375620	+	0.0650592i	−0.846633	+	0.532177i	$0.821374\pi$
$920$	705.402	−	1221.79i	0.0252787	−	0.0437840i
$921$	567.518	+	3218.56i	0.0203044	+	0.115152i
$922$	−5550.17	−	31476.6i	−0.198248	−	1.12432i
$923$	−22190.9	+	38435.7i	−0.791356	+	1.37067i
$924$	4254.99	+	7369.86i	0.151492	+	0.262393i
$925$	−29267.0	+	24557.9i	−1.04032	+	0.872929i
$926$	−6743.82	+	2454.55i	−0.239326	+	0.0871074i
$927$	10370.2	+	3774.45i	0.367425	+	0.133732i
$928$	1119.08	+	939.021i	0.0395858	+	0.0332165i
$929$	−5945.71	+	33719.8i	−0.209981	+	1.19086i	0.679425	+	0.733745i	$0.262229\pi$
$929$	−5945.71	+	33719.8i	−0.209981	+	1.19086i	−0.889406	+	0.457118i	$0.848882\pi$
$930$	1995.36			0.0703552
$931$	3872.30	−	4260.15i	0.136315	−	0.149969i
$932$	2264.76			0.0795973
$933$	−5162.57	+	29278.4i	−0.181152	+	1.02737i
$934$	17477.0	+	14665.0i	0.612276	+	0.513761i
$935$	−4885.53	−	1778.19i	−0.170881	−	0.0621956i
$936$	−4732.23	+	1722.39i	−0.165254	+	0.0601475i
$937$	−12353.7	+	10366.0i	−0.430711	+	0.361410i	−0.832220	−	0.554445i	$-0.812930\pi$
$937$	−12353.7	+	10366.0i	−0.430711	+	0.361410i	0.401509	+	0.915855i	$0.368486\pi$
$938$	−7654.32	−	13257.7i	−0.266442	−	0.461491i
$939$	11388.9	−	19726.2i	0.395808	−	0.685559i
$940$	378.887	+	2148.78i	0.0131468	+	0.0745589i
$941$	317.641	+	1801.43i	0.0110040	+	0.0624070i	0.989815	−	0.142357i	$-0.0454683\pi$
$941$	317.641	+	1801.43i	0.0110040	+	0.0624070i	−0.978811	+	0.204765i	$0.934357\pi$
$942$	3680.54	−	6374.88i	0.127302	−	0.220493i
$943$	−1528.37	−	2647.22i	−0.0527791	−	0.0914161i
$944$	7867.90	−	6601.95i	0.271269	−	0.227622i
$945$	759.182	−	276.320i	0.0261336	−	0.00951183i
$946$	−37984.0	−	13825.0i	−1.30546	−	0.475149i
$947$	9468.69	+	7945.17i	0.324911	+	0.272633i	0.790623	−	0.612304i	$-0.209757\pi$
$947$	9468.69	+	7945.17i	0.324911	+	0.272633i	−0.465711	+	0.884937i	$0.654201\pi$
$948$	−2030.96	+	11518.2i	−0.0695808	+	0.394612i
$949$	−47874.6			−1.63759
$950$	−6140.27	−	19204.8i	−0.209702	−	0.655879i
$951$	−1705.20			−0.0581439
$952$	1539.38	−	8730.25i	0.0524071	−	0.297215i
$953$	38331.7	+	32164.1i	1.30292	+	1.09328i	0.989632	+	0.143624i	$0.0458757\pi$
$953$	38331.7	+	32164.1i	1.30292	+	1.09328i	0.313290	+	0.949657i	$0.398569\pi$
$954$	−1542.17	−	561.304i	−0.0523371	−	0.0190492i
$955$	4572.82	−	1664.37i	0.154946	−	0.0563956i
$956$	18794.8	−	15770.7i	0.635846	−	0.533538i
$957$	2936.49	+	5086.15i	0.0991884	+	0.171799i
$958$	−16341.5	+	28304.3i	−0.551116	+	0.954561i
$959$	5205.87	+	29523.9i	0.175293	+	0.994137i
$960$	60.3254	+	342.122i	0.00202812	+	0.0115020i
$961$	−1995.33	+	3456.02i	−0.0669777	+	0.116009i
$962$	−21952.7	−	38023.1i	−0.735741	−	1.27434i
$963$	3603.33	−	3023.55i	0.120577	−	0.101176i
$964$	−4181.67	+	1522.00i	−0.139712	+	0.0508510i
$965$	120.633	+	43.9066i	0.00402414	+	0.00146467i
$966$	7408.34	+	6216.34i	0.246749	+	0.207047i
$967$	4194.98	−	23790.9i	0.139505	−	0.791172i	−0.832111	−	0.554609i	$-0.812868\pi$
$967$	4194.98	−	23790.9i	0.139505	−	0.791172i	0.971616	−	0.236563i	$-0.0760210\pi$
$968$	−4063.24			−0.134915
$969$	14736.2	−	7746.64i	0.488538	−	0.256819i
$970$	1488.43			0.0492686
$971$	4344.50	−	24638.9i	0.143586	−	0.814314i	−0.824906	−	0.565269i	$-0.808772\pi$
$971$	4344.50	−	24638.9i	0.143586	−	0.814314i	0.968492	−	0.249045i	$-0.0801166\pi$
$972$	744.595	+	624.790i	0.0245709	+	0.0206174i
$973$	−23093.8	−	8405.45i	−0.760897	−	0.276944i
$974$	152.962	−	55.6738i	0.00503207	−	0.00183152i
$975$	19566.2	−	16418.0i	0.642687	−	0.539279i
$976$	1911.11	+	3310.14i	0.0626774	+	0.108560i
$977$	774.074	−	1340.74i	0.0253478	−	0.0439037i	−0.853073	−	0.521791i	$-0.825264\pi$
$977$	774.074	−	1340.74i	0.0253478	−	0.0439037i	0.878421	+	0.477887i	$0.158597\pi$
$978$	3426.59	+	19433.2i	0.112035	+	0.635383i
$979$	−8736.70	−	49548.3i	−0.285216	−	1.61754i
$980$	251.552	−	435.701i	0.00819953	−	0.0142020i
$981$	−4594.31	−	7957.57i	−0.149526	−	0.258987i
$982$	−25377.5	+	21294.2i	−0.824672	+	0.691982i
$983$	−36812.6	+	13398.7i	−1.19445	+	0.434743i	−0.861283	−	0.508126i	$-0.830338\pi$
$983$	−36812.6	+	13398.7i	−1.19445	+	0.434743i	−0.333164	+	0.942869i	$0.608116\pi$
$984$	707.308	+	257.439i	0.0229148	+	0.00834031i
$985$	−3541.29	−	2971.50i	−0.114553	−	0.0961216i
$986$	1062.37	−	6024.99i	0.0343131	−	0.194599i
$987$	−14956.9			−0.482353
$988$	22960.1	−	3116.74i	0.739328	−	0.100361i
$989$	−45936.0			−1.47693
$990$	−242.522	+	1375.41i	−0.00778571	+	0.0441550i
$991$	−9569.06	−	8029.39i	−0.306732	−	0.257378i	0.476408	−	0.879224i	$-0.341939\pi$
$991$	−9569.06	−	8029.39i	−0.306732	−	0.257378i	−0.783140	+	0.621846i	$0.786383\pi$
$992$	−5526.83	−	2011.60i	−0.176892	−	0.0643835i
$993$	−9571.03	+	3483.57i	−0.305869	+	0.111327i
$994$	−16077.1	+	13490.3i	−0.513014	+	0.430470i
$995$	−1798.93	−	3115.84i	−0.0573165	−	0.0992750i
$996$	−2970.72	+	5145.45i	−0.0945090	+	0.163694i
$997$	−3598.26	−	20406.7i	−0.114301	−	0.648233i	−0.987094	−	0.160142i	$-0.948805\pi$
$997$	−3598.26	−	20406.7i	−0.114301	−	0.648233i	0.872793	−	0.488090i	$-0.162306\pi$
$998$	6642.02	+	37668.8i	0.210671	+	1.19477i
$999$	−4237.15	+	7338.96i	−0.134192	+	0.232427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.i.c.55.2	✓	18
19.3	odd	18		2166.4.a.bl.1.5		9
19.9	even	9	inner	114.4.i.c.85.2	yes	18
19.16	even	9		2166.4.a.bk.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.i.c.55.2	✓	18	1.1	even	1	trivial
114.4.i.c.85.2	yes	18	19.9	even	9	inner
2166.4.a.bk.1.5		9	19.16	even	9
2166.4.a.bl.1.5		9	19.3	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)

\(f(q)\)	\(=\)	\(q+(-0.347296 + 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(-1.70026 + 0.618843i) q^{5} +(-4.59627 + 3.85673i) q^{6} +(8.26871 + 14.3218i) q^{7} +(4.00000 - 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +O(q^{10})\)	\(q+(-0.347296 + 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(-1.70026 + 0.618843i) q^{5} +(-4.59627 + 3.85673i) q^{6} +(8.26871 + 14.3218i) q^{7} +(4.00000 - 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +(-0.628389 - 3.56377i) q^{10} +(-21.4412 + 37.1373i) q^{11} +(-6.00000 - 10.3923i) q^{12} +(-53.5798 + 44.9588i) q^{13} +(-31.0802 + 11.3123i) q^{14} +(-5.10077 - 1.85653i) q^{15} +(12.2567 + 10.2846i) q^{16} +(11.6356 - 65.9886i) q^{17} -18.0000 q^{18} +(80.9274 + 17.6000i) q^{19} +7.23750 q^{20} +(-8.61508 + 48.8586i) q^{21} +(-65.6997 - 55.1286i) q^{22} +(-91.5870 - 33.3349i) q^{23} +(22.5526 - 8.20848i) q^{24} +(-93.2476 + 78.2441i) q^{25} +(-69.9435 - 121.146i) q^{26} +(-13.5000 + 23.3827i) q^{27} +(-11.4868 - 65.1447i) q^{28} +(-7.92735 - 44.9582i) q^{29} +(5.42813 - 9.40179i) q^{30} +(91.8990 + 159.174i) q^{31} +(-24.5134 + 20.5692i) q^{32} +(-120.889 + 44.0000i) q^{33} +(125.931 + 45.8352i) q^{34} +(-22.9219 - 19.2338i) q^{35} +(6.25133 - 35.4531i) q^{36} +313.863 q^{37} +(-62.7710 + 153.283i) q^{38} -209.831 q^{39} +(-2.51356 + 14.2551i) q^{40} +(24.0251 + 20.1595i) q^{41} +(-93.2406 - 33.9368i) q^{42} +(442.885 - 161.197i) q^{43} +(131.399 - 110.257i) q^{44} +(-8.14219 - 14.1027i) q^{45} +(97.4649 - 168.814i) q^{46} +(52.3506 + 296.895i) q^{47} +(8.33511 + 47.2708i) q^{48} +(34.7568 - 60.2005i) q^{49} +(-121.726 - 210.836i) q^{50} +(153.990 - 129.213i) q^{51} +(262.902 - 95.6884i) q^{52} +(85.6761 + 31.1836i) q^{53} +(-41.3664 - 34.7105i) q^{54} +(13.4734 - 76.4117i) q^{55} +132.299 q^{56} +(152.043 + 196.504i) q^{57} +91.3036 q^{58} +(111.469 - 632.173i) q^{59} +(16.6327 + 13.9565i) q^{60} +(224.482 + 81.7047i) q^{61} +(-345.427 + 125.725i) q^{62} +(-114.016 + 95.6705i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(63.2770 - 109.599i) q^{65} +(-44.6788 - 253.386i) q^{66} +(80.3728 + 455.817i) q^{67} +(-134.013 + 232.118i) q^{68} +(-146.197 - 253.221i) q^{69} +(45.8438 - 38.4675i) q^{70} +(596.270 - 217.025i) q^{71} +(67.6579 + 24.6255i) q^{72} +(524.338 + 439.972i) q^{73} +(-109.003 + 618.189i) q^{74} -365.178 q^{75} +(-280.109 - 176.870i) q^{76} -709.165 q^{77} +(72.8734 - 413.285i) q^{78} +(-746.628 - 626.495i) q^{79} +(-27.2041 - 9.90148i) q^{80} +(-76.1151 + 27.7036i) q^{81} +(-48.0503 + 40.3190i) q^{82} +(-247.560 - 428.787i) q^{83} +(99.2246 - 171.862i) q^{84} +(21.0531 + 119.398i) q^{85} +(163.684 + 928.296i) q^{86} +(68.4777 - 118.607i) q^{87} +(171.530 + 297.098i) q^{88} +(-898.776 + 754.163i) q^{89} +(30.6046 - 11.1392i) q^{90} +(-1086.93 - 395.610i) q^{91} +(298.650 + 250.597i) q^{92} +(-95.7485 + 543.017i) q^{93} -602.950 q^{94} +(-148.489 + 20.1568i) q^{95} -96.0000 q^{96} +(-71.4232 + 405.061i) q^{97} +(106.501 + 89.3649i) q^{98} +(-362.667 - 132.000i) 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