LMFDB - Embedded newform 114.4.i.d.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} + 603 x^{16} - 1528 x^{15} + 240417 x^{14} - 786198 x^{13} + 54822410 x^{12} + \cdots + 11\!\cdots\!24 $ x^18 + 603x^16 - 1528x^15 + 240417x^14 - 786198x^13 + 54822410x^12 - 261322128x^11 + 9122210535x^10 - 45012474508x^9 + 1000170346788x^8 - 5035551052410x^7 + 79008124941737x^6 - 336274219954836x^5 + 3621639622047612x^4 - 11991799127581216x^3 + 107004711561222960x^2 - 278928948783924960x + 1161091951621493824
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.2
Root			$2.22861 - 3.86007i$ of defining polynomial
Character	$\chi$	$=$	114.55
Dual form			114.4.i.d.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347296 - 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(3.13539 - 1.14119i) q^{5} +(4.59627 - 3.85673i) q^{6} +(-16.8345 - 29.1581i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +O(q^{10})$	\(q+(0.347296 - 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(3.13539 - 1.14119i) q^{5} +(4.59627 - 3.85673i) q^{6} +(-16.8345 - 29.1581i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +(-1.15879 - 6.57184i) q^{10} +(12.2377 - 21.1964i) q^{11} +(-6.00000 - 10.3923i) q^{12} +(47.4414 - 39.8081i) q^{13} +(-63.2769 + 23.0309i) q^{14} +(9.40616 + 3.42356i) q^{15} +(12.2567 + 10.2846i) q^{16} +(20.2485 - 114.835i) q^{17} +18.0000 q^{18} +(1.28292 + 82.8091i) q^{19} -13.3464 q^{20} +(17.5396 - 99.4722i) q^{21} +(-37.4986 - 31.4651i) q^{22} +(-104.898 - 38.1799i) q^{23} +(-22.5526 + 8.20848i) q^{24} +(-87.2272 + 73.1923i) q^{25} +(-61.9304 - 107.267i) q^{26} +(-13.5000 + 23.3827i) q^{27} +(23.3862 + 132.630i) q^{28} +(18.8958 + 107.163i) q^{29} +(10.0098 - 17.3375i) q^{30} +(72.5086 + 125.589i) q^{31} +(24.5134 - 20.5692i) q^{32} +(68.9983 - 25.1133i) q^{33} +(-219.148 - 79.7635i) q^{34} +(-86.0575 - 72.2108i) q^{35} +(6.25133 - 35.4531i) q^{36} +134.882 q^{37} +(163.548 + 26.2324i) q^{38} +185.791 q^{39} +(-4.63517 + 26.2874i) q^{40} +(54.5603 + 45.7815i) q^{41} +(-189.831 - 69.0927i) q^{42} +(232.175 - 84.5048i) q^{43} +(-74.9972 + 62.9301i) q^{44} +(15.0147 + 26.0063i) q^{45} +(-111.630 + 193.350i) q^{46} +(-73.5346 - 417.036i) q^{47} +(8.33511 + 47.2708i) q^{48} +(-395.298 + 684.677i) q^{49} +(113.867 + 197.223i) q^{50} +(267.977 - 224.860i) q^{51} +(-232.782 + 84.7257i) q^{52} +(547.631 + 199.321i) q^{53} +(41.3664 + 34.7105i) q^{54} +(14.1810 - 80.4244i) q^{55} +269.351 q^{56} +(-156.738 + 192.780i) q^{57} +217.633 q^{58} +(-28.6670 + 162.578i) q^{59} +(-30.6719 - 25.7368i) q^{60} +(650.754 + 236.855i) q^{61} +(272.543 - 99.1977i) q^{62} +(232.127 - 194.778i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(103.319 - 178.953i) q^{65} +(-25.5007 - 144.622i) q^{66} +(179.223 + 1016.43i) q^{67} +(-233.213 + 403.937i) q^{68} +(-167.446 - 290.025i) q^{69} +(-172.115 + 144.422i) q^{70} +(-509.764 + 185.539i) q^{71} +(-67.6579 - 24.6255i) q^{72} +(-511.470 - 429.174i) q^{73} +(46.8440 - 265.665i) q^{74} -341.601 q^{75} +(108.467 - 313.016i) q^{76} -824.063 q^{77} +(64.5246 - 365.937i) q^{78} +(-180.164 - 151.176i) q^{79} +(50.1662 + 18.2590i) q^{80} +(-76.1151 + 27.7036i) q^{81} +(109.121 - 91.5630i) q^{82} +(-320.131 - 554.483i) q^{83} +(-202.014 + 349.898i) q^{84} +(-67.5614 - 383.160i) q^{85} +(-85.8085 - 486.644i) q^{86} +(-163.225 + 282.714i) q^{87} +(97.9019 + 169.571i) q^{88} +(840.211 - 705.021i) q^{89} +(56.4370 - 20.5414i) q^{90} +(-1959.38 - 713.156i) q^{91} +(342.056 + 287.019i) q^{92} +(-75.5460 + 428.442i) q^{93} -846.938 q^{94} +(98.5233 + 258.175i) q^{95} +96.0000 q^{96} +(-144.813 + 821.273i) q^{97} +(1211.26 + 1016.37i) q^{98} +(206.995 + 75.3399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 15 q^{5} - 72 q^{8}+O(q^{10}) $ 18 * q + 15 * q^5 - 72 * q^8	\( 18 q + 15 q^{5} - 72 q^{8} - 6 q^{10} - 39 q^{11} - 108 q^{12} - 42 q^{14} + 45 q^{15} + 159 q^{17} + 324 q^{18} + 159 q^{19} + 216 q^{20} + 99 q^{21} - 246 q^{22} + 300 q^{23} - 267 q^{25} - 198 q^{26} - 243 q^{27} + 132 q^{28} - 231 q^{29} - 162 q^{30} - 243 q^{31} - 126 q^{33} - 618 q^{34} + 774 q^{35} + 1422 q^{37} - 270 q^{38} + 594 q^{39} - 24 q^{40} - 69 q^{41} - 126 q^{42} - 60 q^{43} - 492 q^{44} - 243 q^{45} - 456 q^{46} + 540 q^{47} - 2229 q^{49} - 348 q^{50} + 450 q^{51} - 180 q^{52} - 750 q^{53} - 450 q^{55} + 297 q^{57} + 1836 q^{58} + 1263 q^{59} - 144 q^{60} + 1518 q^{61} - 390 q^{62} - 108 q^{63} - 576 q^{64} + 237 q^{65} + 990 q^{66} - 4812 q^{67} - 228 q^{68} - 684 q^{69} + 1548 q^{70} - 1371 q^{71} + 672 q^{73} + 186 q^{74} + 1044 q^{75} - 84 q^{76} - 270 q^{77} + 270 q^{78} - 2301 q^{79} + 240 q^{80} - 138 q^{82} - 2490 q^{83} + 5757 q^{85} + 96 q^{86} - 1377 q^{87} - 312 q^{88} + 7203 q^{89} + 270 q^{90} + 1284 q^{91} + 156 q^{92} - 207 q^{93} - 264 q^{94} + 3270 q^{95} + 1728 q^{96} - 1977 q^{97} + 498 q^{98} - 378 q^{99}+O(q^{100}) \) 18 * q + 15 * q^5 - 72 * q^8 - 6 * q^10 - 39 * q^11 - 108 * q^12 - 42 * q^14 + 45 * q^15 + 159 * q^17 + 324 * q^18 + 159 * q^19 + 216 * q^20 + 99 * q^21 - 246 * q^22 + 300 * q^23 - 267 * q^25 - 198 * q^26 - 243 * q^27 + 132 * q^28 - 231 * q^29 - 162 * q^30 - 243 * q^31 - 126 * q^33 - 618 * q^34 + 774 * q^35 + 1422 * q^37 - 270 * q^38 + 594 * q^39 - 24 * q^40 - 69 * q^41 - 126 * q^42 - 60 * q^43 - 492 * q^44 - 243 * q^45 - 456 * q^46 + 540 * q^47 - 2229 * q^49 - 348 * q^50 + 450 * q^51 - 180 * q^52 - 750 * q^53 - 450 * q^55 + 297 * q^57 + 1836 * q^58 + 1263 * q^59 - 144 * q^60 + 1518 * q^61 - 390 * q^62 - 108 * q^63 - 576 * q^64 + 237 * q^65 + 990 * q^66 - 4812 * q^67 - 228 * q^68 - 684 * q^69 + 1548 * q^70 - 1371 * q^71 + 672 * q^73 + 186 * q^74 + 1044 * q^75 - 84 * q^76 - 270 * q^77 + 270 * q^78 - 2301 * q^79 + 240 * q^80 - 138 * q^82 - 2490 * q^83 + 5757 * q^85 + 96 * q^86 - 1377 * q^87 - 312 * q^88 + 7203 * q^89 + 270 * q^90 + 1284 * q^91 + 156 * q^92 - 207 * q^93 - 264 * q^94 + 3270 * q^95 + 1728 * q^96 - 1977 * q^97 + 498 * q^98 - 378 * 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
$5$	3.13539	−	1.14119i	0.280438	−	0.102071i	−0.197972	−	0.980208i	$-0.563436\pi$
$5$	3.13539	−	1.14119i	0.280438	−	0.102071i	0.478410	+	0.878137i	$0.341213\pi$
$6$	4.59627	−	3.85673i	0.312736	−	0.262417i
$7$	−16.8345	−	29.1581i	−0.908975	−	1.57439i	−0.815490	−	0.578771i	$-0.803533\pi$
$7$	−16.8345	−	29.1581i	−0.908975	−	1.57439i	−0.0934854	−	0.995621i	$-0.529801\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$	1.56283	+	8.86327i	0.0578827	+	0.328269i
$10$	−1.15879	−	6.57184i	−0.0366442	−	0.207820i
$11$	12.2377	−	21.1964i	0.335438	−	0.580995i	−0.648131	−	0.761529i	$-0.724449\pi$
$11$	12.2377	−	21.1964i	0.335438	−	0.580995i	0.983569	+	0.180534i	$0.0577824\pi$
$12$	−6.00000	−	10.3923i	−0.144338	−	0.250000i
$13$	47.4414	−	39.8081i	1.01214	−	0.849290i	0.0235243	−	0.999723i	$-0.492511\pi$
$13$	47.4414	−	39.8081i	1.01214	−	0.849290i	0.988620	+	0.150433i	$0.0480669\pi$
$14$	−63.2769	+	23.0309i	−1.20796	+	0.439662i
$15$	9.40616	+	3.42356i	0.161911	+	0.0589307i
$16$	12.2567	+	10.2846i	0.191511	+	0.160697i
$17$	20.2485	−	114.835i	0.288881	−	1.63833i	−0.402201	−	0.915551i	$-0.631755\pi$
$17$	20.2485	−	114.835i	0.288881	−	1.63833i	0.691082	−	0.722776i	$-0.257134\pi$
$18$	18.0000			0.235702
$19$	1.28292	+	82.8091i	0.0154907	+	0.999880i
$19$	1.28292	+	82.8091i	0.0154907	+	0.999880i
$20$	−13.3464			−0.149218
$21$	17.5396	−	99.4722i	0.182260	−	1.03365i
$22$	−37.4986	−	31.4651i	−0.363397	−	0.304926i
$23$	−104.898	−	38.1799i	−0.950992	−	0.346133i	−0.180495	−	0.983576i	$-0.557770\pi$
$23$	−104.898	−	38.1799i	−0.950992	−	0.346133i	−0.770497	+	0.637443i	$0.779992\pi$
$24$	−22.5526	+	8.20848i	−0.191814	+	0.0698146i
$25$	−87.2272	+	73.1923i	−0.697818	+	0.585539i
$26$	−61.9304	−	107.267i	−0.467136	−	0.809104i
$27$	−13.5000	+	23.3827i	−0.0962250	+	0.166667i
$28$	23.3862	+	132.630i	0.157842	+	0.895166i
$29$	18.8958	+	107.163i	0.120995	+	0.686198i	0.983606	+	0.180330i	$0.0577166\pi$
$29$	18.8958	+	107.163i	0.120995	+	0.686198i	−0.862611	+	0.505868i	$0.831172\pi$
$30$	10.0098	−	17.3375i	0.0609179	−	0.105513i
$31$	72.5086	+	125.589i	0.420095	+	0.727625i	0.995948	−	0.0899274i	$-0.0286635\pi$
$31$	72.5086	+	125.589i	0.420095	+	0.727625i	−0.575854	+	0.817553i	$0.695330\pi$
$32$	24.5134	−	20.5692i	0.135419	−	0.113630i
$33$	68.9983	−	25.1133i	0.363971	−	0.132475i
$34$	−219.148	−	79.7635i	−1.10540	−	0.402333i
$35$	−86.0575	−	72.2108i	−0.415611	−	0.348739i
$36$	6.25133	−	35.4531i	0.0289414	−	0.164135i
$37$	134.882			0.599309			0.299655	−	0.954048i	$-0.403129\pi$
$37$	134.882			0.599309			0.299655	+	0.954048i	$0.403129\pi$
$38$	163.548	+	26.2324i	0.698183	+	0.111986i
$39$	185.791			0.762830
$40$	−4.63517	+	26.2874i	−0.0183221	+	0.103910i
$41$	54.5603	+	45.7815i	0.207826	+	0.174387i	0.740760	−	0.671770i	$-0.234466\pi$
$41$	54.5603	+	45.7815i	0.207826	+	0.174387i	−0.532933	+	0.846157i	$0.678910\pi$
$42$	−189.831	−	69.0927i	−0.697417	−	0.253839i
$43$	232.175	−	84.5048i	0.823404	−	0.299695i	0.104255	−	0.994551i	$-0.466754\pi$
$43$	232.175	−	84.5048i	0.823404	−	0.299695i	0.719149	+	0.694856i	$0.244532\pi$
$44$	−74.9972	+	62.9301i	−0.256960	+	0.215615i
$45$	15.0147	+	26.0063i	0.0497393	+	0.0861509i
$46$	−111.630	+	193.350i	−0.357805	+	0.619736i
$47$	−73.5346	−	417.036i	−0.228216	−	1.29427i	−0.856442	−	0.516244i	$-0.827330\pi$
$47$	−73.5346	−	417.036i	−0.228216	−	1.29427i	0.628226	−	0.778031i	$-0.283781\pi$
$48$	8.33511	+	47.2708i	0.0250640	+	0.142145i
$49$	−395.298	+	684.677i	−1.15247	+	1.99614i
$50$	113.867	+	197.223i	0.322065	+	0.557832i
$51$	267.977	−	224.860i	0.735771	−	0.617385i
$52$	−232.782	+	84.7257i	−0.620789	+	0.225949i
$53$	547.631	+	199.321i	1.41930	+	0.516583i	0.933845	−	0.357678i	$-0.116431\pi$
$53$	547.631	+	199.321i	1.41930	+	0.516583i	0.485456	+	0.874261i	$0.338654\pi$
$54$	41.3664	+	34.7105i	0.104245	+	0.0874723i
$55$	14.1810	−	80.4244i	0.0347666	−	0.197171i
$56$	269.351			0.642743
$57$	−156.738	+	192.780i	−0.364218	+	0.447972i
$58$	217.633			0.492701
$59$	−28.6670	+	162.578i	−0.0632563	+	0.358744i	0.936707	+	0.350116i	$0.113858\pi$
$59$	−28.6670	+	162.578i	−0.0632563	+	0.358744i	−0.999963	+	0.00862852i	$0.997253\pi$
$60$	−30.6719	−	25.7368i	−0.0659954	−	0.0553767i
$61$	650.754	+	236.855i	1.36591	+	0.497151i	0.917877	−	0.396866i	$-0.129902\pi$
$61$	650.754	+	236.855i	1.36591	+	0.497151i	0.448034	+	0.894017i	$0.352124\pi$
$62$	272.543	−	99.1977i	0.558275	−	0.203195i
$63$	232.127	−	194.778i	0.464210	−	0.389519i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	103.319	−	178.953i	0.197156	−	0.341483i
$66$	−25.5007	−	144.622i	−0.0475594	−	0.269723i
$67$	179.223	+	1016.43i	0.326800	+	1.85338i	0.496710	+	0.867917i	$0.334541\pi$
$67$	179.223	+	1016.43i	0.326800	+	1.85338i	−0.169910	+	0.985460i	$0.554348\pi$
$68$	−233.213	+	403.937i	−0.415900	+	0.720361i
$69$	−167.446	−	290.025i	−0.292146	−	0.506012i
$70$	−172.115	+	144.422i	−0.293881	+	0.246596i
$71$	−509.764	+	185.539i	−0.852082	+	0.310133i	−0.730889	−	0.682496i	$-0.760894\pi$
$71$	−509.764	+	185.539i	−0.852082	+	0.310133i	−0.121193	+	0.992629i	$0.538672\pi$
$72$	−67.6579	−	24.6255i	−0.110744	−	0.0403075i
$73$	−511.470	−	429.174i	−0.820041	−	0.688096i	0.132941	−	0.991124i	$-0.457558\pi$
$73$	−511.470	−	429.174i	−0.820041	−	0.688096i	−0.952982	+	0.303028i	$0.902002\pi$
$74$	46.8440	−	265.665i	0.0735879	−	0.417337i
$75$	−341.601			−0.525929
$76$	108.467	−	313.016i	0.163711	−	0.472439i
$77$	−824.063			−1.21962
$78$	64.5246	−	365.937i	0.0936663	−	0.531208i
$79$	−180.164	−	151.176i	−0.256583	−	0.215299i	0.505418	−	0.862875i	$-0.331338\pi$
$79$	−180.164	−	151.176i	−0.256583	−	0.215299i	−0.762001	+	0.647576i	$0.775783\pi$
$80$	50.1662	+	18.2590i	0.0701094	+	0.0255177i
$81$	−76.1151	+	27.7036i	−0.104410	+	0.0380022i
$82$	109.121	−	91.5630i	0.146956	−	0.123310i
$83$	−320.131	−	554.483i	−0.423360	−	0.733282i	0.572905	−	0.819621i	$-0.305816\pi$
$83$	−320.131	−	554.483i	−0.423360	−	0.733282i	−0.996266	+	0.0863399i	$0.972483\pi$
$84$	−202.014	+	349.898i	−0.262399	+	0.454488i
$85$	−67.5614	−	383.160i	−0.0862125	−	0.488935i
$86$	−85.8085	−	486.644i	−0.107593	−	0.610188i
$87$	−163.225	+	282.714i	−0.201144	+	0.348392i
$88$	97.9019	+	169.571i	0.118595	+	0.205413i
$89$	840.211	−	705.021i	1.00070	−	0.839686i	0.0136179	−	0.999907i	$-0.495665\pi$
$89$	840.211	−	705.021i	1.00070	−	0.839686i	0.987081	+	0.160221i	$0.0512207\pi$
$90$	56.4370	−	20.5414i	0.0660998	−	0.0240584i
$91$	−1959.38	−	713.156i	−2.25713	−	0.821528i
$92$	342.056	+	287.019i	0.387628	+	0.325258i
$93$	−75.5460	+	428.442i	−0.0842339	+	0.477714i
$94$	−846.938			−0.929309
$95$	98.5233	+	258.175i	0.106403	+	0.278823i
$96$	96.0000			0.102062
$97$	−144.813	+	821.273i	−0.151582	+	0.859666i	0.810262	+	0.586068i	$0.199325\pi$
$97$	−144.813	+	821.273i	−0.151582	+	0.859666i	−0.961844	+	0.273598i	$0.911786\pi$
$98$	1211.26	+	1016.37i	1.24853	+	1.04764i
$99$	206.995	+	75.3399i	0.210139	+	0.0764843i
$100$	428.000	−	155.779i	0.428000	−	0.155779i
$101$	1412.42	−	1185.16i	1.39150	−	1.16761i	0.426770	−	0.904360i	$-0.359652\pi$
$101$	1412.42	−	1185.16i	1.39150	−	1.16761i	0.964729	−	0.263245i	$-0.0847929\pi$
$102$	−349.819	−	605.905i	−0.339581	−	0.588172i
$103$	374.351	−	648.395i	0.358115	−	0.620274i	−0.629531	−	0.776976i	$-0.716753\pi$
$103$	374.351	−	648.395i	0.358115	−	0.620274i	0.987646	+	0.156702i	$0.0500861\pi$
$104$	86.0327	+	487.916i	0.0811174	+	0.460039i
$105$	−58.5230	−	331.900i	−0.0543929	−	0.308478i
$106$	582.777	−	1009.40i	0.534003	−	0.924920i
$107$	−245.736	−	425.627i	−0.222021	−	0.384551i	0.733401	−	0.679797i	$-0.237932\pi$
$107$	−245.736	−	425.627i	−0.222021	−	0.384551i	−0.955421	+	0.295245i	$0.904599\pi$
$108$	82.7328	−	69.4211i	0.0737127	−	0.0618523i
$109$	784.801	−	285.644i	0.689636	−	0.251007i	0.0266566	−	0.999645i	$-0.491514\pi$
$109$	784.801	−	285.644i	0.689636	−	0.251007i	0.662979	+	0.748638i	$0.269292\pi$
$110$	−153.480	−	55.8622i	−0.133034	−	0.0484205i
$111$	309.976	+	260.101i	0.265060	+	0.222412i
$112$	93.5448	−	530.519i	0.0789210	−	0.447583i
$113$	−1155.92			−0.962299			−0.481149	−	0.876639i	$-0.659781\pi$
$113$	−1155.92			−0.962299			−0.481149	+	0.876639i	$0.659781\pi$
$114$	325.269	+	375.665i	0.267230	+	0.308634i
$115$	−372.467			−0.302024
$116$	75.5832	−	428.654i	0.0604976	−	0.343099i
$117$	426.973	+	358.273i	0.337381	+	0.283097i
$118$	310.261	+	112.926i	0.242049	+	0.0880988i
$119$	−3689.25	+	1342.78i	−2.84196	+	1.03439i
$120$	−61.3438	+	51.4736i	−0.0466658	+	0.0391573i
$121$	365.976	+	633.889i	0.274963	+	0.476250i
$122$	692.518	−	1199.48i	0.513915	−	0.890127i
$123$	37.1034	+	210.424i	0.0271992	+	0.154254i
$124$	−100.728	−	571.257i	−0.0729487	−	0.413713i
$125$	−398.503	+	690.228i	−0.285146	+	0.493887i
$126$	−303.020	−	524.847i	−0.214248	−	0.371088i
$127$	801.240	−	672.320i	0.559831	−	0.469754i	−0.318423	−	0.947949i	$-0.603153\pi$
$127$	801.240	−	672.320i	0.559831	−	0.469754i	0.878254	+	0.478195i	$0.158709\pi$
$128$	−120.281	+	43.7786i	−0.0830579	+	0.0302306i
$129$	696.525	+	253.515i	0.475393	+	0.173029i
$130$	−316.587	−	265.648i	−0.213589	−	0.179222i
$131$	−88.6504	+	502.761i	−0.0591253	+	0.335316i	−0.999994	−	0.00345500i	$-0.998900\pi$
$131$	−88.6504	+	502.761i	−0.0591253	+	0.335316i	0.940869	+	0.338771i	$0.110011\pi$
$132$	−293.706			−0.193665
$133$	2392.96	−	1431.45i	1.56012	−	0.933255i
$134$	2064.21			1.33075
$135$	−15.6437	+	88.7198i	−0.00997330	+	0.0565614i
$136$	714.606	+	599.626i	0.450566	+	0.378070i
$137$	−1115.65	−	406.062i	−0.695738	−	0.253228i	−0.0301479	−	0.999545i	$-0.509598\pi$
$137$	−1115.65	−	406.062i	−0.695738	−	0.253228i	−0.665590	+	0.746318i	$0.731820\pi$
$138$	−629.390	+	229.079i	−0.388241	+	0.141308i
$139$	−550.856	+	462.223i	−0.336137	+	0.282052i	−0.795195	−	0.606354i	$-0.792631\pi$
$139$	−550.856	+	462.223i	−0.336137	+	0.282052i	0.459058	+	0.888406i	$0.348187\pi$
$140$	224.680	+	389.157i	0.135635	+	0.234927i
$141$	635.204	−	1100.21i	0.379389	−	0.657120i
$142$	188.401	+	1068.48i	0.111340	+	0.631440i
$143$	−263.211	−	1492.75i	−0.153922	−	0.872935i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	181.539	+	314.435i	0.103973	+	0.180086i
$146$	−1022.94	+	858.348i	−0.579856	+	0.486557i
$147$	−2228.75	+	811.200i	−1.25051	+	0.455147i
$148$	−506.990	−	184.529i	−0.281583	−	0.102488i
$149$	1074.09	+	901.272i	0.590558	+	0.495537i	0.888395	−	0.459080i	$-0.151821\pi$
$149$	1074.09	+	901.272i	0.590558	+	0.495537i	−0.297837	+	0.954617i	$0.596265\pi$
$150$	−118.637	+	672.823i	−0.0645777	+	0.366238i
$151$	−756.126			−0.407501			−0.203751	−	0.979023i	$-0.565313\pi$
$151$	−756.126			−0.407501			−0.203751	+	0.979023i	$0.565313\pi$
$152$	−578.850	−	322.348i	−0.308888	−	0.172012i
$153$	1049.46			0.554534
$154$	−286.194	+	1623.09i	−0.149754	+	0.849299i
$155$	370.663	+	311.023i	0.192080	+	0.161174i
$156$	−698.346	−	254.177i	−0.358413	−	0.130452i
$157$	1147.32	−	417.589i	0.583222	−	0.212275i	−0.0335236	−	0.999438i	$-0.510673\pi$
$157$	1147.32	−	417.589i	0.583222	−	0.212275i	0.616746	+	0.787162i	$0.288451\pi$
$158$	−360.328	+	302.351i	−0.181432	+	0.152239i
$159$	874.165	+	1514.10i	0.436012	+	0.755194i
$160$	53.3858	−	92.4669i	0.0263782	−	0.0456884i
$161$	652.653	+	3701.38i	0.319480	+	1.81186i
$162$	28.1310	+	159.539i	0.0136431	+	0.0773738i
$163$	482.996	−	836.573i	0.232093	−	0.401997i	−0.726331	−	0.687345i	$-0.758776\pi$
$163$	482.996	−	836.573i	0.232093	−	0.401997i	0.958424	+	0.285348i	$0.0921093\pi$
$164$	−142.447	−	246.725i	−0.0678246	−	0.117476i
$165$	187.677	−	157.480i	0.0885494	−	0.0743018i
$166$	−1203.30	+	437.965i	−0.562615	+	0.204775i
$167$	−2536.99	−	923.389i	−1.17556	−	0.427868i	−0.320927	−	0.947104i	$-0.603995\pi$
$167$	−2536.99	−	923.389i	−1.17556	−	0.427868i	−0.854631	+	0.519236i	$0.826217\pi$
$168$	619.005	+	519.407i	0.284270	+	0.238531i
$169$	284.500	−	1613.48i	0.129495	−	0.734401i
$170$	−778.141			−0.351063
$171$	−731.955	+	140.788i	−0.327333	+	0.0629609i
$172$	−988.302			−0.438124
$173$	−513.951	+	2914.76i	−0.225867	+	1.28096i	0.635154	+	0.772386i	$0.280937\pi$
$173$	−513.951	+	2914.76i	−0.225867	+	1.28096i	−0.861021	+	0.508570i	$0.830174\pi$
$174$	500.150	+	419.676i	0.217910	+	0.182848i
$175$	3602.57	+	1311.23i	1.55617	+	0.566398i
$176$	367.991	−	133.938i	0.157604	−	0.0573632i
$177$	−379.391	+	318.346i	−0.161112	+	0.135189i
$178$	−1096.82	−	1899.74i	−0.461854	−	0.799954i
$179$	966.439	−	1673.92i	0.403548	−	0.698965i	−0.590604	−	0.806962i	$-0.701110\pi$
$179$	966.439	−	1673.92i	0.403548	−	0.698965i	0.994151	+	0.107997i	$0.0344436\pi$
$180$	−20.8583	−	118.293i	−0.00863713	−	0.0489836i
$181$	125.516	+	711.838i	0.0515445	+	0.292323i	0.999673	−	0.0255634i	$-0.00813796\pi$
$181$	125.516	+	711.838i	0.0515445	+	0.292323i	−0.948129	+	0.317887i	$0.897027\pi$
$182$	−2085.13	+	3611.55i	−0.849231	+	1.47091i
$183$	1038.78	+	1799.22i	0.419610	+	0.726786i
$184$	684.111	−	574.038i	0.274094	−	0.229992i
$185$	422.907	−	153.926i	0.168069	−	0.0611721i
$186$	817.630	+	297.593i	0.322320	+	0.117315i
$187$	−2186.29	−	1834.51i	−0.854959	−	0.717396i
$188$	−294.139	+	1668.14i	−0.114108	+	0.647137i
$189$	909.061			0.349865
$190$	542.722	−	104.390i	0.207227	−	0.0398591i
$191$	2281.67			0.864378			0.432189	−	0.901783i	$-0.357741\pi$
$191$	2281.67			0.864378			0.432189	+	0.901783i	$0.357741\pi$
$192$	33.3405	−	189.083i	0.0125320	−	0.0710724i
$193$	−142.275	−	119.383i	−0.0530630	−	0.0445251i	0.615870	−	0.787847i	$-0.288804\pi$
$193$	−142.275	−	119.383i	−0.0530630	−	0.0445251i	−0.668933	+	0.743322i	$0.733249\pi$
$194$	1567.30	+	570.450i	0.580028	+	0.211113i
$195$	582.527	−	212.023i	0.213926	−	0.0778628i
$196$	2422.53	−	2032.74i	0.882845	−	0.740795i
$197$	897.971	+	1555.33i	0.324760	+	0.562502i	0.981464	−	0.191647i	$-0.0613830\pi$
$197$	897.971	+	1555.33i	0.324760	+	0.562502i	−0.656703	+	0.754149i	$0.728050\pi$
$198$	220.279	−	381.535i	0.0790634	−	0.136942i
$199$	211.302	+	1198.35i	0.0752704	+	0.426880i	0.999035	+	0.0439191i	$0.0139844\pi$
$199$	211.302	+	1198.35i	0.0752704	+	0.426880i	−0.923765	+	0.382961i	$0.874905\pi$
$200$	−158.182	−	897.097i	−0.0559259	−	0.317172i
$201$	−1548.16	+	2681.49i	−0.543277	+	0.940984i
$202$	−1843.79	−	3193.53i	−0.642220	−	1.11236i
$203$	2806.59	−	2355.01i	0.970363	−	0.814231i
$204$	−1314.89	+	478.581i	−0.451278	+	0.164252i
$205$	223.313	+	81.2793i	0.0760822	+	0.0276917i
$206$	−1147.08	−	962.512i	−0.387964	−	0.325541i
$207$	174.460	−	989.411i	0.0585787	−	0.332217i
$208$	990.886			0.330315
$209$	1770.95	+	986.203i	0.586122	+	0.326398i
$210$	−674.040			−0.221491
$211$	−196.322	+	1113.40i	−0.0640539	+	0.363268i	0.935886	+	0.352303i	$0.114601\pi$
$211$	−196.322	+	1113.40i	−0.0640539	+	0.363268i	−0.999940	+	0.0109647i	$0.996510\pi$
$212$	−1785.73	−	1498.41i	−0.578512	−	0.485429i
$213$	−1529.29	−	556.617i	−0.491950	−	0.179055i
$214$	−923.666	+	336.187i	−0.295049	+	0.107389i
$215$	631.523	−	529.911i	0.200323	−	0.168091i
$216$	−108.000	−	187.061i	−0.0340207	−	0.0589256i
$217$	2441.29	−	4228.43i	0.763712	−	1.32279i
$218$	−290.051	−	1644.96i	−0.0901134	−	0.511058i
$219$	−347.822	−	1972.60i	−0.107323	−	0.608657i
$220$	−163.330	+	282.896i	−0.0500533	+	0.0866948i
$221$	−3610.74	−	6253.99i	−1.09903	−	1.90357i
$222$	619.953	−	520.202i	0.187426	−	0.157269i
$223$	−4014.43	+	1461.13i	−1.20550	+	0.438765i	−0.865140	−	0.501531i	$-0.832770\pi$
$223$	−4014.43	+	1461.13i	−1.20550	+	0.438765i	−0.340358	+	0.940296i	$0.610548\pi$
$224$	−1012.43	−	368.494i	−0.301990	−	0.109915i
$225$	−785.045	−	658.731i	−0.232606	−	0.195180i
$226$	−401.447	+	2276.72i	−0.118159	+	0.670111i
$227$	1003.53			0.293422			0.146711	−	0.989179i	$-0.453131\pi$
$227$	1003.53			0.293422			0.146711	+	0.989179i	$0.453131\pi$
$228$	852.880	−	510.187i	0.247734	−	0.148193i
$229$	−4210.70			−1.21507			−0.607534	−	0.794293i	$-0.707841\pi$
$229$	−4210.70			−1.21507			−0.607534	+	0.794293i	$0.707841\pi$
$230$	−129.357	+	733.618i	−0.0370849	+	0.210319i
$231$	−1893.81	−	1589.09i	−0.539408	−	0.452617i
$232$	−818.033	−	297.740i	−0.231494	−	0.0842568i
$233$	5007.43	−	1822.55i	1.40793	−	0.512444i	0.477408	−	0.878682i	$-0.341576\pi$
$233$	5007.43	−	1822.55i	1.40793	−	0.512444i	0.930521	+	0.366237i	$0.119354\pi$
$234$	853.945	−	716.545i	0.238565	−	0.200180i
$235$	−706.476	−	1223.65i	−0.196108	−	0.339669i
$236$	330.173	−	571.876i	0.0910696	−	0.157737i
$237$	−122.520	−	694.844i	−0.0335802	−	0.190443i
$238$	1363.49	+	7732.74i	0.371353	+	2.10605i
$239$	607.601	−	1052.40i	0.164445	−	0.284828i	−0.772013	−	0.635607i	$-0.780750\pi$
$239$	607.601	−	1052.40i	0.164445	−	0.284828i	0.936458	+	0.350779i	$0.114083\pi$
$240$	80.0787	+	138.700i	0.0215377	+	0.0373044i
$241$	3181.73	−	2669.79i	0.850429	−	0.713595i	−0.109455	−	0.993992i	$-0.534910\pi$
$241$	3181.73	−	2669.79i	0.850429	−	0.713595i	0.959884	+	0.280397i	$0.0904661\pi$
$242$	1375.62	−	500.684i	0.365405	−	0.132997i
$243$	−228.345	−	83.1109i	−0.0602813	−	0.0219406i
$244$	−2122.00	−	1780.57i	−0.556750	−	0.467169i
$245$	−458.069	+	2597.84i	−0.119449	+	0.677427i
$246$	427.340			0.110757
$247$	3357.34	+	3877.51i	0.864867	+	0.998867i
$248$	−1160.14			−0.297052
$249$	333.541	−	1891.60i	0.0848887	−	0.481428i
$250$	1221.08	+	1024.61i	0.308913	+	0.259208i
$251$	−3072.34	−	1118.24i	−0.772607	−	0.281206i	−0.0745204	−	0.997219i	$-0.523743\pi$
$251$	−3072.34	−	1118.24i	−0.772607	−	0.281206i	−0.698086	+	0.716014i	$0.745965\pi$
$252$	−1138.98	+	414.556i	−0.284719	+	0.103629i
$253$	−2092.99	+	1756.23i	−0.520100	+	0.436416i
$254$	−1045.94	−	1811.63i	−0.258379	−	0.447526i
$255$	583.606	−	1010.83i	0.143321	−	0.248239i
$256$	44.4539	+	252.111i	0.0108530	+	0.0615505i
$257$	323.647	+	1835.50i	0.0785547	+	0.445506i	0.998562	+	0.0536052i	$0.0170713\pi$
$257$	323.647	+	1835.50i	0.0785547	+	0.445506i	−0.920007	+	0.391901i	$0.871818\pi$
$258$	741.227	−	1283.84i	0.178863	−	0.309801i
$259$	−2270.66	−	3932.90i	−0.544757	−	0.943547i
$260$	−633.174	+	531.296i	−0.151030	+	0.126729i
$261$	−920.287	+	334.957i	−0.218254	+	0.0794380i
$262$	959.458	+	349.214i	0.226243	+	0.0823455i
$263$	−1322.65	−	1109.83i	−0.310106	−	0.260210i	0.474430	−	0.880293i	$-0.342654\pi$
$263$	−1322.65	−	1109.83i	−0.310106	−	0.260210i	−0.784536	+	0.620084i	$0.787099\pi$
$264$	−102.003	+	578.487i	−0.0237797	+	0.134861i
$265$	1944.50			0.450753
$266$	−1988.35	−	5210.36i	−0.458321	−	1.20101i
$267$	3290.45			0.754204
$268$	716.893	−	4065.70i	0.163400	−	0.926688i
$269$	6044.97	+	5072.33i	1.37014	+	1.14969i	0.972702	+	0.232057i	$0.0745456\pi$
$269$	6044.97	+	5072.33i	1.37014	+	1.14969i	0.397439	+	0.917628i	$0.369899\pi$
$270$	169.311	+	61.6242i	0.0381627	+	0.0138901i
$271$	2045.24	−	744.408i	0.458449	−	0.166862i	−0.102464	−	0.994737i	$-0.532672\pi$
$271$	2045.24	−	744.408i	0.458449	−	0.166862i	0.560913	+	0.827875i	$0.310450\pi$
$272$	1429.21	−	1199.25i	0.318598	−	0.267336i
$273$	−3127.69	−	5417.32i	−0.693394	−	1.20099i
$274$	−1187.25	+	2056.37i	−0.261767	+	0.453394i
$275$	483.949	+	2744.61i	0.106121	+	0.601841i
$276$	232.613	+	1319.21i	0.0507307	+	0.287708i
$277$	−3255.04	+	5637.90i	−0.706053	+	1.22292i	0.260257	+	0.965539i	$0.416193\pi$
$277$	−3255.04	+	5637.90i	−0.706053	+	1.22292i	−0.966310	+	0.257380i	$0.917141\pi$
$278$	719.091	+	1245.50i	0.155137	+	0.268706i
$279$	−999.807	+	838.938i	−0.214541	+	0.180021i
$280$	844.521	−	307.381i	0.180249	−	0.0656054i
$281$	−1510.88	−	549.914i	−0.320752	−	0.116744i	0.176626	−	0.984278i	$-0.443482\pi$
$281$	−1510.88	−	549.914i	−0.320752	−	0.116744i	−0.497378	+	0.867534i	$0.665704\pi$
$282$	−1946.38	−	1633.20i	−0.411011	−	0.344879i
$283$	−1472.05	+	8348.39i	−0.309202	+	1.75357i	0.293835	+	0.955856i	$0.405068\pi$
$283$	−1472.05	+	8348.39i	−0.309202	+	1.75357i	−0.603037	+	0.797713i	$0.706043\pi$
$284$	2169.92			0.453384
$285$	−271.435	+	783.309i	−0.0564155	+	0.162804i
$286$	−3031.55			−0.626781
$287$	416.411	−	2361.58i	0.0856445	−	0.485714i
$288$	220.621	+	185.123i	0.0451396	+	0.0378766i
$289$	−8160.36	−	2970.13i	−1.66097	−	0.604544i
$290$	682.365	−	248.360i	0.138172	−	0.0502904i
$291$	−1916.51	+	1608.14i	−0.386075	+	0.323955i
$292$	1335.35	+	2312.90i	0.267622	+	0.463535i
$293$	166.965	−	289.191i	0.0332907	−	0.0576612i	−0.848900	−	0.528553i	$-0.822735\pi$
$293$	166.965	−	289.191i	0.0332907	−	0.0576612i	0.882191	+	0.470892i	$0.156068\pi$
$294$	823.714	+	4671.51i	0.163401	+	0.926694i
$295$	95.6505	+	542.461i	0.0188779	+	0.107062i
$296$	−539.527	+	934.489i	−0.105944	+	0.183500i
$297$	330.419	+	572.302i	0.0645550	+	0.111813i
$298$	2148.19	−	1802.54i	0.417588	−	0.350398i
$299$	−6496.39	+	2364.49i	−1.25651	+	0.457332i
$300$	1284.00	+	467.338i	0.247106	+	0.0899392i
$301$	−6372.55	−	5347.20i	−1.22029	−	1.02395i
$302$	−262.600	+	1489.28i	−0.0500362	+	0.283769i
$303$	5531.36			1.04874
$304$	−835.935	+	1028.16i	−0.157711	+	0.193977i
$305$	2310.66			0.433797
$306$	364.473	−	2067.03i	0.0680900	−	0.386158i
$307$	−1504.04	−	1262.04i	−0.279609	−	0.234620i	0.492188	−	0.870489i	$-0.336197\pi$
$307$	−1504.04	−	1262.04i	−0.279609	−	0.234620i	−0.771797	+	0.635869i	$0.780642\pi$
$308$	3097.46	+	1127.38i	0.573033	+	0.208567i
$309$	2110.65	−	768.213i	0.388578	−	0.141431i
$310$	741.326	−	622.046i	0.135821	−	0.113967i
$311$	−1743.17	−	3019.26i	−0.317833	−	0.550503i	0.662203	−	0.749325i	$-0.269622\pi$
$311$	−1743.17	−	3019.26i	−0.317833	−	0.550503i	−0.980036	+	0.198822i	$0.936288\pi$
$312$	−743.164	+	1287.20i	−0.134851	+	0.233568i
$313$	782.545	+	4438.03i	0.141316	+	0.801445i	0.970251	+	0.242100i	$0.0778362\pi$
$313$	782.545	+	4438.03i	0.141316	+	0.801445i	−0.828935	+	0.559345i	$0.811053\pi$
$314$	−424.031	−	2404.80i	−0.0762085	−	0.432200i
$315$	505.530	−	875.604i	0.0904235	−	0.156618i
$316$	470.375	+	814.714i	0.0837363	+	0.145036i
$317$	6133.24	−	5146.40i	1.08668	−	0.911832i	0.0902207	−	0.995922i	$-0.471243\pi$
$317$	6133.24	−	5146.40i	1.08668	−	0.911832i	0.996458	+	0.0840899i	$0.0267983\pi$
$318$	3285.79	−	1195.93i	0.579427	−	0.210894i
$319$	2502.72	+	910.915i	0.439264	+	0.159879i
$320$	−163.583	−	137.263i	−0.0285769	−	0.0239788i
$321$	256.030	−	1452.02i	0.0445177	−	0.252473i
$322$	7516.96			1.30094
$323$	9535.36	+	1529.44i	1.64261	+	0.263468i
$324$	324.000			0.0555556
$325$	−1224.54	+	6944.69i	−0.209000	+	1.18530i
$326$	−1479.98	−	1241.85i	−0.251438	−	0.210981i
$327$	2354.40	+	856.933i	0.398161	+	0.144919i
$328$	−535.425	+	194.879i	−0.0901338	+	0.0328060i
$329$	−10922.1	+	9164.70i	−1.83025	+	1.53576i
$330$	−244.995	−	424.344i	−0.0408683	−	0.0707860i
$331$	−1290.02	+	2234.37i	−0.214217	+	0.371034i	−0.953030	−	0.302876i	$-0.902053\pi$
$331$	−1290.02	+	2234.37i	−0.214217	+	0.371034i	0.738813	+	0.673910i	$0.235387\pi$
$332$	444.721	+	2522.14i	0.0735158	+	0.416929i
$333$	210.798	+	1195.49i	0.0346896	+	0.196735i
$334$	−2699.81	+	4676.21i	−0.442296	+	0.766080i
$335$	1721.87	+	2982.36i	0.280823	+	0.486400i
$336$	1238.01	−	1038.81i	0.201009	−	0.168667i
$337$	−2485.91	+	904.797i	−0.401828	+	0.146254i	−0.535025	−	0.844836i	$-0.679698\pi$
$337$	−2485.91	+	904.797i	−0.401828	+	0.146254i	0.133197	+	0.991090i	$0.457476\pi$
$338$	−3079.13	−	1120.71i	−0.495510	−	0.180351i
$339$	−2656.46	−	2229.03i	−0.425602	−	0.357122i
$340$	−270.245	+	1532.64i	−0.0431062	+	0.244468i
$341$	3549.37			0.563663
$342$	23.0926	+	1490.56i	0.00365119	+	0.235674i
$343$	15070.1			2.37233
$344$	−343.234	+	1946.58i	−0.0537963	+	0.305094i
$345$	−855.980	−	718.252i	−0.133578	−	0.112085i
$346$	5562.47	+	2024.57i	0.864278	+	0.314571i
$347$	−7562.67	+	2752.59i	−1.16999	+	0.425841i	−0.852655	−	0.522474i	$-0.825009\pi$
$347$	−7562.67	+	2752.59i	−1.16999	+	0.425841i	−0.317332	+	0.948314i	$0.602787\pi$
$348$	1000.30	−	839.352i	0.154085	−	0.129293i
$349$	1430.39	+	2477.51i	0.219390	+	0.379994i	0.954622	−	0.297822i	$-0.0962601\pi$
$349$	1430.39	+	2477.51i	0.219390	+	0.379994i	−0.735232	+	0.677816i	$0.762927\pi$
$350$	3833.78	−	6640.30i	0.585498	−	1.01411i
$351$	290.361	+	1646.72i	0.0441547	+	0.250414i
$352$	−136.004	−	771.316i	−0.0205938	−	0.116793i
$353$	3892.10	−	6741.32i	0.586844	−	1.01644i	−0.407799	−	0.913072i	$-0.633704\pi$
$353$	3892.10	−	6741.32i	0.586844	−	1.01644i	0.994643	−	0.103371i	$-0.0329630\pi$
$354$	495.259	+	857.814i	0.0743580	+	0.128792i
$355$	−1386.57	+	1163.47i	−0.207300	+	0.173946i
$356$	−4122.69	+	1500.54i	−0.613770	+	0.223394i
$357$	−11067.7	−	4028.33i	−1.64080	−	0.597204i
$358$	−2961.34	−	2484.86i	−0.437183	−	0.366840i
$359$	−1224.49	+	6944.41i	−0.180017	+	1.02092i	0.752176	+	0.658962i	$0.229004\pi$
$359$	−1224.49	+	6944.41i	−0.180017	+	1.02092i	−0.932193	+	0.361963i	$0.882107\pi$
$360$	−240.236			−0.0351710
$361$	−6855.71	+	212.476i	−0.999520	+	0.0309776i
$362$	1445.64			0.209893
$363$	−381.306	+	2162.49i	−0.0551333	+	0.312676i
$364$	6389.20	+	5361.18i	0.920014	+	0.771984i
$365$	−2093.42	−	761.944i	−0.300205	−	0.109266i
$366$	3904.53	−	1421.13i	0.557631	−	0.202961i
$367$	5860.18	−	4917.27i	0.833512	−	0.699400i	−0.122582	−	0.992458i	$-0.539118\pi$
$367$	5860.18	−	4917.27i	0.833512	−	0.699400i	0.956094	+	0.293059i	$0.0946732\pi$
$368$	−893.044	−	1546.80i	−0.126503	−	0.219110i
$369$	−320.505	+	555.132i	−0.0452164	+	0.0783171i
$370$	−156.300	−	886.422i	−0.0219612	−	0.124548i
$371$	−3407.23	−	19323.4i	−0.476805	−	2.70410i
$372$	870.104	−	1507.06i	0.121271	−	0.210047i
$373$	−2149.92	−	3723.77i	−0.298441	−	0.516915i	0.677338	−	0.735672i	$-0.263133\pi$
$373$	−2149.92	−	3723.77i	−0.298441	−	0.516915i	−0.975779	+	0.218756i	$0.929800\pi$
$374$	−4372.58	+	3669.03i	−0.604547	+	0.507275i
$375$	−2246.82	+	817.777i	−0.309401	+	0.112613i
$376$	3183.45	+	1158.68i	0.436632	+	0.158921i
$377$	5162.41	+	4331.78i	0.705246	+	0.591772i
$378$	315.714	−	1790.50i	0.0429591	−	0.243633i
$379$	1516.98			0.205599			0.102800	−	0.994702i	$-0.467220\pi$
$379$	1516.98			0.205599			0.102800	+	0.994702i	$0.467220\pi$
$380$	−17.1225	−	1105.21i	−0.00231148	−	0.149200i
$381$	3137.83			0.421932
$382$	792.417	−	4494.02i	0.106135	−	0.601922i
$383$	2583.04	+	2167.43i	0.344614	+	0.289166i	0.798623	−	0.601831i	$-0.205562\pi$
$383$	2583.04	+	2167.43i	0.344614	+	0.289166i	−0.454009	+	0.890997i	$0.650007\pi$
$384$	−360.842	−	131.336i	−0.0479535	−	0.0174536i
$385$	−2583.76	+	940.410i	−0.342027	+	0.124488i
$386$	−284.549	+	238.765i	−0.0375212	+	0.0314840i
$387$	1111.84	+	1925.76i	0.146041	+	0.252951i
$388$	1667.88	−	2888.86i	0.218232	−	0.377989i
$389$	−360.862	−	2046.55i	−0.0470345	−	0.266746i	0.952217	−	0.305421i	$-0.0987973\pi$
$389$	−360.862	−	2046.55i	−0.0470345	−	0.266746i	−0.999252	+	0.0386754i	$0.987686\pi$
$390$	−215.293	−	1220.99i	−0.0279533	−	0.158531i
$391$	−6508.42	+	11272.9i	−0.841803	+	1.45805i
$392$	−3162.39	−	5477.41i	−0.407461	−	0.705743i
$393$	−1173.24	+	984.462i	−0.150590	+	0.126360i
$394$	3375.27	−	1228.50i	0.431583	−	0.157083i
$395$	−737.405	−	268.393i	−0.0939313	−	0.0341882i
$396$	−674.975	−	566.371i	−0.0856534	−	0.0718718i
$397$	−1989.08	+	11280.7i	−0.251459	+	1.42610i	0.553541	+	0.832822i	$0.313276\pi$
$397$	−1989.08	+	11280.7i	−0.251459	+	1.42610i	−0.805001	+	0.593274i	$0.797835\pi$
$398$	2433.68			0.306506
$399$	8259.71	+	1324.83i	1.03635	+	0.166226i
$400$	−1821.87			−0.227734
$401$	−2367.37	+	13426.0i	−0.294815	+	1.67198i	0.373139	+	0.927775i	$0.378281\pi$
$401$	−2367.37	+	13426.0i	−0.294815	+	1.67198i	−0.667954	+	0.744203i	$0.732830\pi$
$402$	4743.83	+	3980.55i	0.588560	+	0.493860i
$403$	8439.35	+	3071.67i	1.04316	+	0.379680i
$404$	−6930.37	+	2522.45i	−0.853463	+	0.310635i
$405$	−207.035	+	173.723i	−0.0254017	+	0.0213145i
$406$	−3663.74	−	6345.78i	−0.447853	−	0.775704i
$407$	1650.65	−	2859.01i	0.201031	−	0.348196i
$408$	485.964	+	2756.04i	0.0589677	+	0.334422i
$409$	−2577.19	−	14616.0i	−0.311575	−	1.76703i	−0.590816	−	0.806806i	$-0.701194\pi$
$409$	−2577.19	−	14616.0i	−0.311575	−	1.76703i	0.279241	−	0.960221i	$-0.409917\pi$
$410$	237.645	−	411.613i	0.0286255	−	0.0495808i
$411$	−1780.87	−	3084.56i	−0.213732	−	0.370194i
$412$	−2294.16	+	1925.02i	−0.274332	+	0.230192i
$413$	5223.08	−	1901.04i	0.622302	−	0.226499i
$414$	−1888.17	−	687.238i	−0.224151	−	0.0815843i
$415$	−1636.50	−	1373.19i	−0.193573	−	0.162427i
$416$	344.131	−	1951.66i	0.0405587	−	0.230020i
$417$	−2157.27			−0.253338
$418$	2557.49	−	3145.59i	0.299260	−	0.368077i
$419$	−9162.88			−1.06834			−0.534172	−	0.845376i	$-0.679377\pi$
$419$	−9162.88			−1.06834			−0.534172	+	0.845376i	$0.679377\pi$
$420$	−234.092	+	1327.60i	−0.0271965	+	0.154239i
$421$	−7620.14	−	6394.05i	−0.882144	−	0.740207i	0.0844747	−	0.996426i	$-0.473079\pi$
$421$	−7620.14	−	6394.05i	−0.882144	−	0.740207i	−0.966619	+	0.256219i	$0.917523\pi$
$422$	2124.78	+	773.358i	0.245102	+	0.0892097i
$423$	3581.38	−	1303.51i	0.411661	−	0.149832i
$424$	−3571.46	+	2996.81i	−0.409070	+	0.343250i
$425$	6638.82	+	11498.8i	0.757717	+	1.31241i
$426$	−1627.44	+	2818.81i	−0.185093	+	0.320591i
$427$	−4048.84	−	22962.1i	−0.458869	−	2.60238i
$428$	341.373	+	1936.02i	0.0385535	+	0.218648i
$429$	2273.66	−	3938.10i	0.255882	−	0.443201i
$430$	−824.395	−	1427.89i	−0.0924555	−	0.160138i
$431$	2503.80	−	2100.94i	0.279823	−	0.234799i	−0.492064	−	0.870559i	$-0.663757\pi$
$431$	2503.80	−	2100.94i	0.279823	−	0.234799i	0.771887	+	0.635760i	$0.219313\pi$
$432$	−405.947	+	147.753i	−0.0452110	+	0.0164555i
$433$	5113.47	+	1861.15i	0.567523	+	0.206562i	0.609815	−	0.792544i	$-0.291244\pi$
$433$	5113.47	+	1861.15i	0.567523	+	0.206562i	−0.0422918	+	0.999105i	$0.513466\pi$
$434$	−7480.54	−	6276.92i	−0.827367	−	0.694244i
$435$	−189.144	+	1072.69i	−0.0208477	+	0.118233i
$436$	−3340.67			−0.366948
$437$	3027.07	−	8735.52i	0.331360	−	0.956240i
$438$	−4006.06			−0.437025
$439$	750.706	−	4257.47i	0.0816156	−	0.462865i	−0.916420	−	0.400218i	$-0.868935\pi$
$439$	750.706	−	4257.47i	0.0816156	−	0.462865i	0.998036	−	0.0626475i	$-0.0199544\pi$
$440$	500.473	+	419.947i	0.0542252	+	0.0455004i
$441$	−6686.26	−	2433.60i	−0.721980	−	0.262779i
$442$	−13571.9	+	4939.78i	−1.46052	+	0.531587i
$443$	−3890.70	+	3264.68i	−0.417275	+	0.350135i	−0.827125	−	0.562018i	$-0.810025\pi$
$443$	−3890.70	+	3264.68i	−0.417275	+	0.350135i	0.409851	+	0.912153i	$0.365581\pi$
$444$	−809.291	−	1401.73i	−0.0865028	−	0.149827i
$445$	1829.83	−	3169.35i	0.194926	−	0.337622i
$446$	1483.67	+	8414.32i	0.157520	+	0.893340i
$447$	730.432	+	4142.48i	0.0772891	+	0.438328i
$448$	−1077.41	+	1866.12i	−0.113622	+	0.196799i
$449$	−5242.19	−	9079.75i	−0.550990	−	0.954343i	−0.998203	−	0.0599153i	$-0.980917\pi$
$449$	−5242.19	−	9079.75i	−0.550990	−	0.954343i	0.447214	−	0.894427i	$-0.352416\pi$
$450$	−1570.09	+	1317.46i	−0.164477	+	0.138013i
$451$	1638.10	−	596.219i	0.171031	−	0.0622502i
$452$	4344.84	+	1581.39i	0.452133	+	0.164563i
$453$	−1737.68	−	1458.09i	−0.180228	−	0.151229i
$454$	348.523	−	1976.57i	0.0360286	−	0.204328i
$455$	−6957.26			−0.716838
$456$	−708.671	−	1857.03i	−0.0727775	−	0.190709i
$457$	−12289.0			−1.25789			−0.628946	−	0.777449i	$-0.716513\pi$
$457$	−12289.0			−1.25789			−0.628946	+	0.777449i	$0.716513\pi$
$458$	−1462.36	+	8293.46i	−0.149196	+	0.846130i
$459$	2411.80	+	2023.74i	0.245257	+	0.205795i
$460$	1400.02	+	509.566i	0.141905	+	0.0516492i
$461$	−14564.0	+	5300.86i	−1.47139	+	0.535544i	−0.948479	−	0.316840i	$-0.897378\pi$
$461$	−14564.0	+	5300.86i	−1.47139	+	0.535544i	−0.522916	+	0.852384i	$0.675156\pi$
$462$	−3787.61	+	3178.18i	−0.381419	+	0.320049i
$463$	9443.53	+	16356.7i	0.947901	+	1.64181i	0.749836	+	0.661624i	$0.230133\pi$
$463$	9443.53	+	16356.7i	0.947901	+	1.64181i	0.198065	+	0.980189i	$0.436534\pi$
$464$	−870.533	+	1507.81i	−0.0870980	+	0.150858i
$465$	252.067	+	1429.55i	0.0251384	+	0.142567i
$466$	−1850.67	−	10495.7i	−0.183971	−	1.04335i
$467$	8364.76	−	14488.2i	0.828854	−	1.43562i	−0.0700843	−	0.997541i	$-0.522327\pi$
$467$	8364.76	−	14488.2i	0.828854	−	1.43562i	0.898938	−	0.438076i	$-0.144340\pi$
$468$	−1114.75	−	1930.80i	−0.110105	−	0.190708i
$469$	26620.0	−	22336.8i	2.62089	−	2.19919i
$470$	−2655.48	+	966.516i	−0.260613	+	0.0948554i
$471$	3441.95	+	1252.77i	0.336723	+	0.122557i
$472$	−1011.71	−	848.924i	−0.0986603	−	0.0827858i
$473$	1050.10	−	5955.42i	0.102080	−	0.578923i
$474$	−1411.13			−0.136741
$475$	−6172.90	−	7129.31i	−0.596278	−	0.688664i
$476$	15704.1			1.51217
$477$	−910.783	+	5165.31i	−0.0874254	+	0.495814i
$478$	−1861.80	−	1562.23i	−0.178152	−	0.149487i
$479$	17389.2	+	6329.14i	1.65873	+	0.603729i	0.990162	−	0.139922i	$-0.0446853\pi$
$479$	17389.2	+	6329.14i	1.65873	+	0.603729i	0.668568	+	0.743651i	$0.266908\pi$
$480$	300.997	−	109.554i	0.0286220	−	0.0104176i
$481$	6398.98	−	5369.38i	0.606587	−	0.508987i
$482$	−4153.46	−	7194.00i	−0.392500	−	0.679829i
$483$	−5637.72	+	9764.81i	−0.531108	+	0.919906i
$484$	−508.408	−	2883.33i	−0.0477468	−	0.270786i
$485$	483.183	+	2740.27i	0.0452376	+	0.256555i
$486$	−243.000	+	420.888i	−0.0226805	+	0.0392837i
$487$	−3960.91	−	6860.49i	−0.368554	−	0.638354i	0.620786	−	0.783980i	$-0.286814\pi$
$487$	−3960.91	−	6860.49i	−0.368554	−	0.638354i	−0.989340	+	0.145626i	$0.953480\pi$
$488$	−4244.00	+	3561.14i	−0.393682	+	0.330338i
$489$	2723.20	−	991.165i	0.251836	−	0.0916606i
$490$	4957.65	+	1804.44i	0.457069	+	0.166360i
$491$	−12057.5	−	10117.4i	−1.10824	−	0.929925i	−0.110290	−	0.993899i	$-0.535178\pi$
$491$	−12057.5	−	10117.4i	−1.10824	−	0.929925i	−0.997952	+	0.0639744i	$0.979622\pi$
$492$	148.414	−	841.696i	0.0135996	−	0.0771272i
$493$	12688.7			1.15917
$494$	8803.20	−	5266.01i	0.801770	−	0.479614i
$495$	734.986			0.0667377
$496$	−402.912	+	2285.03i	−0.0364743	+	0.206856i
$497$	13991.6	+	11740.3i	1.26279	+	1.05961i
$498$	−3609.89	−	1313.89i	−0.324826	−	0.118227i
$499$	11312.0	−	4117.24i	1.01482	−	0.369365i	0.219539	−	0.975604i	$-0.429545\pi$
$499$	11312.0	−	4117.24i	1.01482	−	0.369365i	0.795282	+	0.606239i	$0.207323\pi$
$500$	2442.17	−	2049.22i	0.218434	−	0.183288i
$501$	−4049.71	−	7014.31i	−0.361134	−	0.625502i
$502$	−3269.51	+	5662.96i	−0.290688	+	0.503487i
$503$	2091.77	+	11863.0i	0.185422	+	1.05158i	0.925412	+	0.378963i	$0.123719\pi$
$503$	2091.77	+	11863.0i	0.185422	+	1.05158i	−0.739990	+	0.672618i	$0.765170\pi$
$504$	420.951	+	2387.33i	0.0372037	+	0.210993i
$505$	3076.00	−	5327.79i	0.271050	−	0.469472i
$506$	2732.21	+	4732.32i	0.240042	+	0.415766i
$507$	3765.19	−	3159.37i	0.329818	−	0.276751i
$508$	−3931.46	+	1430.94i	−0.343367	+	0.124975i
$509$	−10338.1	−	3762.77i	−0.900254	−	0.327666i	−0.149899	−	0.988701i	$-0.547895\pi$
$509$	−10338.1	−	3762.77i	−0.900254	−	0.327666i	−0.750355	+	0.661036i	$0.770117\pi$
$510$	−1788.27	−	1500.54i	−0.155267	−	0.130284i
$511$	−3903.60	+	22138.4i	−0.337936	+	1.91653i
$512$	512.000			0.0441942
$513$	−1953.62	−	1087.93i	−0.168137	−	0.0936317i
$514$	3727.62			0.319880
$515$	433.795	−	2460.17i	0.0371171	−	0.210501i
$516$	−2271.25	−	1905.81i	−0.193772	−	0.162594i
$517$	−9739.54	−	3544.90i	−0.828520	−	0.301556i
$518$	−8534.90	+	3106.45i	−0.723942	+	0.263493i
$519$	−6801.85	+	5707.43i	−0.575276	+	0.482714i
$520$	826.550	+	1431.63i	0.0697050	+	0.120733i
$521$	−8103.69	+	14036.0i	−0.681438	+	1.18029i	0.293104	+	0.956081i	$0.405312\pi$
$521$	−8103.69	+	14036.0i	−0.681438	+	1.18029i	−0.974542	+	0.224205i	$0.928022\pi$
$522$	340.124	+	1928.94i	0.0285189	+	0.161738i
$523$	3932.47	+	22302.2i	0.328786	+	1.86464i	0.481612	+	0.876385i	$0.340051\pi$
$523$	3932.47	+	22302.2i	0.328786	+	1.86464i	−0.152826	+	0.988253i	$0.548837\pi$
$524$	1021.03	−	1768.48i	0.0851223	−	0.147436i
$525$	5750.67	+	9960.45i	0.478057	+	0.828019i
$526$	−2645.29	+	2219.66i	−0.219278	+	0.183996i
$527$	15890.2	−	5783.54i	1.31345	−	0.478055i
$528$	1103.97	+	401.813i	0.0909928	+	0.0331187i
$529$	225.498	+	189.216i	0.0185336	+	0.0155515i
$530$	675.318	−	3829.92i	0.0553470	−	0.313889i
$531$	−1485.78			−0.121426
$532$	−10952.9	+	2106.74i	−0.892614	+	0.171690i
$533$	4410.89			0.358456
$534$	1142.76	−	6480.93i	0.0926071	−	0.525201i
$535$	−1256.20	−	1054.08i	−0.101514	−	0.0851807i
$536$	−7758.90	−	2824.01i	−0.625249	−	0.227572i
$537$	5448.93	−	1983.25i	0.437875	−	0.159373i
$538$	12089.9	−	10144.7i	0.968836	−	0.812950i
$539$	9675.11	+	16757.8i	0.773166	+	1.33916i
$540$	180.177	−	312.076i	0.0143585	−	0.0248696i
$541$	−1835.71	−	10410.8i	−0.145884	−	0.827349i	−0.966653	−	0.256089i	$-0.917566\pi$
$541$	−1835.71	−	10410.8i	−0.145884	−	0.827349i	0.820769	−	0.571260i	$-0.193545\pi$
$542$	−755.892	−	4286.88i	−0.0599047	−	0.339736i
$543$	−1084.23	+	1877.94i	−0.0856883	+	0.148416i
$544$	−1865.70	−	3231.49i	−0.147043	−	0.254686i
$545$	2134.68	−	1791.21i	0.167779	−	0.140784i
$546$	−11756.3	+	4278.94i	−0.921469	+	0.335387i
$547$	−5476.76	−	1993.38i	−0.428097	−	0.155815i	0.118980	−	0.992897i	$-0.462038\pi$
$547$	−5476.76	−	1993.38i	−0.428097	−	0.155815i	−0.547078	+	0.837082i	$0.684260\pi$
$548$	3637.93	+	3052.59i	0.283585	+	0.237956i
$549$	−1082.29	+	6137.98i	−0.0841367	+	0.477163i
$550$	5573.90			0.432131
$551$	−8849.87	+	1702.23i	−0.684242	+	0.131610i
$552$	2679.13			0.206579
$553$	−1375.04	+	7798.21i	−0.105737	+	0.599663i
$554$	9974.03	+	8369.21i	0.764903	+	0.641830i
$555$	1268.72	+	461.777i	0.0970346	+	0.0353177i
$556$	2702.90	−	983.775i	0.206166	−	0.0750384i
$557$	−672.971	+	564.689i	−0.0511933	+	0.0429563i	−0.668025	−	0.744139i	$-0.732860\pi$
$557$	−672.971	+	564.689i	−0.0511933	+	0.0429563i	0.616832	+	0.787095i	$0.288416\pi$
$558$	1305.16	+	2260.60i	0.0990173	+	0.171503i
$559$	7650.74	−	13251.5i	0.578876	−	1.00264i
$560$	−312.122	−	1770.13i	−0.0235528	−	0.133575i
$561$	−1486.77	−	8431.92i	−0.111892	−	0.634574i
$562$	−1607.84	+	2784.86i	−0.120681	+	0.209026i
$563$	3676.31	+	6367.56i	0.275201	+	0.476662i	0.970186	−	0.242363i	$-0.0779223\pi$
$563$	3676.31	+	6367.56i	0.275201	+	0.476662i	−0.694985	+	0.719024i	$0.744589\pi$
$564$	−3892.75	+	3266.41i	−0.290629	+	0.243866i
$565$	−3624.26	+	1319.12i	−0.269865	+	0.0982228i
$566$	15931.9	+	5798.73i	1.18316	+	0.430634i
$567$	2089.14	+	1753.00i	0.154737	+	0.129840i
$568$	753.605	−	4273.90i	0.0556700	−	0.315720i
$569$	−12329.2			−0.908378			−0.454189	−	0.890905i	$-0.650071\pi$
$569$	−12329.2			−0.908378			−0.454189	+	0.890905i	$0.650071\pi$
$570$	1448.55	+	806.663i	0.106444	+	0.0592761i
$571$	3706.04			0.271616			0.135808	−	0.990735i	$-0.456637\pi$
$571$	3706.04			0.271616			0.135808	+	0.990735i	$0.456637\pi$
$572$	−1052.85	+	5970.99i	−0.0769610	+	0.436468i
$573$	5243.59	+	4399.90i	0.382294	+	0.320782i
$574$	−4506.79	−	1640.34i	−0.327718	−	0.119279i
$575$	11944.5	−	4347.43i	0.866293	−	0.315305i
$576$	441.242	−	370.246i	0.0319185	−	0.0267828i
$577$	−4321.74	−	7485.47i	−0.311813	−	0.540076i	0.666942	−	0.745110i	$-0.267603\pi$
$577$	−4321.74	−	7485.47i	−0.311813	−	0.540076i	−0.978755	+	0.205034i	$0.934270\pi$
$578$	−8684.07	+	15041.3i	−0.624930	+	1.08241i
$579$	−96.7532	−	548.714i	−0.00694460	−	0.0393848i
$580$	−252.192	−	1430.25i	−0.0180546	−	0.102393i
$581$	−10778.5	+	18668.8i	−0.769648	+	1.33307i
$582$	2501.83	+	4333.29i	0.178186	+	0.308627i
$583$	10926.7	−	9168.56i	0.776220	−	0.651326i
$584$	5019.28	−	1826.87i	0.355650	−	0.129446i
$585$	1747.58	+	636.068i	0.123510	+	0.0449541i
$586$	−511.610	−	429.291i	−0.0360655	−	0.0302626i
$587$	−682.204	+	3868.97i	−0.0479686	+	0.272043i	−0.999353	−	0.0359622i	$-0.988550\pi$
$587$	−682.204	+	3868.97i	−0.0479686	+	0.272043i	0.951385	+	0.308006i	$0.0996615\pi$
$588$	9487.16			0.665380
$589$	−10306.9	+	6165.50i	−0.721031	+	0.431316i
$590$	1101.66			0.0768721
$591$	−935.587	+	5305.98i	−0.0651183	+	0.369304i
$592$	1653.21	+	1387.21i	0.114774	+	0.0963071i
$593$	−285.354	−	103.860i	−0.0197607	−	0.00719229i	0.332121	−	0.943237i	$-0.392236\pi$
$593$	−285.354	−	103.860i	−0.0197607	−	0.00719229i	−0.351882	+	0.936045i	$0.614458\pi$
$594$	1241.97	−	452.040i	0.0857889	−	0.0312246i
$595$	−10034.9	+	8420.25i	−0.691410	+	0.580162i
$596$	−2804.26	−	4857.12i	−0.192730	−	0.333818i
$597$	−1825.26	+	3161.44i	−0.125131	+	0.216732i
$598$	2400.97	+	13616.6i	0.164186	+	0.931142i
$599$	−2986.40	−	16936.7i	−0.203708	−	1.15528i	−0.899460	−	0.437003i	$-0.856040\pi$
$599$	−2986.40	−	16936.7i	−0.203708	−	1.15528i	0.695752	−	0.718282i	$-0.255071\pi$
$600$	1366.40	−	2366.68i	0.0929720	−	0.161032i
$601$	12029.4	+	20835.6i	0.816458	+	1.41415i	0.908276	+	0.418371i	$0.137399\pi$
$601$	12029.4	+	20835.6i	0.816458	+	1.41415i	−0.0918185	+	0.995776i	$0.529268\pi$
$602$	−12745.1	+	10694.4i	−0.862876	+	0.724039i
$603$	−8728.76	+	3177.01i	−0.589490	+	0.214557i
$604$	2842.10	+	1034.44i	0.191463	+	0.0696868i
$605$	1870.86	+	1569.84i	0.125721	+	0.105493i
$606$	1921.02	−	10894.7i	0.128773	−	0.730306i
$607$	1335.01			0.0892690			0.0446345	−	0.999003i	$-0.485788\pi$
$607$	1335.01			0.0892690			0.0446345	+	0.999003i	$0.485788\pi$
$608$	1734.77	+	2003.55i	0.115714	+	0.133642i
$609$	10991.2			0.731341
$610$	802.485	−	4551.12i	0.0532650	−	0.302081i
$611$	−20090.0	−	16857.5i	−1.33020	−	1.11617i
$612$	−3944.67	−	1435.74i	−0.260546	−	0.0948309i
$613$	−14398.0	+	5240.44i	−0.948662	+	0.345285i	−0.769581	−	0.638550i	$-0.779535\pi$
$613$	−14398.0	+	5240.44i	−0.948662	+	0.345285i	−0.179081	+	0.983834i	$0.557313\pi$
$614$	−3008.08	+	2524.08i	−0.197713	+	0.165901i
$615$	356.467	+	617.419i	0.0233726	+	0.0404825i
$616$	3296.25	−	5709.27i	0.215600	−	0.373431i
$617$	−1336.81	−	7581.41i	−0.0872250	−	0.494677i	−0.996854	−	0.0792565i	$-0.974745\pi$
$617$	−1336.81	−	7581.41i	−0.0872250	−	0.494677i	0.909629	−	0.415421i	$-0.136366\pi$
$618$	−780.064	−	4423.96i	−0.0507747	−	0.287958i
$619$	−2459.41	+	4259.83i	−0.159697	+	0.276603i	−0.934759	−	0.355282i	$-0.884385\pi$
$619$	−2459.41	+	4259.83i	−0.159697	+	0.276603i	0.775063	+	0.631884i	$0.217718\pi$
$620$	−967.732	−	1676.16i	−0.0626856	−	0.108575i
$621$	2308.88	−	1937.38i	0.149198	−	0.125192i
$622$	−6552.18	+	2384.80i	−0.422377	+	0.153733i
$623$	−34701.6	−	12630.4i	−2.23161	−	0.812238i
$624$	2277.19	+	1910.79i	0.146090	+	0.122584i
$625$	2009.82	−	11398.2i	0.128628	−	0.729488i
$626$	9012.99			0.575450
$627$	2168.13	+	5681.47i	0.138097	+	0.361876i
$628$	−4883.80			−0.310326
$629$	2731.16	−	15489.2i	0.173129	−	0.981865i
$630$	−1549.03	−	1299.79i	−0.0979604	−	0.0821985i
$631$	−7771.42	−	2828.57i	−0.490294	−	0.178452i	0.0850296	−	0.996378i	$-0.472902\pi$
$631$	−7771.42	−	2828.57i	−0.490294	−	0.178452i	−0.575323	+	0.817926i	$0.695124\pi$
$632$	1768.03	−	643.511i	0.111279	−	0.0405024i
$633$	−2598.21	+	2180.16i	−0.163143	+	0.136893i
$634$	−8006.38	−	13867.5i	−0.501536	−	0.868686i
$635$	1744.95	−	3022.35i	0.109049	−	0.188879i
$636$	−1214.38	−	6887.08i	−0.0757126	−	0.429388i
$637$	8502.15	+	48218.1i	0.528834	+	2.99917i
$638$	2663.34	−	4613.04i	0.165270	−	0.286257i
$639$	−2441.16	−	4228.21i	−0.151128	−	0.261761i
$640$	−327.167	+	274.526i	−0.0202069	+	0.0169556i
$641$	−20428.6	+	7435.40i	−1.25878	+	0.458160i	−0.883361	−	0.468693i	$-0.844725\pi$
$641$	−20428.6	+	7435.40i	−1.25878	+	0.458160i	−0.375423	+	0.926853i	$0.622503\pi$
$642$	−2771.00	−	1008.56i	−0.170347	−	0.0620011i
$643$	−14203.1	−	11917.8i	−0.871099	−	0.730939i	0.0932304	−	0.995645i	$-0.470281\pi$
$643$	−14203.1	−	11917.8i	−0.871099	−	0.730939i	−0.964329	+	0.264706i	$0.914725\pi$
$644$	2610.61	−	14805.5i	0.159740	−	0.905930i
$645$	2473.19			0.150979
$646$	6324.00	−	18249.8i	0.385162	−	1.11150i
$647$	20316.3			1.23449			0.617244	−	0.786771i	$-0.288249\pi$
$647$	20316.3			1.23449			0.617244	+	0.786771i	$0.288249\pi$
$648$	112.524	−	638.155i	0.00682154	−	0.0386869i
$649$	3095.25	+	2597.23i	0.187210	+	0.157088i
$650$	13253.1	+	4823.73i	0.799737	+	0.291081i
$651$	13764.4	−	5009.82i	0.828676	−	0.301613i
$652$	−2959.97	+	2483.71i	−0.177793	+	0.149186i
$653$	−5584.90	−	9673.33i	−0.334692	−	0.579704i	0.648733	−	0.761016i	$-0.275299\pi$
$653$	−5584.90	−	9673.33i	−0.334692	−	0.579704i	−0.983426	+	0.181312i	$0.941966\pi$
$654$	2505.50	−	4339.66i	0.149806	−	0.259471i
$655$	295.792	+	1677.52i	0.0176451	+	0.100070i
$656$	197.885	+	1122.26i	0.0117776	+	0.0667941i
$657$	3004.54	−	5204.02i	0.178415	−	0.309023i
$658$	14257.7	+	24695.1i	0.844719	+	1.46310i
$659$	−16645.0	+	13966.8i	−0.983911	+	0.825600i	−0.984675	−	0.174400i	$-0.944201\pi$
$659$	−16645.0	+	13966.8i	−0.983911	+	0.825600i	0.000763533		1.00000i	$0.499757\pi$
$660$	−920.881	+	335.173i	−0.0543110	+	0.0197676i
$661$	4281.78	+	1558.44i	0.251954	+	0.0917039i	0.464910	−	0.885358i	$-0.346087\pi$
$661$	4281.78	+	1558.44i	0.251954	+	0.0917039i	−0.212956	+	0.977062i	$0.568309\pi$
$662$	3952.84	+	3316.83i	0.232072	+	0.194731i
$663$	3761.99	−	21335.3i	0.220367	−	1.24977i
$664$	5122.09			0.299361
$665$	5869.31	−	7218.99i	0.342259	−	0.420963i
$666$	2427.87			0.141259
$667$	2109.35	−	11962.7i	0.122450	−	0.694450i
$668$	8272.70	+	6941.62i	0.479162	+	0.402065i
$669$	−12043.3	−	4383.40i	−0.695994	−	0.253321i
$670$	6472.11	−	2355.65i	0.373193	−	0.135831i
$671$	12984.2	−	10895.1i	0.747020	−	0.626825i
$672$	−1616.11	−	2799.18i	−0.0927719	−	0.160686i
$673$	−6336.35	+	10974.9i	−0.362925	+	0.628604i	−0.988441	−	0.151607i	$-0.951555\pi$
$673$	−6336.35	+	10974.9i	−0.362925	+	0.628604i	0.625516	+	0.780211i	$0.284888\pi$
$674$	918.755	+	5210.52i	0.0525061	+	0.297777i
$675$	−533.866	−	3027.70i	−0.0304422	−	0.172646i
$676$	−3276.74	+	5675.48i	−0.186432	+	0.322911i
$677$	−6539.59	−	11326.9i	−0.371251	−	0.643026i	0.618507	−	0.785779i	$-0.287738\pi$
$677$	−6539.59	−	11326.9i	−0.371251	−	0.643026i	−0.989758	+	0.142753i	$0.954404\pi$
$678$	−5312.91	+	4458.06i	−0.300946	+	0.252524i
$679$	26384.6	−	9603.22i	1.49124	−	0.542765i
$680$	2924.85	+	1064.56i	0.164946	+	0.0600353i
$681$	2306.25	+	1935.17i	0.129773	+	0.108893i
$682$	1232.68	−	6990.89i	0.0692109	−	0.392514i
$683$	−4662.01			−0.261181			−0.130591	−	0.991436i	$-0.541687\pi$
$683$	−4662.01			−0.261181			−0.130591	+	0.991436i	$0.541687\pi$
$684$	2943.86	+	472.184i	0.164563	+	0.0263953i
$685$	−3961.38			−0.220958
$686$	5233.79	−	29682.3i	0.291293	−	1.65200i
$687$	−9676.74	−	8119.75i	−0.537396	−	0.450929i
$688$	3714.80	+	1352.08i	0.205851	+	0.0749236i
$689$	33915.0	−	12344.0i	1.87527	−	0.682541i
$690$	−1711.96	+	1436.50i	−0.0944539	+	0.0792562i
$691$	8074.66	+	13985.7i	0.444536	+	0.769959i	0.998020	−	0.0629009i	$-0.0200352\pi$
$691$	8074.66	+	13985.7i	0.444536	+	0.769959i	−0.553484	+	0.832860i	$0.686702\pi$
$692$	5919.46	−	10252.8i	0.325179	−	0.563227i
$693$	−1287.87	−	7303.89i	−0.0705949	−	0.400363i
$694$	2795.05	+	15851.5i	0.152880	+	0.867025i
$695$	−1199.66	+	2077.88i	−0.0654760	+	0.113408i
$696$	−1305.80	−	2261.71i	−0.0711152	−	0.123175i
$697$	6362.08	−	5338.42i	0.345740	−	0.290111i
$698$	5376.51	−	1956.89i	0.291553	−	0.106116i
$699$	15022.3	+	5467.66i	0.812868	+	0.295860i
$700$	−11747.4	−	9857.23i	−0.634299	−	0.532240i
$701$	−2190.02	+	12420.2i	−0.117997	+	0.669196i	0.867225	+	0.497916i	$0.165901\pi$
$701$	−2190.02	+	12420.2i	−0.117997	+	0.669196i	−0.985222	+	0.171280i	$0.945210\pi$
$702$	3344.24			0.179801
$703$	173.043	+	11169.4i	0.00928370	+	0.599237i
$704$	−1566.43			−0.0838594
$705$	736.069	−	4174.46i	0.0393220	−	0.223006i
$706$	−11926.1	−	10007.2i	−0.635757	−	0.533464i
$707$	−58334.5	−	21232.0i	−3.10311	−	1.12944i
$708$	1861.57	−	677.555i	0.0988163	−	0.0359662i
$709$	−2378.53	+	1995.82i	−0.125991	+	0.105719i	−0.703606	−	0.710590i	$-0.748428\pi$
$709$	−2378.53	+	1995.82i	−0.125991	+	0.105719i	0.577615	+	0.816309i	$0.303983\pi$
$710$	1810.04	+	3135.09i	0.0956756	+	0.165715i
$711$	1058.34	−	1833.11i	0.0558242	−	0.0966904i
$712$	1523.68	+	8641.24i	0.0802001	+	0.454837i
$713$	−2811.08	−	15942.4i	−0.147652	−	0.837375i
$714$	−11778.0	+	20400.2i	−0.617342	+	1.06927i
$715$	−2528.77	−	4379.97i	−0.132267	−	0.229093i
$716$	−5922.68	+	4969.72i	−0.309135	+	0.259395i
$717$	3425.75	−	1246.87i	0.178434	−	0.0649445i
$718$	13252.6	+	4823.54i	0.688832	+	0.250714i
$719$	13548.3	+	11368.3i	0.702732	+	0.589662i	0.922550	−	0.385879i	$-0.126102\pi$
$719$	13548.3	+	11368.3i	0.702732	+	0.589662i	−0.219817	+	0.975541i	$0.570546\pi$
$720$	−83.4331	+	473.172i	−0.00431857	+	0.0244918i
$721$	−25208.0			−1.30207
$722$	−1962.47	+	13576.9i	−0.101157	+	0.699834i
$723$	12460.4			0.640949
$724$	502.065	−	2847.35i	0.0257722	−	0.146162i
$725$	−9491.77	−	7964.54i	−0.486228	−	0.407994i
$726$	4126.86	+	1502.05i	0.210967	+	0.0767857i
$727$	−13796.3	+	5021.45i	−0.703820	+	0.256170i	−0.669041	−	0.743225i	$-0.733295\pi$
$727$	−13796.3	+	5021.45i	−0.703820	+	0.256170i	−0.0347791	+	0.999395i	$0.511073\pi$
$728$	12778.4	−	10722.4i	0.650548	−	0.545875i
$729$	−364.500	−	631.333i	−0.0185185	−	0.0320750i
$730$	−2227.77	+	3858.62i	−0.112950	+	0.195635i
$731$	−5002.91	−	28372.9i	−0.253132	−	1.43558i
$732$	−1443.05	−	8183.97i	−0.0728645	−	0.413235i
$733$	16643.3	−	28827.1i	0.838656	−	1.45259i	−0.0523631	−	0.998628i	$-0.516675\pi$
$733$	16643.3	−	28827.1i	0.838656	−	1.45259i	0.891019	−	0.453966i	$-0.149991\pi$
$734$	−7649.92	−	13250.1i	−0.384692	−	0.666306i
$735$	−6062.27	+	5086.85i	−0.304232	+	0.255281i
$736$	−3356.75	+	1221.76i	−0.168113	+	0.0611882i
$737$	23737.8	+	8639.87i	1.18642	+	0.431823i
$738$	982.085	+	824.067i	0.0489852	+	0.0411034i
$739$	303.654	−	1722.11i	0.0151151	−	0.0857223i	−0.976317	−	0.216345i	$-0.930586\pi$
$739$	303.654	−	1722.11i	0.0151151	−	0.0857223i	0.991432	+	0.130623i	$0.0416976\pi$
$740$	−1800.19			−0.0894276
$741$	238.356	+	15385.2i	0.0118168	+	0.762739i
$742$	−39242.9			−1.94158
$743$	−3916.77	+	22213.1i	−0.193395	+	1.09680i	0.721291	+	0.692632i	$0.243549\pi$
$743$	−3916.77	+	22213.1i	−0.193395	+	1.09680i	−0.914686	+	0.404165i	$0.867562\pi$
$744$	−2666.15	−	2237.17i	−0.131379	−	0.110240i
$745$	4396.22	+	1600.09i	0.216195	+	0.0786884i
$746$	−8081.05	+	2941.26i	−0.396606	+	0.144353i
$747$	4414.22	−	3703.97i	0.216209	−	0.181421i
$748$	5708.00	+	9886.54i	0.279017	+	0.483272i
$749$	−8273.67	+	14330.4i	−0.403623	+	0.699095i
$750$	830.392	+	4709.39i	0.0404288	+	0.229283i
$751$	6655.70	+	37746.3i	0.323395	+	1.83407i	0.520721	+	0.853727i	$0.325663\pi$
$751$	6655.70	+	37746.3i	0.323395	+	1.83407i	−0.197325	+	0.980338i	$0.563226\pi$
$752$	3387.75	−	5867.76i	0.164280	−	0.284541i
$753$	−4904.27	−	8494.45i	−0.237346	−	0.411095i
$754$	10324.8	−	8663.56i	0.498684	−	0.418446i
$755$	−2370.75	+	862.882i	−0.114279	+	0.0415940i
$756$	−3416.95	−	1243.67i	−0.164383	−	0.0598304i
$757$	−9799.44	−	8222.71i	−0.470498	−	0.394794i	0.376478	−	0.926425i	$-0.377135\pi$
$757$	−9799.44	−	8222.71i	−0.470498	−	0.394794i	−0.846976	+	0.531631i	$0.821579\pi$
$758$	526.842	−	2987.87i	0.0252451	−	0.143172i
$759$	−8196.63			−0.391988
$760$	−2182.78	−	350.110i	−0.104181	−	0.0167103i
$761$	6981.41			0.332557			0.166278	−	0.986079i	$-0.446825\pi$
$761$	6981.41			0.332557			0.166278	+	0.986079i	$0.446825\pi$
$762$	1089.76	−	6180.32i	0.0518081	−	0.293818i
$763$	−21540.6	−	18074.7i	−1.02205	−	0.857598i
$764$	−8576.29	−	3121.51i	−0.406125	−	0.147817i
$765$	3290.46	−	1197.63i	0.155512	−	0.0566018i
$766$	5166.08	−	4334.86i	0.243679	−	0.204471i
$767$	5111.93	+	8854.12i	0.240653	+	0.416824i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	−3160.09	−	17921.7i	−0.148187	−	0.840409i	−0.964753	−	0.263157i	$-0.915236\pi$
$769$	−3160.09	−	17921.7i	−0.148187	−	0.840409i	0.816566	−	0.577252i	$-0.195875\pi$
$770$	954.918	+	5415.61i	0.0446920	+	0.253461i
$771$	−2795.72	+	4842.32i	−0.130590	+	0.226189i
$772$	371.453	+	643.375i	0.0173172	+	0.0299943i
$773$	−638.829	+	536.041i	−0.0297246	+	0.0249419i	−0.657529	−	0.753429i	$-0.728398\pi$
$773$	−638.829	+	536.041i	−0.0297246	+	0.0249419i	0.627804	+	0.778371i	$0.283954\pi$
$774$	4179.15	−	1521.09i	0.194078	−	0.0706387i
$775$	−15516.8	−	5647.67i	−0.719202	−	0.261768i
$776$	−5110.69	−	4288.38i	−0.236422	−	0.198381i
$777$	2365.78	−	13417.0i	0.109230	−	0.619475i
$778$	−4156.24			−0.191528
$779$	−3721.13	+	4576.83i	−0.171147	+	0.210503i
$780$	−2479.65			−0.113828
$781$	−2305.60	+	13075.7i	−0.105635	+	0.599086i
$782$	19943.0	+	16734.1i	0.911967	+	0.765232i
$783$	−2760.86	−	1004.87i	−0.126009	−	0.0458636i
$784$	−11886.7	+	4326.40i	−0.541485	+	0.197084i
$785$	3120.74	−	2618.61i	0.141890	−	0.119060i
$786$	1531.55	+	2652.73i	0.0695021	+	0.120381i
$787$	−8509.77	+	14739.4i	−0.385439	+	0.667600i	−0.991830	−	0.127566i	$-0.959283\pi$
$787$	−8509.77	+	14739.4i	−0.385439	+	0.667600i	0.606391	+	0.795167i	$0.292617\pi$
$788$	−1247.45	−	7074.63i	−0.0563941	−	0.319827i
$789$	−899.459	−	5101.08i	−0.0405850	−	0.230169i
$790$	−784.730	+	1359.19i	−0.0353410	+	0.0612125i
$791$	19459.3	+	33704.5i	0.874706	+	1.51504i
$792$	−1349.95	+	1132.74i	−0.0605661	+	0.0508210i
$793$	40301.4	−	14668.5i	1.80472	−	0.656866i
$794$	21527.8	+	7835.46i	0.962206	+	0.350214i
$795$	4468.72	+	3749.70i	0.199357	+	0.167281i
$796$	845.208	−	4793.42i	0.0376352	−	0.213440i
$797$	−10965.7			−0.487361			−0.243680	−	0.969856i	$-0.578355\pi$
$797$	−10965.7			−0.487361			−0.243680	+	0.969856i	$0.578355\pi$
$798$	5477.97	−	15808.4i	0.243005	−	0.701265i
$799$	−49379.2			−2.18637
$800$	−632.730	+	3588.39i	−0.0279630	+	0.158586i
$801$	7561.90	+	6345.19i	0.333566	+	0.279895i
$802$	25621.9	+	9325.61i	1.12811	+	0.410597i
$803$	−15356.2	+	5589.18i	−0.674853	+	0.245626i
$804$	9487.67	−	7961.10i	0.416175	−	0.349212i
$805$	6270.29	+	10860.5i	0.274532	+	0.475504i
$806$	8980.97	−	15555.5i	0.392483	−	0.679800i
$807$	4110.85	+	23313.8i	0.179317	+	1.01696i
$808$	2561.36	+	14526.2i	0.111520	+	0.632463i
$809$	3969.22	−	6874.88i	0.172497	−	0.298774i	−0.766795	−	0.641892i	$-0.778150\pi$
$809$	3969.22	−	6874.88i	0.172497	−	0.298774i	0.939292	+	0.343118i	$0.111483\pi$
$810$	270.265	+	468.113i	0.0117237	+	0.0203060i
$811$	−6597.21	+	5535.71i	−0.285646	+	0.239686i	−0.774340	−	0.632770i	$-0.781918\pi$
$811$	−6597.21	+	5535.71i	−0.285646	+	0.239686i	0.488694	+	0.872455i	$0.337474\pi$
$812$	−13771.1	+	5012.29i	−0.595163	+	0.216622i
$813$	6135.73	+	2233.22i	0.264686	+	0.0963378i
$814$	−5057.88	−	4244.06i	−0.217787	−	0.182745i
$815$	559.692	−	3174.17i	0.0240554	−	0.136425i
$816$	5597.11			0.240120
$817$	7295.64	+	19117.8i	0.312414	+	0.818663i
$818$	−29682.9			−1.26875
$819$	3258.71	−	18481.1i	0.139034	−	0.788499i
$820$	−728.186	−	611.020i	−0.0310114	−	0.0260217i
$821$	43087.7	+	15682.6i	1.83163	+	0.666660i	0.992425	+	0.122851i	$0.0392038\pi$
$821$	43087.7	+	15682.6i	1.83163	+	0.666660i	0.839209	+	0.543809i	$0.183018\pi$
$822$	−6693.88	+	2436.37i	−0.284034	+	0.103380i
$823$	−18224.6	+	15292.2i	−0.771894	+	0.647696i	−0.941193	−	0.337869i	$-0.890294\pi$
$823$	−18224.6	+	15292.2i	−0.771894	+	0.647696i	0.169299	+	0.985565i	$0.445850\pi$
$824$	2994.81	+	5187.16i	0.126613	+	0.219300i
$825$	−4180.42	+	7240.71i	−0.176417	+	0.305562i
$826$	−1930.37	−	10947.7i	−0.0813150	−	0.461160i
$827$	−5058.25	−	28686.8i	−0.212688	−	1.20621i	−0.884874	−	0.465830i	$-0.845756\pi$
$827$	−5058.25	−	28686.8i	−0.212688	−	1.20621i	0.672187	−	0.740382i	$-0.265355\pi$
$828$	−2009.35	+	3480.29i	−0.0843354	+	0.146073i
$829$	3779.24	+	6545.83i	0.158333	+	0.274241i	0.934268	−	0.356572i	$-0.116055\pi$
$829$	3779.24	+	6545.83i	0.158333	+	0.274241i	−0.775934	+	0.630814i	$0.782721\pi$
$830$	−3273.01	+	2746.38i	−0.136877	+	0.114853i
$831$	−18352.4	+	6679.74i	−0.766112	+	0.278842i
$832$	−3724.51	−	1355.61i	−0.155197	−	0.0564872i
$833$	70620.6	+	59257.7i	2.93741	+	2.46478i
$834$	−749.213	+	4249.00i	−0.0311069	+	0.176416i
$835$	−9008.21			−0.373344
$836$	−5307.40	−	6129.72i	−0.219570	−	0.253589i
$837$	−3915.47			−0.161695
$838$	−3182.24	+	18047.4i	−0.131180	+	0.743956i
$839$	53.5618	+	44.9437i	0.00220400	+	0.00184938i	0.643889	−	0.765119i	$-0.277320\pi$
$839$	53.5618	+	44.9437i	0.00220400	+	0.00184938i	−0.641685	+	0.766968i	$0.721764\pi$
$840$	2533.56	+	922.142i	0.104067	+	0.0378773i
$841$	11791.2	−	4291.65i	0.483464	−	0.175967i
$842$	−15240.3	+	12788.1i	−0.623770	+	0.523405i
$843$	−2411.76	−	4177.30i	−0.0985356	−	0.170669i
$844$	2261.15	−	3916.42i	0.0922179	−	0.159726i
$845$	−949.265	−	5383.55i	−0.0386458	−	0.219171i
$846$	−1323.62	−	7506.64i	−0.0537909	−	0.305063i
$847$	12322.0	−	21342.3i	0.499869	−	0.865799i
$848$	4662.22	+	8075.19i	0.188799	+	0.327009i
$849$	−19481.7	+	16347.1i	−0.787526	+	0.660813i
$850$	24953.8	−	9082.44i	1.00695	−	0.366500i
$851$	−14148.9	−	5149.77i	−0.569938	−	0.207441i
$852$	4986.76	+	4184.39i	0.200521	+	0.168257i
$853$	−3895.06	+	22090.0i	−0.156347	+	0.886690i	0.801196	+	0.598402i	$0.204197\pi$
$853$	−3895.06	+	22090.0i	−0.156347	+	0.886690i	−0.957544	+	0.288288i	$0.906914\pi$
$854$	−46632.7			−1.86855
$855$	−2134.30	+	1276.72i	−0.0853701	+	0.0510678i
$856$	3931.78			0.156992
$857$	4936.96	−	27998.9i	0.196783	−	1.11601i	−0.713073	−	0.701090i	$-0.752697\pi$
$857$	4936.96	−	27998.9i	0.196783	−	1.11601i	0.909856	−	0.414924i	$-0.136192\pi$
$858$	−6966.90	−	5845.93i	−0.277210	−	0.232607i
$859$	38313.1	+	13944.8i	1.52180	+	0.553891i	0.961597	−	0.274464i	$-0.0885004\pi$
$859$	38313.1	+	13944.8i	1.52180	+	0.553891i	0.560204	+	0.828354i	$0.310723\pi$
$860$	−3098.71	+	1127.84i	−0.122867	+	0.0447198i
$861$	5510.96	−	4624.24i	0.218134	−	0.183036i
$862$	−3268.48	−	5661.17i	−0.129147	−	0.223689i
$863$	21040.2	−	36442.7i	0.829916	−	1.43746i	−0.0681876	−	0.997673i	$-0.521722\pi$
$863$	21040.2	−	36442.7i	0.829916	−	1.43746i	0.898104	−	0.439784i	$-0.144945\pi$
$864$	150.032	+	850.874i	0.00590763	+	0.0335038i
$865$	1714.86	+	9725.43i	0.0674067	+	0.382283i
$866$	5441.64	−	9425.20i	0.213527	−	0.369840i
$867$	−13026.1	−	22561.9i	−0.510253	−	0.883785i
$868$	−14961.1	+	12553.8i	−0.585037	+	0.490904i
$869$	−5409.18	+	1968.78i	−0.211155	+	0.0768542i
$870$	2047.09	+	745.081i	0.0797735	+	0.0290352i
$871$	48964.6	+	41086.1i	1.90482	+	1.59834i
$872$	−1160.20	+	6579.84i	−0.0450567	+	0.255529i
$873$	−7505.48			−0.290976
$874$	−16154.3	−	8995.97i	−0.625204	−	0.348162i
$875$	26834.3			1.03676
$876$	−1391.29	+	7890.39i	−0.0536613	+	0.304328i
$877$	11953.6	+	10030.3i	0.460257	+	0.386201i	0.843226	−	0.537560i	$-0.180654\pi$
$877$	11953.6	+	10030.3i	0.460257	+	0.386201i	−0.382969	+	0.923761i	$0.625098\pi$
$878$	−8124.86	−	2957.21i	−0.312301	−	0.113668i
$879$	941.373	−	342.632i	0.0361226	−	0.0131475i
$880$	1000.95	−	839.893i	0.0383430	−	0.0321736i
$881$	14676.2	+	25419.9i	0.561241	+	0.972098i	0.997389	+	0.0722225i	$0.0230092\pi$
$881$	14676.2	+	25419.9i	0.561241	+	0.972098i	−0.436148	+	0.899875i	$0.643657\pi$
$882$	−7115.37	+	12324.2i	−0.271640	+	0.470495i
$883$	2118.57	+	12015.0i	0.0807424	+	0.457913i	0.998194	+	0.0600664i	$0.0191313\pi$
$883$	2118.57	+	12015.0i	0.0807424	+	0.457913i	−0.917452	+	0.397847i	$0.869758\pi$
$884$	5015.99	+	28447.1i	0.190844	+	1.08233i
$885$	−826.244	+	1431.10i	−0.0313829	+	0.0543568i
$886$	5078.95	+	8797.00i	0.192585	+	0.333568i
$887$	−2084.54	+	1749.14i	−0.0789087	+	0.0662123i	−0.681389	−	0.731922i	$-0.738624\pi$
$887$	−2084.54	+	1749.14i	−0.0789087	+	0.0662123i	0.602480	+	0.798134i	$0.294179\pi$
$888$	−3041.94	+	1107.18i	−0.114956	+	0.0418405i
$889$	−33092.0	−	12044.5i	−1.24845	−	0.454398i
$890$	−5606.92	−	4704.76i	−0.211173	−	0.177195i
$891$	−344.260	+	1952.39i	−0.0129440	+	0.0734093i
$892$	17088.3			0.641432
$893$	34440.0	−	6624.37i	1.29058	−	0.248237i
$894$	8412.78			0.314726
$895$	1119.90	−	6351.28i	0.0418259	−	0.237207i
$896$	3301.36	+	2770.17i	0.123092	+	0.103287i
$897$	−19489.2	−	7093.48i	−0.725446	−	0.264041i
$898$	−19704.2	+	7171.74i	−0.732225	+	0.266508i
$899$	−12088.4	+	10143.4i	−0.448466	+	0.376307i
$900$	2049.61	+	3550.02i	0.0759114	+	0.131482i
$901$	33977.8	−	58851.3i	1.25634	−	2.17605i
$902$	−605.416	−	3433.49i	−0.0223483	−	0.126743i
$903$	−4333.62	−	24577.2i	−0.159705	−	0.905733i
$904$	4623.68	−	8008.45i	0.170112	−	0.294643i
$905$	1205.88	+	2088.65i	0.0442927	+	0.0767173i
$906$	−3475.36	+	2916.17i	−0.127440	+	0.106935i
$907$	37092.7	−	13500.6i	1.35793	−	0.494246i	0.442516	−	0.896761i	$-0.354086\pi$
$907$	37092.7	−	13500.6i	1.35793	−	0.494246i	0.915413	+	0.402515i	$0.131864\pi$
$908$	−3772.05	−	1372.91i	−0.137863	−	0.0501781i
$909$	12711.8	+	10666.5i	0.463833	+	0.389202i
$910$	−2416.23	+	13703.1i	−0.0880190	+	0.499181i
$911$	8902.80			0.323779			0.161890	−	0.986809i	$-0.448241\pi$
$911$	8902.80			0.323779			0.161890	+	0.986809i	$0.448241\pi$
$912$	−3903.76	+	750.868i	−0.141739	+	0.0272629i
$913$	−15670.7			−0.568044
$914$	−4267.94	+	24204.7i	−0.154454	+	0.875951i
$915$	5310.21	+	4455.80i	0.191858	+	0.160988i
$916$	15827.0	+	5760.57i	0.570896	+	0.207789i
$917$	16152.0	−	5878.83i	0.581663	−	0.211708i
$918$	4823.59	−	4047.47i	0.173423	−	0.145519i
$919$	−15628.1	−	27068.6i	−0.560960	−	0.971611i	−0.997413	−	0.0718842i	$-0.977099\pi$
$919$	−15628.1	−	27068.6i	−0.560960	−	0.971611i	0.436453	−	0.899727i	$-0.356235\pi$
$920$	1489.87	−	2580.53i	0.0533908	−	0.0924756i
$921$	−1022.81	−	5800.66i	−0.0365937	−	0.207533i
$922$	5382.64	+	30526.4i	0.192264	+	1.09038i
$923$	−16798.0	+	29094.9i	−0.599038	+	1.03756i
$924$	4944.38	+	8563.91i	0.176037	+	0.304905i
$925$	−11765.4	+	9872.31i	−0.418208	+	0.350919i
$926$	35496.1	−	12919.5i	1.25969	−	0.458490i
$927$	6331.95	+	2304.64i	0.224346	+	0.0816551i
$928$	2667.47	+	2238.27i	0.0943576	+	0.0791755i
$929$	3492.97	−	19809.6i	0.123359	−	0.699605i	−0.858910	−	0.512127i	$-0.828858\pi$
$929$	3492.97	−	19809.6i	0.123359	−	0.699605i	0.982269	−	0.187478i	$-0.0600312\pi$
$930$	2903.20			0.102365
$931$	−57204.6	−	31855.9i	−2.01375	−	1.12141i
$932$	−21315.2			−0.749144
$933$	1816.19	−	10300.1i	0.0637292	−	0.361426i
$934$	−25631.1	−	21507.0i	−0.897939	−	0.753460i
$935$	−8948.39	−	3256.95i	−0.312988	−	0.113918i
$936$	−4190.08	+	1525.06i	−0.146321	+	0.0532567i
$937$	24141.0	−	20256.7i	0.841678	−	0.706252i	−0.116263	−	0.993218i	$-0.537091\pi$
$937$	24141.0	−	20256.7i	0.841678	−	0.706252i	0.957940	+	0.286967i	$0.0926470\pi$
$938$	−34749.9	−	60188.6i	−1.20962	−	2.09512i
$939$	−6759.74	+	11708.2i	−0.234926	+	0.406904i
$940$	981.426	+	5565.94i	0.0340538	+	0.193129i
$941$	−6909.32	−	39184.7i	−0.239360	−	1.35748i	−0.833235	−	0.552919i	$-0.813514\pi$
$941$	−6909.32	−	39184.7i	−0.239360	−	1.35748i	0.593876	−	0.804557i	$-0.297597\pi$
$942$	3662.85	−	6344.24i	0.126690	−	0.219434i
$943$	−3975.35	−	6885.51i	−0.137280	−	0.237776i
$944$	−2023.42	+	1697.85i	−0.0697633	+	0.0585384i
$945$	2850.26	−	1037.41i	0.0981153	−	0.0357110i
$946$	−11365.2	−	4136.59i	−0.390607	−	0.142169i
$947$	31637.4	+	26546.9i	1.08561	+	0.910939i	0.996375	−	0.0850712i	$-0.0271118\pi$
$947$	31637.4	+	26546.9i	1.08561	+	0.910939i	0.0892399	+	0.996010i	$0.471556\pi$
$948$	−490.079	+	2779.38i	−0.0167901	+	0.0952214i
$949$	−41349.4			−1.41439
$950$	−16185.8	+	9682.25i	−0.552776	+	0.330667i
$951$	24019.1			0.819005
$952$	5453.96	−	30931.0i	0.185676	−	1.05302i
$953$	−43560.6	−	36551.6i	−1.48066	−	1.24242i	−0.905481	−	0.424387i	$-0.860490\pi$
$953$	−43560.6	−	36551.6i	−1.48066	−	1.24242i	−0.575175	−	0.818030i	$-0.695066\pi$
$954$	9857.36	+	3587.79i	0.334532	+	0.121760i
$955$	7153.94	−	2603.82i	0.242404	−	0.0882279i
$956$	−3723.59	+	3124.47i	−0.125972	+	0.105703i
$957$	3995.01	+	6919.55i	0.134943	+	0.233728i
$958$	18505.2	−	32051.9i	0.624087	−	1.08095i
$959$	6941.29	+	39366.0i	0.233729	+	1.32554i
$960$	−111.244	−	630.897i	−0.00373999	−	0.0212105i
$961$	4380.49	−	7587.24i	0.147041	−	0.254682i
$962$	−8353.28	−	14468.3i	−0.279959	−	0.484903i
$963$	3388.41	−	2843.21i	0.113385	−	0.0951414i
$964$	−15611.9	+	5682.27i	−0.521603	+	0.189848i
$965$	−582.324	−	211.949i	−0.0194256	−	0.00707033i
$966$	17275.0	+	14495.4i	0.575376	+	0.482798i
$967$	8916.70	−	50569.1i	0.296527	−	1.68169i	−0.364404	−	0.931241i	$-0.618727\pi$
$967$	8916.70	−	50569.1i	0.296527	−	1.68169i	0.660931	−	0.750447i	$-0.270162\pi$
$968$	−5855.61			−0.194428
$969$	18964.2	+	21902.5i	0.628709	+	0.726119i
$970$	5565.08			0.184210
$971$	−1369.14	+	7764.76i	−0.0452499	+	0.256625i	−0.999038	−	0.0438554i	$-0.986036\pi$
$971$	−1369.14	+	7764.76i	−0.0452499	+	0.256625i	0.953788	+	0.300480i	$0.0971470\pi$
$972$	744.595	+	624.790i	0.0245709	+	0.0206174i
$973$	22750.9	+	8280.66i	0.749600	+	0.272832i
$974$	−14888.1	+	5418.84i	−0.489781	+	0.178266i
$975$	−16206.0	+	13598.5i	−0.532316	+	0.446667i
$976$	5540.15	+	9595.81i	0.181696	+	0.314708i
$977$	−24354.7	+	42183.5i	−0.797518	+	1.38134i	0.123710	+	0.992318i	$0.460521\pi$
$977$	−24354.7	+	42183.5i	−0.797518	+	1.38134i	−0.921228	+	0.389023i	$0.872813\pi$
$978$	−1006.46	−	5707.89i	−0.0329069	−	0.186624i
$979$	−4661.61	−	26437.3i	−0.152181	−	0.863064i
$980$	5275.82	−	9138.00i	0.171969	−	0.297860i
$981$	3758.26	+	6509.49i	0.122316	+	0.211857i
$982$	−24115.0	+	20234.9i	−0.783645	+	0.657556i
$983$	−4891.63	+	1780.41i	−0.158717	+	0.0577683i	−0.420157	−	0.907451i	$-0.638025\pi$
$983$	−4891.63	+	1780.41i	−0.158717	+	0.0577683i	0.261440	+	0.965220i	$0.415803\pi$
$984$	−1606.27	−	584.636i	−0.0520388	−	0.0189406i
$985$	4590.42	+	3851.82i	0.148490	+	0.124598i
$986$	4406.75	−	24991.9i	0.142332	−	0.807205i
$987$	−42773.2			−1.37942
$988$	−7314.71	−	19167.8i	−0.235538	−	0.617215i
$989$	−27581.2			−0.886785
$990$	255.258	−	1447.64i	0.00819458	−	0.0464737i
$991$	−31949.8	−	26809.1i	−1.02414	−	0.859352i	−0.0339946	−	0.999422i	$-0.510823\pi$
$991$	−31949.8	−	26809.1i	−1.02414	−	0.859352i	−0.990142	+	0.140070i	$0.955267\pi$
$992$	4360.69	+	1587.16i	0.139569	+	0.0507989i
$993$	−7273.32	+	2647.27i	−0.232439	+	0.0846008i
$994$	27983.1	−	23480.6i	0.892929	−	0.749256i
$995$	2030.06	+	3516.17i	0.0646807	+	0.112030i
$996$	−3841.57	+	6653.79i	−0.122214	+	0.211680i
$997$	−2073.93	−	11761.9i	−0.0658797	−	0.373623i	−0.999867	−	0.0163160i	$-0.994806\pi$
$997$	−2073.93	−	11761.9i	−0.0658797	−	0.373623i	0.933987	−	0.357307i	$-0.116305\pi$
$998$	−4180.75	−	23710.2i	−0.132605	−	0.752038i
$999$	−1820.90	+	3153.90i	−0.0576685	+	0.0998849i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.i.d.55.2	✓	18	1.1	even	1	trivial
114.4.i.d.85.2	yes	18	19.9	even	9	inner
2166.4.a.bj.1.5		9	19.3	odd	18
2166.4.a.bm.1.5		9	19.16	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.347296 - 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(3.13539 - 1.14119i) q^{5} +(4.59627 - 3.85673i) q^{6} +(-16.8345 - 29.1581i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +O(q^{10})\)	\(q+(0.347296 - 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(3.13539 - 1.14119i) q^{5} +(4.59627 - 3.85673i) q^{6} +(-16.8345 - 29.1581i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +(-1.15879 - 6.57184i) q^{10} +(12.2377 - 21.1964i) q^{11} +(-6.00000 - 10.3923i) q^{12} +(47.4414 - 39.8081i) q^{13} +(-63.2769 + 23.0309i) q^{14} +(9.40616 + 3.42356i) q^{15} +(12.2567 + 10.2846i) q^{16} +(20.2485 - 114.835i) q^{17} +18.0000 q^{18} +(1.28292 + 82.8091i) q^{19} -13.3464 q^{20} +(17.5396 - 99.4722i) q^{21} +(-37.4986 - 31.4651i) q^{22} +(-104.898 - 38.1799i) q^{23} +(-22.5526 + 8.20848i) q^{24} +(-87.2272 + 73.1923i) q^{25} +(-61.9304 - 107.267i) q^{26} +(-13.5000 + 23.3827i) q^{27} +(23.3862 + 132.630i) q^{28} +(18.8958 + 107.163i) q^{29} +(10.0098 - 17.3375i) q^{30} +(72.5086 + 125.589i) q^{31} +(24.5134 - 20.5692i) q^{32} +(68.9983 - 25.1133i) q^{33} +(-219.148 - 79.7635i) q^{34} +(-86.0575 - 72.2108i) q^{35} +(6.25133 - 35.4531i) q^{36} +134.882 q^{37} +(163.548 + 26.2324i) q^{38} +185.791 q^{39} +(-4.63517 + 26.2874i) q^{40} +(54.5603 + 45.7815i) q^{41} +(-189.831 - 69.0927i) q^{42} +(232.175 - 84.5048i) q^{43} +(-74.9972 + 62.9301i) q^{44} +(15.0147 + 26.0063i) q^{45} +(-111.630 + 193.350i) q^{46} +(-73.5346 - 417.036i) q^{47} +(8.33511 + 47.2708i) q^{48} +(-395.298 + 684.677i) q^{49} +(113.867 + 197.223i) q^{50} +(267.977 - 224.860i) q^{51} +(-232.782 + 84.7257i) q^{52} +(547.631 + 199.321i) q^{53} +(41.3664 + 34.7105i) q^{54} +(14.1810 - 80.4244i) q^{55} +269.351 q^{56} +(-156.738 + 192.780i) q^{57} +217.633 q^{58} +(-28.6670 + 162.578i) q^{59} +(-30.6719 - 25.7368i) q^{60} +(650.754 + 236.855i) q^{61} +(272.543 - 99.1977i) q^{62} +(232.127 - 194.778i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(103.319 - 178.953i) q^{65} +(-25.5007 - 144.622i) q^{66} +(179.223 + 1016.43i) q^{67} +(-233.213 + 403.937i) q^{68} +(-167.446 - 290.025i) q^{69} +(-172.115 + 144.422i) q^{70} +(-509.764 + 185.539i) q^{71} +(-67.6579 - 24.6255i) q^{72} +(-511.470 - 429.174i) q^{73} +(46.8440 - 265.665i) q^{74} -341.601 q^{75} +(108.467 - 313.016i) q^{76} -824.063 q^{77} +(64.5246 - 365.937i) q^{78} +(-180.164 - 151.176i) q^{79} +(50.1662 + 18.2590i) q^{80} +(-76.1151 + 27.7036i) q^{81} +(109.121 - 91.5630i) q^{82} +(-320.131 - 554.483i) q^{83} +(-202.014 + 349.898i) q^{84} +(-67.5614 - 383.160i) q^{85} +(-85.8085 - 486.644i) q^{86} +(-163.225 + 282.714i) q^{87} +(97.9019 + 169.571i) q^{88} +(840.211 - 705.021i) q^{89} +(56.4370 - 20.5414i) q^{90} +(-1959.38 - 713.156i) q^{91} +(342.056 + 287.019i) q^{92} +(-75.5460 + 428.442i) q^{93} -846.938 q^{94} +(98.5233 + 258.175i) q^{95} +96.0000 q^{96} +(-144.813 + 821.273i) q^{97} +(1211.26 + 1016.37i) q^{98} +(206.995 + 75.3399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 15 q^{5} - 72 q^{8}+O(q^{10}) \) 18 * q + 15 * q^5 - 72 * q^8	\( 18 q + 15 q^{5} - 72 q^{8} - 6 q^{10} - 39 q^{11} - 108 q^{12} - 42 q^{14} + 45 q^{15} + 159 q^{17} + 324 q^{18} + 159 q^{19} + 216 q^{20} + 99 q^{21} - 246 q^{22} + 300 q^{23} - 267 q^{25} - 198 q^{26} - 243 q^{27} + 132 q^{28} - 231 q^{29} - 162 q^{30} - 243 q^{31} - 126 q^{33} - 618 q^{34} + 774 q^{35} + 1422 q^{37} - 270 q^{38} + 594 q^{39} - 24 q^{40} - 69 q^{41} - 126 q^{42} - 60 q^{43} - 492 q^{44} - 243 q^{45} - 456 q^{46} + 540 q^{47} - 2229 q^{49} - 348 q^{50} + 450 q^{51} - 180 q^{52} - 750 q^{53} - 450 q^{55} + 297 q^{57} + 1836 q^{58} + 1263 q^{59} - 144 q^{60} + 1518 q^{61} - 390 q^{62} - 108 q^{63} - 576 q^{64} + 237 q^{65} + 990 q^{66} - 4812 q^{67} - 228 q^{68} - 684 q^{69} + 1548 q^{70} - 1371 q^{71} + 672 q^{73} + 186 q^{74} + 1044 q^{75} - 84 q^{76} - 270 q^{77} + 270 q^{78} - 2301 q^{79} + 240 q^{80} - 138 q^{82} - 2490 q^{83} + 5757 q^{85} + 96 q^{86} - 1377 q^{87} - 312 q^{88} + 7203 q^{89} + 270 q^{90} + 1284 q^{91} + 156 q^{92} - 207 q^{93} - 264 q^{94} + 3270 q^{95} + 1728 q^{96} - 1977 q^{97} + 498 q^{98} - 378 q^{99}+O(q^{100}) \) 18 * q + 15 * q^5 - 72 * q^8 - 6 * q^10 - 39 * q^11 - 108 * q^12 - 42 * q^14 + 45 * q^15 + 159 * q^17 + 324 * q^18 + 159 * q^19 + 216 * q^20 + 99 * q^21 - 246 * q^22 + 300 * q^23 - 267 * q^25 - 198 * q^26 - 243 * q^27 + 132 * q^28 - 231 * q^29 - 162 * q^30 - 243 * q^31 - 126 * q^33 - 618 * q^34 + 774 * q^35 + 1422 * q^37 - 270 * q^38 + 594 * q^39 - 24 * q^40 - 69 * q^41 - 126 * q^42 - 60 * q^43 - 492 * q^44 - 243 * q^45 - 456 * q^46 + 540 * q^47 - 2229 * q^49 - 348 * q^50 + 450 * q^51 - 180 * q^52 - 750 * q^53 - 450 * q^55 + 297 * q^57 + 1836 * q^58 + 1263 * q^59 - 144 * q^60 + 1518 * q^61 - 390 * q^62 - 108 * q^63 - 576 * q^64 + 237 * q^65 + 990 * q^66 - 4812 * q^67 - 228 * q^68 - 684 * q^69 + 1548 * q^70 - 1371 * q^71 + 672 * q^73 + 186 * q^74 + 1044 * q^75 - 84 * q^76 - 270 * q^77 + 270 * q^78 - 2301 * q^79 + 240 * q^80 - 138 * q^82 - 2490 * q^83 + 5757 * q^85 + 96 * q^86 - 1377 * q^87 - 312 * q^88 + 7203 * q^89 + 270 * q^90 + 1284 * q^91 + 156 * q^92 - 207 * q^93 - 264 * q^94 + 3270 * q^95 + 1728 * q^96 - 1977 * q^97 + 498 * q^98 - 378 * q^99

Introduction

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