LMFDB - Embedded newform 380.3.b.a.191.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(191,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("380.191");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.b (of order $2$, degree $1$, 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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.5
Character	$\chi$	$=$	380.191
Dual form			380.3.b.a.191.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98112 - 0.274141i) q^{2} +4.09700i q^{3} +(3.84969 + 1.08622i) q^{4} -2.23607 q^{5} +(1.12316 - 8.11666i) q^{6} +4.68200i q^{7} +(-7.32894 - 3.20729i) q^{8} -7.78542 q^{9} +O(q^{10})$	\(q+(-1.98112 - 0.274141i) q^{2} +4.09700i q^{3} +(3.84969 + 1.08622i) q^{4} -2.23607 q^{5} +(1.12316 - 8.11666i) q^{6} +4.68200i q^{7} +(-7.32894 - 3.20729i) q^{8} -7.78542 q^{9} +(4.42992 + 0.612999i) q^{10} -9.08728i q^{11} +(-4.45022 + 15.7722i) q^{12} -7.35790 q^{13} +(1.28353 - 9.27563i) q^{14} -9.16117i q^{15} +(13.6403 + 8.36319i) q^{16} -30.9280 q^{17} +(15.4239 + 2.13430i) q^{18} -4.35890i q^{19} +(-8.60818 - 2.42885i) q^{20} -19.1822 q^{21} +(-2.49120 + 18.0030i) q^{22} -1.71049i q^{23} +(13.1403 - 30.0267i) q^{24} +5.00000 q^{25} +(14.5769 + 2.01710i) q^{26} +4.97615i q^{27} +(-5.08566 + 18.0243i) q^{28} +4.12877 q^{29} +(-2.51146 + 18.1494i) q^{30} -10.4578i q^{31} +(-24.7304 - 20.3079i) q^{32} +37.2306 q^{33} +(61.2721 + 8.47863i) q^{34} -10.4693i q^{35} +(-29.9715 - 8.45664i) q^{36} +15.2530 q^{37} +(-1.19495 + 8.63551i) q^{38} -30.1453i q^{39} +(16.3880 + 7.17171i) q^{40} -26.7323 q^{41} +(38.0022 + 5.25863i) q^{42} -54.3319i q^{43} +(9.87074 - 34.9832i) q^{44} +17.4087 q^{45} +(-0.468915 + 3.38868i) q^{46} -40.3388i q^{47} +(-34.2640 + 55.8842i) q^{48} +27.0788 q^{49} +(-9.90561 - 1.37071i) q^{50} -126.712i q^{51} +(-28.3257 - 7.99226i) q^{52} +7.18411 q^{53} +(1.36417 - 9.85836i) q^{54} +20.3198i q^{55} +(15.0165 - 34.3141i) q^{56} +17.8584 q^{57} +(-8.17960 - 1.13187i) q^{58} -42.0612i q^{59} +(9.95100 - 35.2677i) q^{60} -99.7009 q^{61} +(-2.86692 + 20.7182i) q^{62} -36.4514i q^{63} +(43.4266 + 47.0120i) q^{64} +16.4528 q^{65} +(-73.7584 - 10.2064i) q^{66} +92.4132i q^{67} +(-119.063 - 33.5944i) q^{68} +7.00786 q^{69} +(-2.87006 + 20.7409i) q^{70} -106.241i q^{71} +(57.0588 + 24.9701i) q^{72} -71.5812 q^{73} +(-30.2180 - 4.18147i) q^{74} +20.4850i q^{75} +(4.73470 - 16.7804i) q^{76} +42.5467 q^{77} +(-8.26408 + 59.7216i) q^{78} -3.32756i q^{79} +(-30.5006 - 18.7007i) q^{80} -90.4560 q^{81} +(52.9600 + 7.32844i) q^{82} -29.8503i q^{83} +(-73.8455 - 20.8360i) q^{84} +69.1570 q^{85} +(-14.8946 + 107.638i) q^{86} +16.9156i q^{87} +(-29.1455 + 66.6001i) q^{88} +5.75188 q^{89} +(-34.4888 - 4.77245i) q^{90} -34.4497i q^{91} +(1.85796 - 6.58484i) q^{92} +42.8456 q^{93} +(-11.0585 + 79.9161i) q^{94} +9.74679i q^{95} +(83.2013 - 101.320i) q^{96} +48.3233 q^{97} +(-53.6465 - 7.42343i) q^{98} +70.7483i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.98112	−	0.274141i	−0.990561	−	0.137071i
$2$	−1.98112	−	0.274141i	−0.990561	−	0.137071i
$3$			4.09700i			1.36567i	0.730574	+	0.682833i	$0.239253\pi$
$3$			4.09700i			1.36567i	−0.730574	+	0.682833i	$0.760747\pi$
$4$	3.84969	+	1.08622i	0.962423	+	0.271554i
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$	1.12316	−	8.11666i	0.187193	−	1.35278i
$7$			4.68200i			0.668858i	0.942421	+	0.334429i	$0.108543\pi$
$7$			4.68200i			0.668858i	−0.942421	+	0.334429i	$0.891457\pi$
$8$	−7.32894	−	3.20729i	−0.916117	−	0.400911i
$9$	−7.78542			−0.865046
$10$	4.42992	+	0.612999i	0.442992	+	0.0612999i
$11$		−	9.08728i		−	0.826116i	−0.910705	−	0.413058i	$-0.864461\pi$
$11$		−	9.08728i		−	0.826116i	0.910705	−	0.413058i	$-0.135539\pi$
$12$	−4.45022	+	15.7722i	−0.370852	+	1.31435i
$13$	−7.35790			−0.565992			−0.282996	−	0.959121i	$-0.591328\pi$
$13$	−7.35790			−0.565992			−0.282996	+	0.959121i	$0.591328\pi$
$14$	1.28353	−	9.27563i	0.0916808	−	0.662545i
$15$		−	9.16117i		−	0.610745i
$16$	13.6403	+	8.36319i	0.852517	+	0.522699i
$17$	−30.9280			−1.81929			−0.909646	−	0.415384i	$-0.863647\pi$
$17$	−30.9280			−1.81929			−0.909646	+	0.415384i	$0.863647\pi$
$18$	15.4239	+	2.13430i	0.856881	+	0.118572i
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	−8.60818	−	2.42885i	−0.430409	−	0.121443i
$21$	−19.1822			−0.913437
$22$	−2.49120	+	18.0030i	−0.113236	+	0.818319i
$23$		−	1.71049i		−	0.0743689i	−0.999308	−	0.0371845i	$-0.988161\pi$
$23$		−	1.71049i		−	0.0743689i	0.999308	−	0.0371845i	$-0.0118389\pi$
$24$	13.1403	−	30.0267i	0.547510	−	1.25111i
$25$	5.00000			0.200000
$26$	14.5769	+	2.01710i	0.560650	+	0.0775810i
$27$			4.97615i			0.184302i
$28$	−5.08566	+	18.0243i	−0.181631	+	0.643724i
$29$	4.12877			0.142371			0.0711857	−	0.997463i	$-0.477322\pi$
$29$	4.12877			0.142371			0.0711857	+	0.997463i	$0.477322\pi$
$30$	−2.51146	+	18.1494i	−0.0837152	+	0.604980i
$31$		−	10.4578i		−	0.337349i	−0.985672	−	0.168674i	$-0.946051\pi$
$31$		−	10.4578i		−	0.337349i	0.985672	−	0.168674i	$-0.0539486\pi$
$32$	−24.7304	−	20.3079i	−0.772824	−	0.634621i
$33$	37.2306			1.12820
$34$	61.2721	+	8.47863i	1.80212	+	0.249372i
$35$		−	10.4693i		−	0.299122i
$36$	−29.9715	−	8.45664i	−0.832541	−	0.234907i
$37$	15.2530			0.412242			0.206121	−	0.978527i	$-0.433916\pi$
$37$	15.2530			0.412242			0.206121	+	0.978527i	$0.433916\pi$
$38$	−1.19495	+	8.63551i	−0.0314462	+	0.227250i
$39$		−	30.1453i		−	0.772957i
$40$	16.3880	+	7.17171i	0.409700	+	0.179293i
$41$	−26.7323			−0.652008			−0.326004	−	0.945368i	$-0.605702\pi$
$41$	−26.7323			−0.652008			−0.326004	+	0.945368i	$0.605702\pi$
$42$	38.0022	+	5.25863i	0.904815	+	0.125205i
$43$		−	54.3319i		−	1.26353i	−0.775159	−	0.631766i	$-0.782330\pi$
$43$		−	54.3319i		−	1.26353i	0.775159	−	0.631766i	$-0.217670\pi$
$44$	9.87074	−	34.9832i	0.224335	−	0.795074i
$45$	17.4087			0.386860
$46$	−0.468915	+	3.38868i	−0.0101938	+	0.0736670i
$47$		−	40.3388i		−	0.858272i	−0.903240	−	0.429136i	$-0.858818\pi$
$47$		−	40.3388i		−	0.858272i	0.903240	−	0.429136i	$-0.141182\pi$
$48$	−34.2640	+	55.8842i	−0.713833	+	1.16425i
$49$	27.0788			0.552629
$50$	−9.90561	−	1.37071i	−0.198112	−	0.0274141i
$51$		−	126.712i		−	2.48455i
$52$	−28.3257	−	7.99226i	−0.544724	−	0.153697i
$53$	7.18411			0.135549			0.0677747	−	0.997701i	$-0.478410\pi$
$53$	7.18411			0.135549			0.0677747	+	0.997701i	$0.478410\pi$
$54$	1.36417	−	9.85836i	0.0252624	−	0.182562i
$55$			20.3198i			0.369451i
$56$	15.0165	−	34.3141i	0.268152	−	0.612752i
$57$	17.8584			0.313305
$58$	−8.17960	−	1.13187i	−0.141028	−	0.0195149i
$59$		−	42.0612i		−	0.712901i	−0.934314	−	0.356451i	$-0.883987\pi$
$59$		−	42.0612i		−	0.712901i	0.934314	−	0.356451i	$-0.116013\pi$
$60$	9.95100	−	35.2677i	0.165850	−	0.587795i
$61$	−99.7009			−1.63444			−0.817221	−	0.576325i	$-0.804486\pi$
$61$	−99.7009			−1.63444			−0.817221	+	0.576325i	$0.804486\pi$
$62$	−2.86692	+	20.7182i	−0.0462406	+	0.334164i
$63$		−	36.4514i		−	0.578593i
$64$	43.4266	+	47.0120i	0.678541	+	0.734562i
$65$	16.4528			0.253120
$66$	−73.7584	−	10.2064i	−1.11755	−	0.154643i
$67$			92.4132i			1.37930i	0.724142	+	0.689650i	$0.242236\pi$
$67$			92.4132i			1.37930i	−0.724142	+	0.689650i	$0.757764\pi$
$68$	−119.063	−	33.5944i	−1.75093	−	0.494036i
$69$	7.00786			0.101563
$70$	−2.87006	+	20.7409i	−0.0410009	+	0.296299i
$71$		−	106.241i		−	1.49635i	−0.663502	−	0.748174i	$-0.730931\pi$
$71$		−	106.241i		−	1.49635i	0.663502	−	0.748174i	$-0.269069\pi$
$72$	57.0588	+	24.9701i	0.792484	+	0.346806i
$73$	−71.5812			−0.980564			−0.490282	−	0.871564i	$-0.663106\pi$
$73$	−71.5812			−0.980564			−0.490282	+	0.871564i	$0.663106\pi$
$74$	−30.2180	−	4.18147i	−0.408351	−	0.0565063i
$75$			20.4850i			0.273133i
$76$	4.73470	−	16.7804i	0.0622987	−	0.220795i
$77$	42.5467			0.552554
$78$	−8.26408	+	59.7216i	−0.105950	+	0.765661i
$79$		−	3.32756i		−	0.0421210i	−0.999778	−	0.0210605i	$-0.993296\pi$
$79$		−	3.32756i		−	0.0421210i	0.999778	−	0.0210605i	$-0.00670426\pi$
$80$	−30.5006	−	18.7007i	−0.381257	−	0.233758i
$81$	−90.4560			−1.11674
$82$	52.9600	+	7.32844i	0.645854	+	0.0893712i
$83$		−	29.8503i		−	0.359642i	−0.983699	−	0.179821i	$-0.942448\pi$
$83$		−	29.8503i		−	0.359642i	0.983699	−	0.179821i	$-0.0575519\pi$
$84$	−73.8455	−	20.8360i	−0.879113	−	0.248047i
$85$	69.1570			0.813612
$86$	−14.8946	+	107.638i	−0.173193	+	1.25161i
$87$			16.9156i			0.194432i
$88$	−29.1455	+	66.6001i	−0.331199	+	0.756819i
$89$	5.75188			0.0646278			0.0323139	−	0.999478i	$-0.489712\pi$
$89$	5.75188			0.0646278			0.0323139	+	0.999478i	$0.489712\pi$
$90$	−34.4888	−	4.77245i	−0.383209	−	0.0530272i
$91$		−	34.4497i		−	0.378568i
$92$	1.85796	−	6.58484i	0.0201952	−	0.0715744i
$93$	42.8456			0.460706
$94$	−11.0585	+	79.9161i	−0.117644	+	0.850171i
$95$			9.74679i			0.102598i
$96$	83.2013	−	101.320i	0.866681	−	1.05542i
$97$	48.3233			0.498178			0.249089	−	0.968481i	$-0.419869\pi$
$97$	48.3233			0.498178			0.249089	+	0.968481i	$0.419869\pi$
$98$	−53.6465	−	7.42343i	−0.547413	−	0.0757493i
$99$			70.7483i			0.714629i
$100$	19.2485	+	5.43108i	0.192485	+	0.0543108i
$101$	−77.9319			−0.771603			−0.385801	−	0.922582i	$-0.626075\pi$
$101$	−77.9319			−0.771603			−0.385801	+	0.922582i	$0.626075\pi$
$102$	−34.7370	+	251.032i	−0.340559	+	2.46110i
$103$			18.2144i			0.176839i	0.996083	+	0.0884195i	$0.0281816\pi$
$103$			18.2144i			0.176839i	−0.996083	+	0.0884195i	$0.971818\pi$
$104$	53.9256	+	23.5989i	0.518515	+	0.226912i
$105$	42.8927			0.408501
$106$	−14.2326	−	1.96946i	−0.134270	−	0.0185798i
$107$			118.184i			1.10452i	0.833671	+	0.552262i	$0.186235\pi$
$107$			118.184i			1.10452i	−0.833671	+	0.552262i	$0.813765\pi$
$108$	−5.40517	+	19.1566i	−0.0500478	+	0.177376i
$109$	−26.6085			−0.244115			−0.122057	−	0.992523i	$-0.538949\pi$
$109$	−26.6085			−0.244115			−0.122057	+	0.992523i	$0.538949\pi$
$110$	5.57049	−	40.2560i	0.0506408	−	0.365963i
$111$			62.4914i			0.562985i
$112$	−39.1565	+	63.8638i	−0.349612	+	0.570213i
$113$	125.951			1.11461			0.557307	−	0.830306i	$-0.311835\pi$
$113$	125.951			1.11461			0.557307	+	0.830306i	$0.311835\pi$
$114$	−35.3797	−	4.89573i	−0.310348	−	0.0429450i
$115$			3.82476i			0.0332588i
$116$	15.8945	+	4.48473i	0.137022	+	0.0386615i
$117$	57.2843			0.489610
$118$	−11.5307	+	83.3283i	−0.0977178	+	0.706172i
$119$		−	144.805i		−	1.21685i
$120$	−29.3825	+	67.1417i	−0.244854	+	0.559514i
$121$	38.4213			0.317532
$122$	197.520	+	27.3321i	1.61901	+	0.224034i
$123$		−	109.522i		−	0.890426i
$124$	11.3594	−	40.2593i	0.0916083	−	0.324672i
$125$	−11.1803			−0.0894427
$126$	−9.99282	+	72.2146i	−0.0793081	+	0.573132i
$127$			29.6522i			0.233482i	0.993162	+	0.116741i	$0.0372447\pi$
$127$			29.6522i			0.233482i	−0.993162	+	0.116741i	$0.962755\pi$
$128$	−73.1456	−	105.042i	−0.571450	−	0.820637i
$129$	222.598			1.72556
$130$	−32.5949	−	4.51038i	−0.250730	−	0.0346953i
$131$			125.086i			0.954856i	0.878671	+	0.477428i	$0.158431\pi$
$131$			125.086i			0.954856i	−0.878671	+	0.477428i	$0.841569\pi$
$132$	143.326	+	40.4404i	1.08581	+	0.306367i
$133$	20.4084			0.153447
$134$	25.3343	−	183.082i	0.189062	−	1.36628i
$135$		−	11.1270i		−	0.0824223i
$136$	226.669	+	99.1948i	1.66668	+	0.729374i
$137$	−76.5392			−0.558681			−0.279340	−	0.960192i	$-0.590116\pi$
$137$	−76.5392			−0.558681			−0.279340	+	0.960192i	$0.590116\pi$
$138$	−13.8834	−	1.92114i	−0.100605	−	0.0139213i
$139$			225.224i			1.62031i	0.586213	+	0.810157i	$0.300618\pi$
$139$			225.224i			1.62031i	−0.586213	+	0.810157i	$0.699382\pi$
$140$	11.3719	−	40.3035i	0.0812278	−	0.287882i
$141$	165.268			1.17211
$142$	−29.1250	+	210.476i	−0.205105	+	1.48222i
$143$			66.8633i			0.467576i
$144$	−106.195	−	65.1109i	−0.737467	−	0.452159i
$145$	−9.23221			−0.0636704
$146$	141.811	+	19.6234i	0.971309	+	0.134407i
$147$			110.942i			0.754707i
$148$	58.7192	+	16.5680i	0.396751	+	0.111946i
$149$	−216.517			−1.45314			−0.726568	−	0.687094i	$-0.758886\pi$
$149$	−216.517			−1.45314			−0.726568	+	0.687094i	$0.758886\pi$
$150$	5.61579	−	40.5833i	0.0374386	−	0.270555i
$151$			282.192i			1.86882i	0.356196	+	0.934411i	$0.384073\pi$
$151$			282.192i			1.86882i	−0.356196	+	0.934411i	$0.615927\pi$
$152$	−13.9802	+	31.9461i	−0.0919752	+	0.210172i
$153$	240.787			1.57377
$154$	−84.2902	−	11.6638i	−0.547339	−	0.0757390i
$155$			23.3844i			0.150867i
$156$	32.7443	−	116.050i	0.209899	−	0.743912i
$157$	−227.774			−1.45079			−0.725395	−	0.688333i	$-0.758343\pi$
$157$	−227.774			−1.45079			−0.725395	+	0.688333i	$0.758343\pi$
$158$	−0.912221	+	6.59230i	−0.00577355	+	0.0417234i
$159$			29.4333i			0.185115i
$160$	55.2988	+	45.4098i	0.345617	+	0.283811i
$161$	8.00850			0.0497422
$162$	179.204	+	24.7977i	1.10620	+	0.153072i
$163$		−	151.874i		−	0.931743i	−0.884852	−	0.465872i	$-0.845741\pi$
$163$		−	151.874i		−	0.931743i	0.884852	−	0.465872i	$-0.154259\pi$
$164$	−102.911	−	29.0371i	−0.627508	−	0.177055i
$165$	−83.2502			−0.504546
$166$	−8.18320	+	59.1371i	−0.0492964	+	0.356248i
$167$		−	195.105i		−	1.16830i	−0.811647	−	0.584148i	$-0.801429\pi$
$167$		−	195.105i		−	1.16830i	0.811647	−	0.584148i	$-0.198571\pi$
$168$	140.585	+	61.5227i	0.836815	+	0.366207i
$169$	−114.861			−0.679653
$170$	−137.009	−	18.9588i	−0.805933	−	0.111522i
$171$			33.9358i			0.198455i
$172$	59.0161	−	209.161i	0.343117	−	1.21605i
$173$	−260.142			−1.50371			−0.751857	−	0.659327i	$-0.770841\pi$
$173$	−260.142			−1.50371			−0.751857	+	0.659327i	$0.770841\pi$
$174$	4.63726	−	33.5118i	0.0266509	−	0.192597i
$175$			23.4100i			0.133772i
$176$	75.9987	−	123.953i	0.431811	−	0.704278i
$177$	172.325			0.973585
$178$	−11.3952	−	1.57683i	−0.0640178	−	0.00885858i
$179$			286.780i			1.60212i	0.598584	+	0.801060i	$0.295730\pi$
$179$			286.780i			1.60212i	−0.598584	+	0.801060i	$0.704270\pi$
$180$	67.0182	+	18.9096i	0.372324	+	0.105053i
$181$	−219.869			−1.21475			−0.607373	−	0.794417i	$-0.707777\pi$
$181$	−219.869			−1.21475			−0.607373	+	0.794417i	$0.707777\pi$
$182$	−9.44409	+	68.2491i	−0.0518906	+	0.374995i
$183$		−	408.475i		−	2.23210i
$184$	−5.48601	+	12.5360i	−0.0298153	+	0.0681307i
$185$	−34.1066			−0.184360
$186$	−84.8825	−	11.7458i	−0.456357	−	0.0631492i
$187$			281.051i			1.50295i
$188$	43.8166	−	155.292i	0.233067	−	0.826021i
$189$	−23.2983			−0.123272
$190$	2.67200	−	19.3096i	0.0140632	−	0.101629i
$191$		−	317.541i		−	1.66252i	−0.555884	−	0.831260i	$-0.687620\pi$
$191$		−	317.541i		−	1.66252i	0.555884	−	0.831260i	$-0.312380\pi$
$192$	−192.608	+	177.919i	−1.00317	+	0.926661i
$193$	−15.6267			−0.0809672			−0.0404836	−	0.999180i	$-0.512890\pi$
$193$	−15.6267			−0.0809672			−0.0404836	+	0.999180i	$0.512890\pi$
$194$	−95.7343	−	13.2474i	−0.493476	−	0.0682856i
$195$			67.4070i			0.345677i
$196$	104.245	+	29.4134i	0.531863	+	0.150069i
$197$	−247.488			−1.25628			−0.628142	−	0.778098i	$-0.716184\pi$
$197$	−247.488			−1.25628			−0.628142	+	0.778098i	$0.716184\pi$
$198$	19.3950	−	140.161i	0.0979547	−	0.707884i
$199$		−	85.5894i		−	0.430097i	−0.976603	−	0.215049i	$-0.931009\pi$
$199$		−	85.5894i		−	0.430097i	0.976603	−	0.215049i	$-0.0689910\pi$
$200$	−36.6447	−	16.0364i	−0.183223	−	0.0801821i
$201$	−378.617			−1.88367
$202$	154.393	+	21.3643i	0.764320	+	0.105764i
$203$			19.3309i			0.0952262i
$204$	137.636	−	487.802i	0.674688	−	2.39119i
$205$	59.7753			0.291587
$206$	4.99332	−	36.0850i	0.0242394	−	0.175170i
$207$			13.3168i			0.0643326i
$208$	−100.364	−	61.5355i	−0.482518	−	0.295844i
$209$	−39.6105			−0.189524
$210$	−84.9756	−	11.7586i	−0.404646	−	0.0559936i
$211$		−	266.180i		−	1.26152i	−0.775979	−	0.630758i	$-0.782744\pi$
$211$		−	266.180i		−	1.26152i	0.775979	−	0.630758i	$-0.217256\pi$
$212$	27.6566	+	7.80349i	0.130456	+	0.0368089i
$213$	435.268			2.04351
$214$	32.3991	−	234.137i	0.151398	−	1.09410i
$215$			121.490i			0.565069i
$216$	15.9599	−	36.4699i	0.0738885	−	0.168842i
$217$	48.9635			0.225638
$218$	52.7148	+	7.29450i	0.241811	+	0.0334610i
$219$		−	293.268i		−	1.33912i
$220$	−22.0717	+	78.2249i	−0.100326	+	0.355568i
$221$	227.565			1.02971
$222$	17.1315	−	123.803i	0.0771688	−	0.557671i
$223$		−	119.382i		−	0.535346i	−0.963510	−	0.267673i	$-0.913745\pi$
$223$		−	119.382i		−	0.535346i	0.963510	−	0.267673i	$-0.0862548\pi$
$224$	95.0815	−	115.788i	0.424471	−	0.516909i
$225$	−38.9271			−0.173009
$226$	−249.525	−	34.5285i	−1.10409	−	0.152781i
$227$			289.352i			1.27468i	0.770583	+	0.637340i	$0.219965\pi$
$227$			289.352i			1.27468i	−0.770583	+	0.637340i	$0.780035\pi$
$228$	68.7494	+	19.3981i	0.301532	+	0.0850793i
$229$	−344.625			−1.50491			−0.752457	−	0.658642i	$-0.771131\pi$
$229$	−344.625			−1.50491			−0.752457	+	0.658642i	$0.771131\pi$
$230$	1.04853	−	7.57732i	0.00455881	−	0.0329449i
$231$			174.314i			0.754605i
$232$	−30.2595	−	13.2421i	−0.130429	−	0.0570782i
$233$	−156.504			−0.671689			−0.335844	−	0.941917i	$-0.609022\pi$
$233$	−156.504			−0.671689			−0.335844	+	0.941917i	$0.609022\pi$
$234$	−113.487	−	15.7040i	−0.484988	−	0.0671111i
$235$			90.2003i			0.383831i
$236$	45.6875	−	161.923i	0.193591	−	0.686113i
$237$	13.6330			0.0575233
$238$	−39.6970	+	286.876i	−0.166794	+	1.20536i
$239$			320.805i			1.34228i	0.741330	+	0.671141i	$0.234195\pi$
$239$			320.805i			1.34228i	−0.741330	+	0.671141i	$0.765805\pi$
$240$	76.6166	−	124.961i	0.319236	−	0.520670i
$241$	456.969			1.89614			0.948069	−	0.318063i	$-0.103032\pi$
$241$	456.969			1.89614			0.948069	+	0.318063i	$0.103032\pi$
$242$	−76.1173	−	10.5329i	−0.314534	−	0.0435243i
$243$		−	325.813i		−	1.34079i
$244$	−383.818	−	108.297i	−1.57302	−	0.443839i
$245$	−60.5501			−0.247143
$246$	−30.0246	+	216.977i	−0.122051	+	0.882022i
$247$			32.0723i			0.129848i
$248$	−33.5412	+	76.6446i	−0.135247	+	0.309051i
$249$	122.297			0.491152
$250$	22.1496	+	3.06499i	0.0885985	+	0.0122600i
$251$			188.567i			0.751261i	0.926769	+	0.375631i	$0.122574\pi$
$251$			188.567i			0.751261i	−0.926769	+	0.375631i	$0.877426\pi$
$252$	39.5940	−	140.327i	0.157119	−	0.556851i
$253$	−15.5437			−0.0614374
$254$	8.12890	−	58.7447i	0.0320035	−	0.231278i
$255$			283.336i			1.11112i
$256$	116.114	+	228.152i	0.453571	+	0.891220i
$257$	−28.8121			−0.112109			−0.0560546	−	0.998428i	$-0.517852\pi$
$257$	−28.8121			−0.112109			−0.0560546	+	0.998428i	$0.517852\pi$
$258$	−440.993	−	61.0232i	−1.70928	−	0.236524i
$259$			71.4144i			0.275731i
$260$	63.3381	+	17.8712i	0.243608	+	0.0687356i
$261$	−32.1442			−0.123158
$262$	34.2913	−	247.811i	0.130883	−	0.945844i
$263$			314.605i			1.19622i	0.801415	+	0.598109i	$0.204081\pi$
$263$			314.605i			1.19622i	−0.801415	+	0.598109i	$0.795919\pi$
$264$	−272.861	−	119.409i	−1.03356	−	0.452307i
$265$	−16.0642			−0.0606195
$266$	−40.4315	−	5.59478i	−0.151998	−	0.0210330i
$267$			23.5654i			0.0882601i
$268$	−100.381	+	355.762i	−0.374554	+	1.32747i
$269$	−344.788			−1.28174			−0.640869	−	0.767650i	$-0.721426\pi$
$269$	−344.788			−1.28174			−0.640869	+	0.767650i	$0.721426\pi$
$270$	−3.05037	+	22.0440i	−0.0112977	+	0.0816443i
$271$		−	336.488i		−	1.24165i	−0.783948	−	0.620827i	$-0.786797\pi$
$271$		−	336.488i		−	1.24165i	0.783948	−	0.620827i	$-0.213203\pi$
$272$	−421.866	−	258.656i	−1.55098	−	0.950943i
$273$	141.141			0.516998
$274$	151.634	+	20.9826i	0.553407	+	0.0765787i
$275$		−	45.4364i		−	0.165223i
$276$	26.9781	+	7.61204i	0.0977468	+	0.0275799i
$277$	−45.4388			−0.164039			−0.0820195	−	0.996631i	$-0.526137\pi$
$277$	−45.4388			−0.164039			−0.0820195	+	0.996631i	$0.526137\pi$
$278$	61.7431	−	446.195i	0.222097	−	1.60502i
$279$			81.4184i			0.291822i
$280$	−33.5780	+	76.7287i	−0.119921	+	0.274031i
$281$	494.834			1.76097			0.880487	−	0.474070i	$-0.157216\pi$
$281$	494.834			1.76097			0.880487	+	0.474070i	$0.157216\pi$
$282$	−327.416	−	45.3068i	−1.16105	−	0.160662i
$283$		−	70.4448i		−	0.248921i	−0.992225	−	0.124461i	$-0.960280\pi$
$283$		−	70.4448i		−	0.248921i	0.992225	−	0.124461i	$-0.0397201\pi$
$284$	115.400	−	408.994i	0.406339	−	1.44012i
$285$	−39.9326			−0.140114
$286$	18.3300	−	132.464i	0.0640909	−	0.463162i
$287$		−	125.161i		−	0.436101i
$288$	192.536	+	158.105i	0.668528	+	0.548976i
$289$	667.539			2.30982
$290$	18.2901	+	2.53093i	0.0630695	+	0.00872735i
$291$			197.981i			0.680345i
$292$	−275.566	−	77.7526i	−0.943718	−	0.266276i
$293$	103.544			0.353391			0.176695	−	0.984266i	$-0.443459\pi$
$293$	103.544			0.353391			0.176695	+	0.984266i	$0.443459\pi$
$294$	30.4138	−	219.790i	0.103448	−	0.747584i
$295$			94.0516i			0.318819i
$296$	−111.788	−	48.9206i	−0.377662	−	0.165272i
$297$	45.2197			0.152255
$298$	428.947	+	59.3564i	1.43942	+	0.199182i
$299$			12.5856i			0.0420923i
$300$	−22.2511	+	78.8610i	−0.0741704	+	0.262870i
$301$	254.382			0.845123
$302$	77.3605	−	559.057i	0.256161	−	1.85118i
$303$		−	319.287i		−	1.05375i
$304$	36.4543	−	59.4566i	0.119915	−	0.195581i
$305$	222.938			0.730944
$306$	−477.029	−	66.0097i	−1.55892	−	0.215718i
$307$			6.17290i			0.0201072i	0.999949	+	0.0100536i	$0.00320021\pi$
$307$			6.17290i			0.0201072i	−0.999949	+	0.0100536i	$0.996800\pi$
$308$	163.792	+	46.2149i	0.531791	+	0.150048i
$309$	−74.6244			−0.241503
$310$	6.41062	−	46.3273i	0.0206794	−	0.149443i
$311$		−	437.326i		−	1.40619i	−0.711094	−	0.703097i	$-0.751800\pi$
$311$		−	437.326i		−	1.40619i	0.711094	−	0.703097i	$-0.248200\pi$
$312$	−96.6847	+	220.933i	−0.309887	+	0.708119i
$313$	−472.226			−1.50871			−0.754355	−	0.656467i	$-0.772050\pi$
$313$	−472.226			−1.50871			−0.754355	+	0.656467i	$0.772050\pi$
$314$	451.248	+	62.4423i	1.43710	+	0.198861i
$315$			81.5077i			0.258755i
$316$	3.61444	−	12.8101i	0.0114381	−	0.0405382i
$317$	−49.3220			−0.155590			−0.0777949	−	0.996969i	$-0.524788\pi$
$317$	−49.3220			−0.155590			−0.0777949	+	0.996969i	$0.524788\pi$
$318$	8.06889	−	58.3110i	0.0253739	−	0.183368i
$319$		−	37.5193i		−	0.117615i
$320$	−97.1049	−	105.122i	−0.303453	−	0.328506i
$321$	−484.200			−1.50841
$322$	−15.8658	−	2.19546i	−0.0492727	−	0.00681820i
$323$			134.812i			0.417374i
$324$	−348.228	−	98.2547i	−1.07478	−	0.303255i
$325$	−36.7895			−0.113198
$326$	−41.6350	+	300.881i	−0.127715	+	0.922949i
$327$		−	109.015i		−	0.333380i
$328$	195.920	+	85.7382i	0.597316	+	0.261397i
$329$	188.866			0.574062
$330$	164.929	+	22.8223i	0.499784	+	0.0691585i
$331$			177.660i			0.536737i	0.963316	+	0.268369i	$0.0864845\pi$
$331$			177.660i			0.536737i	−0.963316	+	0.268369i	$0.913515\pi$
$332$	32.4239	−	114.915i	0.0976622	−	0.346128i
$333$	−118.751			−0.356608
$334$	−53.4865	+	386.528i	−0.160139	+	1.15727i
$335$		−	206.642i		−	0.616842i
$336$	−261.650	−	160.424i	−0.778721	−	0.477453i
$337$	540.590			1.60412			0.802062	−	0.597240i	$-0.203736\pi$
$337$	540.590			1.60412			0.802062	+	0.597240i	$0.203736\pi$
$338$	227.554	+	31.4882i	0.673238	+	0.0931604i
$339$			516.023i			1.52219i
$340$	266.233	+	75.1194i	0.783039	+	0.220939i
$341$	−95.0330			−0.278689
$342$	9.30322	−	67.2311i	0.0272024	−	0.196582i
$343$			356.201i			1.03849i
$344$	−174.258	+	398.195i	−0.506563	+	1.15754i
$345$	−15.6701			−0.0454204
$346$	515.374	+	71.3158i	1.48952	+	0.206115i
$347$		−	361.084i		−	1.04059i	−0.853987	−	0.520294i	$-0.825823\pi$
$347$		−	361.084i		−	1.04059i	0.853987	−	0.520294i	$-0.174177\pi$
$348$	−18.3740	+	65.1198i	−0.0527987	+	0.187126i
$349$	301.293			0.863304			0.431652	−	0.902040i	$-0.357931\pi$
$349$	301.293			0.863304			0.431652	+	0.902040i	$0.357931\pi$
$350$	6.41766	−	46.3781i	0.0183362	−	0.132509i
$351$		−	36.6140i		−	0.104313i
$352$	−184.543	+	224.732i	−0.524271	+	0.638442i
$353$	43.3365			0.122766			0.0613832	−	0.998114i	$-0.480449\pi$
$353$	43.3365			0.122766			0.0613832	+	0.998114i	$0.480449\pi$
$354$	−341.396	−	47.2413i	−0.964396	−	0.133450i
$355$			237.562i			0.669187i
$356$	22.1430	+	6.24778i	0.0621993	+	0.0175499i
$357$	593.266			1.66181
$358$	78.6181	−	568.145i	0.219604	−	1.58700i
$359$			200.427i			0.558292i	0.960249	+	0.279146i	$0.0900513\pi$
$359$			200.427i			0.558292i	−0.960249	+	0.279146i	$0.909949\pi$
$360$	−127.587	−	55.8347i	−0.354410	−	0.155096i
$361$	−19.0000			−0.0526316
$362$	435.588	+	60.2752i	1.20328	+	0.166506i
$363$			157.412i			0.433642i
$364$	37.4198	−	132.621i	0.102802	−	0.364343i
$365$	160.060			0.438522
$366$	−111.980	+	809.239i	−0.305956	+	2.21103i
$367$		−	357.817i		−	0.974980i	−0.873129	−	0.487490i	$-0.837913\pi$
$367$		−	357.817i		−	0.974980i	0.873129	−	0.487490i	$-0.162087\pi$
$368$	14.3051	−	23.3315i	0.0388726	−	0.0634008i
$369$	208.122			0.564017
$370$	67.5694	+	9.35004i	0.182620	+	0.0252704i
$371$			33.6361i			0.0906632i
$372$	164.943	+	46.5396i	0.443394	+	0.125106i
$373$	−494.225			−1.32500			−0.662500	−	0.749062i	$-0.730505\pi$
$373$	−494.225			−1.32500			−0.662500	+	0.749062i	$0.730505\pi$
$374$	77.0477	−	556.797i	0.206010	−	1.48876i
$375$		−	45.8059i		−	0.122149i
$376$	−129.378	+	295.640i	−0.344090	+	0.786278i
$377$	−30.3791			−0.0805811
$378$	46.1569	+	6.38704i	0.122108	+	0.0168969i
$379$		−	113.030i		−	0.298233i	−0.988820	−	0.149116i	$-0.952357\pi$
$379$		−	113.030i		−	0.298233i	0.988820	−	0.149116i	$-0.0476429\pi$
$380$	−10.5871	+	37.5222i	−0.0278608	+	0.0987425i
$381$	−121.485			−0.318859
$382$	−87.0512	+	629.088i	−0.227883	+	1.64683i
$383$		−	576.103i		−	1.50419i	−0.659057	−	0.752093i	$-0.729044\pi$
$383$		−	576.103i		−	1.50419i	0.659057	−	0.752093i	$-0.270956\pi$
$384$	430.355	−	299.677i	1.12072	−	0.780410i
$385$	−95.1373			−0.247110
$386$	30.9583	+	4.28391i	0.0802029	+	0.0110982i
$387$			422.996i			1.09301i
$388$	186.030	+	52.4895i	0.479458	+	0.135282i
$389$	−103.532			−0.266150			−0.133075	−	0.991106i	$-0.542485\pi$
$389$	−103.532			−0.266150			−0.133075	+	0.991106i	$0.542485\pi$
$390$	18.4790	−	133.542i	0.0473822	−	0.342414i
$391$			52.9018i			0.135299i
$392$	−198.459	−	86.8495i	−0.506273	−	0.221555i
$393$	−512.478			−1.30402
$394$	490.304	+	67.8467i	1.24443	+	0.172200i
$395$			7.44065i			0.0188371i
$396$	−76.8478	+	272.359i	−0.194060	+	0.687776i
$397$	517.436			1.30336			0.651682	−	0.758492i	$-0.274064\pi$
$397$	517.436			1.30336			0.651682	+	0.758492i	$0.274064\pi$
$398$	−23.4636	+	169.563i	−0.0589537	+	0.426038i
$399$			83.6132i			0.209557i
$400$	68.2014	+	41.8159i	0.170503	+	0.104540i
$401$	−18.7030			−0.0466410			−0.0233205	−	0.999728i	$-0.507424\pi$
$401$	−18.7030			−0.0466410			−0.0233205	+	0.999728i	$0.507424\pi$
$402$	750.086	+	103.795i	1.86589	+	0.258195i
$403$			76.9475i			0.190937i
$404$	−300.014	−	84.6508i	−0.742608	−	0.209532i
$405$	202.266			0.499422
$406$	5.29941	−	38.2969i	0.0130527	−	0.0943274i
$407$		−	138.608i		−	0.340560i
$408$	−406.401	+	928.664i	−0.996082	+	2.27614i
$409$	−460.325			−1.12549			−0.562745	−	0.826631i	$-0.690255\pi$
$409$	−460.325			−1.12549			−0.562745	+	0.826631i	$0.690255\pi$
$410$	−118.422	−	16.3869i	−0.288835	−	0.0399680i
$411$		−	313.581i		−	0.762972i
$412$	−19.7848	+	70.1199i	−0.0480213	+	0.170194i
$413$	196.931			0.476829
$414$	3.65070	−	26.3823i	0.00881811	−	0.0637254i
$415$			66.7473i			0.160837i
$416$	181.964	+	149.423i	0.437412	+	0.359191i
$417$	−922.741			−2.21281
$418$	78.4733	+	10.8589i	0.187735	+	0.0259782i
$419$			635.189i			1.51596i	0.652275	+	0.757982i	$0.273815\pi$
$419$			635.189i			1.51596i	−0.652275	+	0.757982i	$0.726185\pi$
$420$	165.124	+	46.5906i	0.393151	+	0.110930i
$421$	468.509			1.11285			0.556424	−	0.830899i	$-0.312173\pi$
$421$	468.509			1.11285			0.556424	+	0.830899i	$0.312173\pi$
$422$	−72.9709	+	527.335i	−0.172917	+	1.24961i
$423$			314.054i			0.742445i
$424$	−52.6519	−	23.0415i	−0.124179	−	0.0543432i
$425$	−154.640			−0.363858
$426$	−862.320	−	119.325i	−2.02423	−	0.280106i
$427$		−	466.800i		−	1.09321i
$428$	−128.373	+	454.972i	−0.299938	+	1.06302i
$429$	−273.939			−0.638553
$430$	33.3054	−	240.686i	0.0774543	−	0.559735i
$431$			679.119i			1.57568i	0.615878	+	0.787842i	$0.288801\pi$
$431$			679.119i			1.57568i	−0.615878	+	0.787842i	$0.711199\pi$
$432$	−41.6165	+	67.8760i	−0.0963344	+	0.157120i
$433$	−416.004			−0.960749			−0.480375	−	0.877063i	$-0.659499\pi$
$433$	−416.004			−0.960749			−0.480375	+	0.877063i	$0.659499\pi$
$434$	−97.0027	−	13.4229i	−0.223508	−	0.0309284i
$435$		−	37.8244i		−	0.0869526i
$436$	−102.435	−	28.9026i	−0.234942	−	0.0662903i
$437$	−7.45583			−0.0170614
$438$	−80.3969	+	581.000i	−0.183555	+	1.32648i
$439$			371.919i			0.847196i	0.905850	+	0.423598i	$0.139233\pi$
$439$			371.919i			0.847196i	−0.905850	+	0.423598i	$0.860767\pi$
$440$	65.1713	−	148.922i	0.148117	−	0.338460i
$441$	−210.820			−0.478050
$442$	−450.834	−	62.3850i	−1.01999	−	0.141142i
$443$			95.1497i			0.214785i	0.994217	+	0.107392i	$0.0342501\pi$
$443$			95.1497i			0.214785i	−0.994217	+	0.107392i	$0.965750\pi$
$444$	−67.8791	+	240.573i	−0.152881	+	0.541830i
$445$	−12.8616			−0.0289024
$446$	−32.7276	+	236.511i	−0.0733803	+	0.530293i
$447$		−	887.072i		−	1.98450i
$448$	−220.110	+	203.324i	−0.491318	+	0.453848i
$449$	258.413			0.575530			0.287765	−	0.957701i	$-0.407088\pi$
$449$	258.413			0.575530			0.287765	+	0.957701i	$0.407088\pi$
$450$	77.1193	+	10.6715i	0.171376	+	0.0237145i
$451$			242.924i			0.538635i
$452$	484.874	+	136.810i	1.07273	+	0.302678i
$453$	−1156.14			−2.55219
$454$	79.3234	−	573.243i	0.174721	−	1.26265i
$455$			77.0319i			0.169301i
$456$	−130.883	−	57.2770i	−0.287025	−	0.125608i
$457$	−155.625			−0.340535			−0.170268	−	0.985398i	$-0.554463\pi$
$457$	−155.625			−0.340535			−0.170268	+	0.985398i	$0.554463\pi$
$458$	682.745	+	94.4760i	1.49071	+	0.206280i
$459$		−	153.902i		−	0.335299i
$460$	−4.15451	+	14.7242i	−0.00903155	+	0.0320090i
$461$	−108.858			−0.236134			−0.118067	−	0.993006i	$-0.537670\pi$
$461$	−108.858			−0.236134			−0.118067	+	0.993006i	$0.537670\pi$
$462$	47.7866	−	345.337i	0.103434	−	0.747483i
$463$		−	310.490i		−	0.670604i	−0.942111	−	0.335302i	$-0.891162\pi$
$463$		−	310.490i		−	0.670604i	0.942111	−	0.335302i	$-0.108838\pi$
$464$	56.3176	+	34.5297i	0.121374	+	0.0744174i
$465$	−95.8057			−0.206034
$466$	310.053	+	42.9041i	0.665349	+	0.0920689i
$467$		−	385.896i		−	0.826330i	−0.910656	−	0.413165i	$-0.864423\pi$
$467$		−	385.896i		−	0.826330i	0.910656	−	0.413165i	$-0.135577\pi$
$468$	220.527	+	62.2231i	0.471212	+	0.132955i
$469$	−432.679			−0.922556
$470$	24.7276	−	178.698i	0.0526120	−	0.380208i
$471$		−	933.191i		−	1.98130i
$472$	−134.902	+	308.264i	−0.285810	+	0.653101i
$473$	−493.729			−1.04382
$474$	−27.0087	−	3.73737i	−0.0569803	−	0.00788475i
$475$		−	21.7945i		−	0.0458831i
$476$	157.289	−	557.454i	0.330440	−	1.17112i
$477$	−55.9313			−0.117256
$478$	87.9460	−	635.555i	0.183987	−	1.32961i
$479$			316.726i			0.661223i	0.943767	+	0.330611i	$0.107255\pi$
$479$			316.726i			0.661223i	−0.943767	+	0.330611i	$0.892745\pi$
$480$	−186.044	+	226.559i	−0.387591	+	0.471998i
$481$	−112.230			−0.233326
$482$	−905.313	−	125.274i	−1.87824	−	0.259905i
$483$			32.8108i			0.0679313i
$484$	147.910	+	41.7338i	0.305600	+	0.0862269i
$485$	−108.054			−0.222792
$486$	−89.3188	+	645.476i	−0.183784	+	1.32814i
$487$			710.776i			1.45950i	0.683714	+	0.729750i	$0.260363\pi$
$487$			710.776i			1.45950i	−0.683714	+	0.729750i	$0.739637\pi$
$488$	730.702	+	319.769i	1.49734	+	0.655265i
$489$	622.229			1.27245
$490$	119.957	+	16.5993i	0.244811	+	0.0338761i
$491$			766.341i			1.56078i	0.625295	+	0.780388i	$0.284978\pi$
$491$			766.341i			1.56078i	−0.625295	+	0.780388i	$0.715022\pi$
$492$	118.965	−	421.628i	0.241799	−	0.856967i
$493$	−127.695			−0.259015
$494$	8.79236	−	63.5393i	0.0177983	−	0.128622i
$495$		−	158.198i		−	0.319592i
$496$	87.4606	−	142.647i	0.176332	−	0.287595i
$497$	497.420			1.00084
$498$	−242.285	−	33.5266i	−0.486516	−	0.0673225i
$499$			306.177i			0.613581i	0.951777	+	0.306790i	$0.0992550\pi$
$499$			306.177i			0.613581i	−0.951777	+	0.306790i	$0.900745\pi$
$500$	−43.0409	−	12.1443i	−0.0860818	−	0.0242885i
$501$	799.347			1.59550
$502$	51.6939	−	373.573i	0.102976	−	0.744170i
$503$			202.229i			0.402046i	0.979587	+	0.201023i	$0.0644266\pi$
$503$			202.229i			0.402046i	−0.979587	+	0.201023i	$0.935573\pi$
$504$	−116.910	+	267.150i	−0.231964	+	0.530059i
$505$	174.261			0.345071
$506$	30.7939	+	4.26116i	0.0608575	+	0.00842127i
$507$		−	470.587i		−	0.928179i
$508$	−32.2087	+	114.152i	−0.0634029	+	0.224709i
$509$	529.979			1.04122			0.520608	−	0.853796i	$-0.325705\pi$
$509$	529.979			1.04122			0.520608	+	0.853796i	$0.325705\pi$
$510$	77.6742	−	561.324i	0.152302	−	1.10064i
$511$		−	335.143i		−	0.655858i
$512$	−167.490	−	483.830i	−0.327129	−	0.944980i
$513$	21.6905			0.0422817
$514$	57.0802	+	7.89858i	0.111051	+	0.0153669i
$515$		−	40.7287i		−	0.0790848i
$516$	856.933	+	241.789i	1.66072	+	0.468583i
$517$	−366.570			−0.709033
$518$	19.5776	−	141.481i	0.0377947	−	0.273129i
$519$		−	1065.80i		−	2.05357i
$520$	−120.581	−	52.7687i	−0.231887	−	0.101478i
$521$	461.936			0.886633			0.443317	−	0.896365i	$-0.353802\pi$
$521$	461.936			0.886633			0.443317	+	0.896365i	$0.353802\pi$
$522$	63.6816	+	8.81205i	0.121995	+	0.0168813i
$523$		−	616.545i		−	1.17886i	−0.807819	−	0.589431i	$-0.799352\pi$
$523$		−	616.545i		−	1.17886i	0.807819	−	0.589431i	$-0.200648\pi$
$524$	−135.870	+	481.543i	−0.259295	+	0.918976i
$525$	−95.9109			−0.182687
$526$	86.2463	−	623.271i	0.163966	−	1.18493i
$527$			323.439i			0.613736i
$528$	507.836	+	311.367i	0.961810	+	0.589709i
$529$	526.074			0.994469
$530$	31.8251	+	4.40385i	0.0600473	+	0.00830915i
$531$			327.464i			0.616692i
$532$	78.5660	+	22.1679i	0.147680	+	0.0416690i
$533$	196.694			0.369032
$534$	6.46026	−	46.6860i	0.0120979	−	0.0874270i
$535$		−	264.268i		−	0.493958i
$536$	296.395	−	677.290i	0.552976	−	1.26360i
$537$	−1174.94			−2.18796
$538$	683.067	+	94.5206i	1.26964	+	0.175689i
$539$		−	246.073i		−	0.456536i
$540$	12.0863	−	42.8356i	0.0223821	−	0.0793251i
$541$	764.056			1.41230			0.706152	−	0.708060i	$-0.250430\pi$
$541$	764.056			1.41230			0.706152	+	0.708060i	$0.250430\pi$
$542$	−92.2453	+	666.624i	−0.170194	+	1.22993i
$543$		−	900.804i		−	1.65894i
$544$	764.860	+	628.081i	1.40599	+	1.15456i
$545$	59.4985			0.109172
$546$	−279.617	−	38.6925i	−0.512119	−	0.0708653i
$547$		−	72.7555i		−	0.133008i	−0.997786	−	0.0665041i	$-0.978815\pi$
$547$		−	72.7555i		−	0.133008i	0.997786	−	0.0665041i	$-0.0211846\pi$
$548$	−294.653	−	83.1381i	−0.537687	−	0.151712i
$549$	776.213			1.41387
$550$	−12.4560	+	90.0151i	−0.0226473	+	0.163664i
$551$		−	17.9969i		−	0.0326622i
$552$	−51.3602	−	22.4762i	−0.0930438	−	0.0407178i
$553$	15.5796			0.0281730
$554$	90.0198	+	12.4567i	0.162491	+	0.0224849i
$555$		−	139.735i		−	0.251775i
$556$	−244.641	+	867.042i	−0.440002	+	1.55943i
$557$	−45.5188			−0.0817215			−0.0408607	−	0.999165i	$-0.513010\pi$
$557$	−45.5188			−0.0817215			−0.0408607	+	0.999165i	$0.513010\pi$
$558$	22.3201	−	161.300i	0.0400002	−	0.289068i
$559$			399.769i			0.715150i
$560$	87.5566	−	142.804i	0.156351	−	0.255007i
$561$	−1151.47			−2.05253
$562$	−980.326	−	135.654i	−1.74435	−	0.241378i
$563$		−	379.265i		−	0.673650i	−0.941567	−	0.336825i	$-0.890647\pi$
$563$		−	379.265i		−	0.673650i	0.941567	−	0.336825i	$-0.109353\pi$
$564$	636.231	+	179.517i	1.12807	+	0.318292i
$565$	−281.636			−0.498471
$566$	−19.3118	+	139.560i	−0.0341198	+	0.246572i
$567$		−	423.516i		−	0.746941i
$568$	−340.744	+	778.632i	−0.599902	+	1.37083i
$569$	−198.623			−0.349075			−0.174537	−	0.984651i	$-0.555843\pi$
$569$	−198.623			−0.349075			−0.174537	+	0.984651i	$0.555843\pi$
$570$	79.1114	+	10.9472i	0.138792	+	0.0192056i
$571$		−	932.485i		−	1.63307i	−0.577293	−	0.816537i	$-0.695891\pi$
$571$		−	932.485i		−	1.63307i	0.577293	−	0.816537i	$-0.304109\pi$
$572$	−72.6280	+	257.403i	−0.126972	+	0.450006i
$573$	1300.97			2.27045
$574$	−34.3118	+	247.959i	−0.0597766	+	0.431985i
$575$		−	8.55243i		−	0.0148738i
$576$	−338.095	−	366.008i	−0.586970	−	0.635430i
$577$	324.368			0.562163			0.281082	−	0.959684i	$-0.409307\pi$
$577$	324.368			0.562163			0.281082	+	0.959684i	$0.409307\pi$
$578$	−1322.48	−	183.000i	−2.28802	−	0.316609i
$579$		−	64.0224i		−	0.110574i
$580$	−35.5412	−	10.0282i	−0.0612779	−	0.0172899i
$581$	139.759			0.240550
$582$	54.2746	−	392.224i	0.0932554	−	0.673924i
$583$		−	65.2841i		−	0.111980i
$584$	524.614	+	229.581i	0.898312	+	0.393119i
$585$	−128.092			−0.218960
$586$	−205.132	−	28.3856i	−0.350055	−	0.0484395i
$587$			599.280i			1.02092i	0.859901	+	0.510460i	$0.170525\pi$
$587$			599.280i			1.02092i	−0.859901	+	0.510460i	$0.829475\pi$
$588$	−120.507	+	427.093i	−0.204944	+	0.726348i
$589$	−45.5845			−0.0773931
$590$	25.7834	−	186.328i	0.0437007	−	0.315810i
$591$		−	1013.96i		−	1.71567i
$592$	208.054	+	127.563i	0.351443	+	0.215479i
$593$	−448.563			−0.756430			−0.378215	−	0.925718i	$-0.623462\pi$
$593$	−448.563			−0.756430			−0.378215	+	0.925718i	$0.623462\pi$
$594$	−89.5857	−	12.3966i	−0.150818	−	0.0208697i
$595$			323.794i			0.544191i
$596$	−833.526	−	235.184i	−1.39853	−	0.394605i
$597$	350.660			0.587370
$598$	3.45023	−	24.9336i	0.00576961	−	0.0416950i
$599$		−	228.135i		−	0.380859i	−0.981701	−	0.190430i	$-0.939012\pi$
$599$		−	228.135i		−	0.380859i	0.981701	−	0.190430i	$-0.0609881\pi$
$600$	65.7013	−	150.133i	0.109502	−	0.250222i
$601$	−480.561			−0.799602			−0.399801	−	0.916602i	$-0.630921\pi$
$601$	−480.561			−0.799602			−0.399801	+	0.916602i	$0.630921\pi$
$602$	−503.962	−	69.7367i	−0.837146	−	0.115842i
$603$		−	719.475i		−	1.19316i
$604$	−306.521	+	1086.35i	−0.507486	+	1.79860i
$605$	−85.9127			−0.142004
$606$	−87.5297	+	632.547i	−0.144439	+	1.04381i
$607$			214.535i			0.353435i	0.984262	+	0.176717i	$0.0565479\pi$
$607$			214.535i			0.353435i	−0.984262	+	0.176717i	$0.943452\pi$
$608$	−88.5199	+	107.797i	−0.145592	+	0.177298i
$609$	−79.1988			−0.130047
$610$	−441.668	−	61.1165i	−0.724045	−	0.100191i
$611$			296.809i			0.485775i
$612$	926.957	+	261.547i	1.51463	+	0.427364i
$613$	−71.1766			−0.116112			−0.0580559	−	0.998313i	$-0.518490\pi$
$613$	−71.1766			−0.116112			−0.0580559	+	0.998313i	$0.518490\pi$
$614$	1.69225	−	12.2293i	0.00275610	−	0.0199174i
$615$			244.900i			0.398211i
$616$	−311.822	−	136.459i	−0.506205	−	0.221525i
$617$	−428.579			−0.694617			−0.347309	−	0.937751i	$-0.612904\pi$
$617$	−428.579			−0.694617			−0.347309	+	0.937751i	$0.612904\pi$
$618$	147.840	+	20.4576i	0.239224	+	0.0331030i
$619$			802.576i			1.29657i	0.761398	+	0.648285i	$0.224513\pi$
$619$			802.576i			1.29657i	−0.761398	+	0.648285i	$0.775487\pi$
$620$	−25.4004	+	90.0226i	−0.0409685	+	0.145198i
$621$	8.51163			0.0137063
$622$	−119.889	+	866.397i	−0.192748	+	1.39292i
$623$			26.9303i			0.0432268i
$624$	252.111	−	411.191i	0.404024	−	0.658959i
$625$	25.0000			0.0400000
$626$	935.538	+	129.457i	1.49447	+	0.206800i
$627$		−	162.284i		−	0.258827i
$628$	−876.860	−	247.412i	−1.39627	−	0.393968i
$629$	−471.743			−0.749989
$630$	22.3446	−	161.477i	0.0354677	−	0.256312i
$631$		−	879.059i		−	1.39312i	−0.717498	−	0.696560i	$-0.754713\pi$
$631$		−	879.059i		−	1.39312i	0.717498	−	0.696560i	$-0.245287\pi$
$632$	−10.6724	+	24.3875i	−0.0168868	+	0.0385878i
$633$	1090.54			1.72281
$634$	97.7128	+	13.5212i	0.154121	+	0.0213268i
$635$		−	66.3044i		−	0.104416i
$636$	−31.9709	+	113.309i	−0.0502687	+	0.178159i
$637$	−199.243			−0.312784
$638$	−10.2856	+	74.3303i	−0.0161216	+	0.116505i
$639$			827.129i			1.29441i
$640$	163.558	+	234.880i	0.255560	+	0.367000i
$641$	834.981			1.30262			0.651311	−	0.758811i	$-0.274219\pi$
$641$	834.981			1.30262			0.651311	+	0.758811i	$0.274219\pi$
$642$	959.260	+	132.739i	1.49417	+	0.206759i
$643$			487.259i			0.757790i	0.925440	+	0.378895i	$0.123696\pi$
$643$			487.259i			0.757790i	−0.925440	+	0.378895i	$0.876304\pi$
$644$	30.8303	+	8.69895i	0.0478731	+	0.0135077i
$645$	−497.744			−0.771696
$646$	36.9575	−	267.079i	0.0572098	−	0.413435i
$647$			817.447i			1.26344i	0.775196	+	0.631721i	$0.217651\pi$
$647$			817.447i			1.26344i	−0.775196	+	0.631721i	$0.782349\pi$
$648$	662.947	+	290.118i	1.02307	+	0.447713i
$649$	−382.222			−0.588939
$650$	72.8845	+	10.0855i	0.112130	+	0.0155162i
$651$			200.603i			0.308147i
$652$	164.968	−	584.669i	0.253018	−	0.896731i
$653$	1206.41			1.84749			0.923746	−	0.383007i	$-0.125111\pi$
$653$	1206.41			1.84749			0.923746	+	0.383007i	$0.125111\pi$
$654$	−29.8856	+	215.972i	−0.0456966	+	0.330233i
$655$		−	279.701i		−	0.427025i
$656$	−364.636	−	223.568i	−0.555848	−	0.340804i
$657$	557.289			0.848234
$658$	−374.167	−	51.7761i	−0.568644	−	0.0786871i
$659$			674.050i			1.02284i	0.859332	+	0.511418i	$0.170880\pi$
$659$			674.050i			1.02284i	−0.859332	+	0.511418i	$0.829120\pi$
$660$	−320.488	−	90.4276i	−0.485587	−	0.137011i
$661$	−21.4946			−0.0325182			−0.0162591	−	0.999868i	$-0.505176\pi$
$661$	−21.4946			−0.0325182			−0.0162591	+	0.999868i	$0.505176\pi$
$662$	48.7040	−	351.966i	0.0735709	−	0.531671i
$663$			932.334i			1.40624i
$664$	−95.7385	+	218.771i	−0.144184	+	0.329475i
$665$	−45.6345			−0.0686234
$666$	235.260	+	32.5545i	0.353243	+	0.0488806i
$667$		−	7.06220i		−	0.0105880i
$668$	211.926	−	751.096i	0.317255	−	1.12440i
$669$	489.109			0.731105
$670$	−56.6491	+	409.383i	−0.0845510	+	0.611020i
$671$			906.010i			1.35024i
$672$	474.382	+	389.549i	0.705926	+	0.579686i
$673$	−450.510			−0.669406			−0.334703	−	0.942324i	$-0.608636\pi$
$673$	−450.510			−0.669406			−0.334703	+	0.942324i	$0.608636\pi$
$674$	−1070.98	−	148.198i	−1.58898	−	0.219878i
$675$			24.8807i			0.0368604i
$676$	−442.181	−	124.764i	−0.654113	−	0.184562i
$677$	101.601			0.150075			0.0750375	−	0.997181i	$-0.476092\pi$
$677$	101.601			0.150075			0.0750375	+	0.997181i	$0.476092\pi$
$678$	141.463	−	1022.31i	0.208648	−	1.50782i
$679$			226.250i			0.333210i
$680$	−506.848	−	221.806i	−0.745364	−	0.326186i
$681$	−1185.48			−1.74079
$682$	188.272	+	26.0525i	0.276059	+	0.0382001i
$683$		−	496.372i		−	0.726752i	−0.931642	−	0.363376i	$-0.881624\pi$
$683$		−	496.372i		−	0.726752i	0.931642	−	0.363376i	$-0.118376\pi$
$684$	−36.8616	+	130.643i	−0.0538913	+	0.190998i
$685$	171.147			0.249850
$686$	97.6495	−	705.679i	0.142346	−	1.02869i
$687$		−	1411.93i		−	2.05521i
$688$	454.388	−	741.102i	0.660447	−	1.07718i
$689$	−52.8600			−0.0767199
$690$	31.0443	+	4.29581i	0.0449917	+	0.00622581i
$691$		−	1224.31i		−	1.77179i	−0.463887	−	0.885894i	$-0.653546\pi$
$691$		−	1224.31i		−	1.77179i	0.463887	−	0.885894i	$-0.346454\pi$
$692$	−1001.47	−	282.571i	−1.44721	−	0.408339i
$693$	−331.244			−0.477985
$694$	−98.9880	+	715.351i	−0.142634	+	1.03077i
$695$		−	503.615i		−	0.724626i
$696$	54.2531	−	123.973i	0.0779498	−	0.178122i
$697$	826.777			1.18619
$698$	−596.898	−	82.5969i	−0.855155	−	0.118334i
$699$		−	641.195i		−	0.917303i
$700$	−25.4283	+	90.1214i	−0.0363262	+	0.128745i
$701$	276.408			0.394306			0.197153	−	0.980373i	$-0.436830\pi$
$701$	276.408			0.394306			0.197153	+	0.980373i	$0.436830\pi$
$702$	−10.0374	+	72.5368i	−0.0142983	+	0.103329i
$703$		−	66.4861i		−	0.0945748i
$704$	427.211	−	394.630i	0.606834	−	0.560554i
$705$	−369.551			−0.524185
$706$	−85.8550	−	11.8803i	−0.121608	−	0.0168277i
$707$		−	364.877i		−	0.516092i
$708$	663.397	+	187.182i	0.937001	+	0.264381i
$709$	352.466			0.497131			0.248565	−	0.968615i	$-0.420041\pi$
$709$	352.466			0.497131			0.248565	+	0.968615i	$0.420041\pi$
$710$	65.1254	−	470.639i	0.0917260	−	0.662871i
$711$			25.9064i			0.0364366i
$712$	−42.1551	−	18.4479i	−0.0592067	−	0.0259100i
$713$	−17.8879			−0.0250882
$714$	−1175.33	−	162.639i	−1.64612	−	0.227785i
$715$		−	149.511i		−	0.209106i
$716$	−311.504	+	1104.01i	−0.435062	+	1.54192i
$717$	−1314.34			−1.83311
$718$	54.9453	−	397.070i	0.0765254	−	0.553022i
$719$		−	384.058i		−	0.534156i	−0.963675	−	0.267078i	$-0.913942\pi$
$719$		−	384.058i		−	0.534156i	0.963675	−	0.267078i	$-0.0860582\pi$
$720$	237.460	+	145.592i	0.329805	+	0.202212i
$721$	−85.2799			−0.118280
$722$	37.6413	+	5.20869i	0.0521348	+	0.00721425i
$723$			1872.20i			2.58949i
$724$	−846.429	−	238.825i	−1.16910	−	0.329869i
$725$	20.6439			0.0284743
$726$	43.1532	−	311.853i	0.0594396	−	0.429549i
$727$		−	493.038i		−	0.678182i	−0.940754	−	0.339091i	$-0.889881\pi$
$727$		−	493.038i		−	0.678182i	0.940754	−	0.339091i	$-0.110119\pi$
$728$	−110.490	+	252.480i	−0.151772	+	0.346813i
$729$	520.752			0.714338
$730$	−317.099	−	43.8792i	−0.434383	−	0.0601085i
$731$			1680.37i			2.29873i
$732$	443.691	−	1572.50i	0.606136	−	2.14823i
$733$	1233.99			1.68348			0.841740	−	0.539884i	$-0.181532\pi$
$733$	1233.99			1.68348			0.841740	+	0.539884i	$0.181532\pi$
$734$	−98.0926	+	708.880i	−0.133641	+	0.965777i
$735$		−	248.074i		−	0.337515i
$736$	−34.7363	+	42.3009i	−0.0471961	+	0.0574741i
$737$	839.784			1.13946
$738$	−412.316	−	57.0550i	−0.558694	−	0.0773102i
$739$			170.581i			0.230826i	0.993318	+	0.115413i	$0.0368192\pi$
$739$			170.581i			0.230826i	−0.993318	+	0.115413i	$0.963181\pi$
$740$	−131.300	−	37.0472i	−0.177433	−	0.0500637i
$741$	−131.400			−0.177329
$742$	9.22103	−	66.6371i	0.0124273	−	0.0898075i
$743$		−	1339.76i		−	1.80318i	−0.432596	−	0.901588i	$-0.642402\pi$
$743$		−	1339.76i		−	1.80318i	0.432596	−	0.901588i	$-0.357598\pi$
$744$	−314.013	−	137.418i	−0.422060	−	0.184702i
$745$	484.148			0.649863
$746$	979.121	+	135.488i	1.31249	+	0.181619i
$747$			232.397i			0.311107i
$748$	−305.282	+	1081.96i	−0.408131	+	1.44647i
$749$	−553.338			−0.738770
$750$	−12.5573	+	90.7470i	−0.0167430	+	0.120996i
$751$		−	1167.89i		−	1.55512i	−0.628810	−	0.777559i	$-0.716458\pi$
$751$		−	1167.89i		−	1.55512i	0.628810	−	0.777559i	$-0.283542\pi$
$752$	337.361	−	550.232i	0.448618	−	0.731692i
$753$	−772.557			−1.02597
$754$	60.1847	+	8.32816i	0.0798206	+	0.0110453i
$755$		−	631.001i		−	0.835763i
$756$	−89.6915	−	25.3070i	−0.118640	−	0.0334749i
$757$	273.227			0.360934			0.180467	−	0.983581i	$-0.442239\pi$
$757$	273.227			0.360934			0.180467	+	0.983581i	$0.442239\pi$
$758$	−30.9863	+	223.927i	−0.0408790	+	0.295418i
$759$		−	63.6824i		−	0.0839030i
$760$	31.2608	−	71.4336i	0.0411326	−	0.0939916i
$761$	−516.059			−0.678133			−0.339067	−	0.940762i	$-0.610111\pi$
$761$	−516.059			−0.678133			−0.339067	+	0.940762i	$0.610111\pi$
$762$	240.677	+	33.3041i	0.315849	+	0.0437062i
$763$		−	124.581i		−	0.163278i
$764$	344.918	−	1222.44i	0.451463	−	1.60005i
$765$	−538.416			−0.703812
$766$	−157.934	+	1141.33i	−0.206180	+	1.48999i
$767$			309.482i			0.403497i
$768$	−934.741	+	475.720i	−1.21711	+	0.619427i
$769$	−575.920			−0.748920			−0.374460	−	0.927243i	$-0.622172\pi$
$769$	−575.920			−0.748920			−0.374460	+	0.927243i	$0.622172\pi$
$770$	188.479	+	26.0811i	0.244777	+	0.0338715i
$771$		−	118.043i		−	0.153104i
$772$	−60.1579	−	16.9739i	−0.0779247	−	0.0219869i
$773$	593.593			0.767908			0.383954	−	0.923352i	$-0.374562\pi$
$773$	593.593			0.767908			0.383954	+	0.923352i	$0.374562\pi$
$774$	115.961	−	838.008i	0.149820	−	1.08270i
$775$		−	52.2890i		−	0.0674697i
$776$	−354.158	−	154.987i	−0.456390	−	0.199725i
$777$	−292.585			−0.376557
$778$	205.110	+	28.3825i	0.263638	+	0.0364814i
$779$			116.524i			0.149581i
$780$	−73.2185	+	259.496i	−0.0938699	+	0.332688i
$781$	−965.440			−1.23616
$782$	14.5026	−	104.805i	0.0185455	−	0.134022i
$783$			20.5454i			0.0262393i
$784$	369.363	+	226.465i	0.471126	+	0.288859i
$785$	509.318			0.648813
$786$	1015.28	+	140.491i	1.29171	+	0.178742i
$787$		−	1302.99i		−	1.65564i	−0.560992	−	0.827821i	$-0.689580\pi$
$787$		−	1302.99i		−	1.65564i	0.560992	−	0.827821i	$-0.310420\pi$
$788$	−952.753	−	268.825i	−1.20908	−	0.341149i
$789$	−1288.94			−1.63363
$790$	2.03979	−	14.7408i	0.00258201	−	0.0186593i
$791$			589.705i			0.745519i
$792$	226.910	−	518.510i	0.286502	−	0.654684i
$793$	733.590			0.925081
$794$	−1025.10	−	141.850i	−1.29106	−	0.178653i
$795$		−	65.8149i		−	0.0827860i
$796$	92.9685	−	329.493i	0.116795	−	0.413936i
$797$	111.198			0.139521			0.0697603	−	0.997564i	$-0.477777\pi$
$797$	111.198			0.139521			0.0697603	+	0.997564i	$0.477777\pi$
$798$	22.9218	−	165.648i	0.0287241	−	0.207579i
$799$			1247.60i			1.56145i
$800$	−123.652	−	101.539i	−0.154565	−	0.126924i
$801$	−44.7808			−0.0559061
$802$	37.0530	+	5.12728i	0.0462008	+	0.00639311i
$803$			650.478i			0.810060i
$804$	−1457.56	−	411.259i	−1.81288	−	0.511517i
$805$	−17.9076			−0.0222454
$806$	21.0945	−	152.442i	0.0261718	−	0.189135i
$807$		−	1412.60i		−	1.75043i
$808$	571.158	+	249.950i	0.706878	+	0.309344i
$809$	−974.325			−1.20436			−0.602178	−	0.798362i	$-0.705700\pi$
$809$	−974.325			−1.20436			−0.602178	+	0.798362i	$0.705700\pi$
$810$	−400.713	−	55.4494i	−0.494708	−	0.0684561i
$811$		−	488.558i		−	0.602415i	−0.953559	−	0.301207i	$-0.902610\pi$
$811$		−	488.558i		−	0.602415i	0.953559	−	0.301207i	$-0.0973896\pi$
$812$	−20.9975	+	74.4181i	−0.0258590	+	0.0916479i
$813$	1378.59			1.69569
$814$	−37.9982	+	274.599i	−0.0466808	+	0.337345i
$815$			339.601i			0.416688i
$816$	1059.72	−	1728.39i	1.29867	−	2.11812i
$817$	−236.827			−0.289874
$818$	911.961	+	126.194i	1.11487	+	0.154272i
$819$			268.206i			0.327479i
$820$	230.117	+	64.9289i	0.280630	+	0.0791816i
$821$	175.380			0.213617			0.106809	−	0.994280i	$-0.465937\pi$
$821$	175.380			0.213617			0.106809	+	0.994280i	$0.465937\pi$
$822$	−85.9656	+	621.243i	−0.104581	+	0.755770i
$823$		−	303.070i		−	0.368250i	−0.982903	−	0.184125i	$-0.941055\pi$
$823$		−	303.070i		−	0.368250i	0.982903	−	0.184125i	$-0.0589452\pi$
$824$	58.4188	−	133.492i	0.0708966	−	0.162005i
$825$	186.153			0.225640
$826$	−390.144	−	53.9868i	−0.472329	−	0.0653593i
$827$			913.320i			1.10438i	0.833719	+	0.552189i	$0.186207\pi$
$827$			913.320i			1.10438i	−0.833719	+	0.552189i	$0.813793\pi$
$828$	−14.4650	+	51.2658i	−0.0174698	+	0.0619152i
$829$	−1284.39			−1.54933			−0.774663	−	0.632375i	$-0.782080\pi$
$829$	−1284.39			−1.54933			−0.774663	+	0.632375i	$0.782080\pi$
$830$	18.2982	−	132.235i	0.0220460	−	0.159319i
$831$		−	186.163i		−	0.224023i
$832$	−319.529	−	345.910i	−0.384049	−	0.415757i
$833$	−837.493			−1.00539
$834$	1828.06	+	252.961i	2.19192	+	0.303311i
$835$			436.269i			0.522478i
$836$	−152.488	−	43.0256i	−0.182402	−	0.0514660i
$837$	52.0396			0.0621739
$838$	174.132	−	1258.39i	0.207794	−	1.50166i
$839$			671.812i			0.800730i	0.916356	+	0.400365i	$0.131117\pi$
$839$			671.812i			0.800730i	−0.916356	+	0.400365i	$0.868883\pi$
$840$	−314.358	−	137.569i	−0.374235	−	0.163773i
$841$	−823.953			−0.979730
$842$	−928.174	−	128.438i	−1.10234	−	0.152539i
$843$			2027.33i			2.40490i
$844$	289.129	−	1024.71i	0.342570	−	1.21411i
$845$	256.838			0.303950
$846$	86.0953	−	622.180i	0.101767	−	0.735437i
$847$			179.889i			0.212383i
$848$	97.9933	+	60.0821i	0.115558	+	0.0708515i
$849$	288.612			0.339944
$850$	306.360	+	42.3932i	0.360424	+	0.0498743i
$851$		−	26.0900i		−	0.0306580i
$852$	1675.65	+	472.795i	1.96673	+	0.554924i
$853$	983.634			1.15315			0.576573	−	0.817045i	$-0.304390\pi$
$853$	983.634			1.15315			0.576573	+	0.817045i	$0.304390\pi$
$854$	−127.969	+	924.788i	−0.149847	+	1.08289i
$855$		−	75.8829i		−	0.0887519i
$856$	379.050	−	866.164i	0.442815	−	1.01187i
$857$	−302.002			−0.352394			−0.176197	−	0.984355i	$-0.556380\pi$
$857$	−302.002			−0.352394			−0.176197	+	0.984355i	$0.556380\pi$
$858$	542.707	+	75.0980i	0.632526	+	0.0875268i
$859$		−	236.808i		−	0.275678i	−0.990455	−	0.137839i	$-0.955984\pi$
$859$		−	236.808i		−	0.275678i	0.990455	−	0.137839i	$-0.0440157\pi$
$860$	−131.964	+	467.698i	−0.153447	+	0.543835i
$861$	512.785			0.595569
$862$	186.175	−	1345.42i	0.215980	−	1.56081i
$863$			1194.77i			1.38443i	0.721689	+	0.692217i	$0.243366\pi$
$863$			1194.77i			1.38443i	−0.721689	+	0.692217i	$0.756634\pi$
$864$	101.055	−	123.062i	0.116962	−	0.142433i
$865$	581.696			0.672481
$866$	824.156	+	114.044i	0.951681	+	0.131691i
$867$			2734.91i			3.15445i
$868$	188.494	+	53.1849i	0.217159	+	0.0612729i
$869$	−30.2385			−0.0347969
$870$	−10.3692	+	74.9347i	−0.0119187	+	0.0861319i
$871$		−	679.967i		−	0.780674i
$872$	195.012	+	85.3411i	0.223638	+	0.0978683i
$873$	−376.217			−0.430947
$874$	14.7709	+	2.04395i	0.0169004	+	0.00233862i
$875$		−	52.3464i		−	0.0598245i
$876$	318.552	−	1128.99i	0.363644	−	1.28880i
$877$	−733.510			−0.836385			−0.418193	−	0.908358i	$-0.637336\pi$
$877$	−733.510			−0.836385			−0.418193	+	0.908358i	$0.637336\pi$
$878$	101.958	−	736.818i	0.116126	−	0.839200i
$879$			424.218i			0.482614i
$880$	−169.938	+	277.167i	−0.193112	+	0.314963i
$881$	−544.620			−0.618184			−0.309092	−	0.951032i	$-0.600025\pi$
$881$	−544.620			−0.618184			−0.309092	+	0.951032i	$0.600025\pi$
$882$	417.660	+	57.7945i	0.473538	+	0.0655266i
$883$		−	643.155i		−	0.728375i	−0.931326	−	0.364188i	$-0.881347\pi$
$883$		−	643.155i		−	0.728375i	0.931326	−	0.364188i	$-0.118653\pi$
$884$	876.055	+	247.184i	0.991013	+	0.279620i
$885$	−385.330			−0.435401
$886$	26.0845	−	188.503i	0.0294407	−	0.212758i
$887$		−	544.549i		−	0.613922i	−0.951722	−	0.306961i	$-0.900688\pi$
$887$		−	544.549i		−	0.613922i	0.951722	−	0.306961i	$-0.0993121\pi$
$888$	200.428	−	457.995i	0.225707	−	0.515761i
$889$	−138.832			−0.156166
$890$	25.4804	+	3.52589i	0.0286296	+	0.00396168i
$891$			821.999i			0.922558i
$892$	129.675	−	459.585i	0.145375	−	0.515230i
$893$	−175.833			−0.196901
$894$	−243.183	+	1757.40i	−0.272017	+	1.96577i
$895$		−	641.259i		−	0.716490i
$896$	491.805	−	342.468i	0.548889	−	0.382219i
$897$	−51.5631			−0.0574840
$898$	−511.948	−	70.8417i	−0.570098	−	0.0788883i
$899$		−	43.1779i		−	0.0480288i
$900$	−149.857	−	42.2832i	−0.166508	−	0.0469813i
$901$	−222.190			−0.246604
$902$	66.5956	−	481.263i	0.0738310	−	0.533551i
$903$			1042.20i			1.15416i
$904$	−923.090	−	403.962i	−1.02112	−	0.446861i
$905$	491.642			0.543251
$906$	2290.46	+	316.946i	2.52810	+	0.349830i
$907$			1611.25i			1.77646i	0.459403	+	0.888228i	$0.348063\pi$
$907$			1611.25i			1.77646i	−0.459403	+	0.888228i	$0.651937\pi$
$908$	−314.299	+	1113.92i	−0.346144	+	1.22678i
$909$	606.732			0.667472
$910$	21.1176	−	152.610i	0.0232062	−	0.167703i
$911$			1048.13i			1.15053i	0.817967	+	0.575265i	$0.195101\pi$
$911$			1048.13i			1.15053i	−0.817967	+	0.575265i	$0.804899\pi$
$912$	243.594	+	149.353i	0.267098	+	0.163765i
$913$	−271.258			−0.297106
$914$	308.311	+	42.6631i	0.337321	+	0.0466774i
$915$			913.377i			0.998227i
$916$	−1326.70	−	374.337i	−1.44836	−	0.408665i
$917$	−585.654			−0.638663
$918$	−42.1909	+	304.899i	−0.0459596	+	0.332134i
$919$		−	1056.61i		−	1.14974i	−0.818246	−	0.574868i	$-0.805053\pi$
$919$		−	1056.61i		−	1.14974i	0.818246	−	0.574868i	$-0.194947\pi$
$920$	12.2671	−	28.0314i	0.0133338	−	0.0304690i
$921$	−25.2904			−0.0274597
$922$	215.661	+	29.8424i	0.233905	+	0.0323671i
$923$			781.709i			0.846922i
$924$	−189.342	+	671.055i	−0.204916	+	0.726250i
$925$	76.2648			0.0824484
$926$	−85.1181	+	615.118i	−0.0919202	+	0.664275i
$927$		−	141.807i		−	0.152974i
$928$	−102.106	−	83.8465i	−0.110028	−	0.0903519i
$929$	1279.28			1.37705			0.688525	−	0.725213i	$-0.258259\pi$
$929$	1279.28			1.37705			0.688525	+	0.725213i	$0.258259\pi$
$930$	189.803	+	26.2643i	0.204089	+	0.0282412i
$931$		−	118.034i		−	0.126782i
$932$	−602.491	−	169.997i	−0.646449	−	0.182400i
$933$	1791.73			1.92039
$934$	−105.790	+	764.508i	−0.113266	+	0.818531i
$935$		−	628.449i		−	0.672138i
$936$	−419.833	−	183.727i	−0.448540	−	0.196290i
$937$	−222.564			−0.237529			−0.118764	−	0.992922i	$-0.537893\pi$
$937$	−222.564			−0.237529			−0.118764	+	0.992922i	$0.537893\pi$
$938$	857.190	+	118.615i	0.913848	+	0.126455i
$939$		−	1934.71i		−	2.06039i
$940$	−97.9769	+	347.243i	−0.104231	+	0.369408i
$941$	−126.788			−0.134738			−0.0673688	−	0.997728i	$-0.521460\pi$
$941$	−126.788			−0.134738			−0.0673688	+	0.997728i	$0.521460\pi$
$942$	−255.826	+	1848.76i	−0.271578	+	1.96260i
$943$			45.7253i			0.0484892i
$944$	351.765	−	573.726i	0.372633	−	0.607760i
$945$	52.0967			0.0551288
$946$	978.138	+	135.352i	1.03397	+	0.143078i
$947$			1379.37i			1.45657i	0.685273	+	0.728286i	$0.259683\pi$
$947$			1379.37i			1.45657i	−0.685273	+	0.728286i	$0.740317\pi$
$948$	52.4829	+	14.8084i	0.0553617	+	0.0156207i
$949$	526.687			0.554992
$950$	−5.97477	+	43.1776i	−0.00628923	+	0.0454501i
$951$		−	202.072i		−	0.212484i
$952$	−464.431	+	1061.27i	−0.487847	+	1.11478i
$953$	−331.516			−0.347866			−0.173933	−	0.984758i	$-0.555648\pi$
$953$	−331.516			−0.347866			−0.173933	+	0.984758i	$0.555648\pi$
$954$	110.807	+	15.3331i	0.116150	+	0.0160724i
$955$			710.044i			0.743501i
$956$	−348.464	+	1235.00i	−0.364502	+	1.29184i
$957$	153.717			0.160623
$958$	86.8276	−	627.472i	0.0906342	−	0.654982i
$959$		−	358.357i		−	0.373678i
$960$	430.685	−	397.839i	0.448630	−	0.414416i
$961$	851.634			0.886196
$962$	222.341	+	30.7668i	0.231124	+	0.0319821i
$963$		−	920.112i		−	0.955464i
$964$	1759.19	+	496.367i	1.82489	+	0.514904i
$965$	34.9423			0.0362096
$966$	8.99481	−	65.0023i	0.00931139	−	0.0672901i
$967$		−	1215.50i		−	1.25698i	−0.777819	−	0.628489i	$-0.783674\pi$
$967$		−	1215.50i		−	1.25698i	0.777819	−	0.628489i	$-0.216326\pi$
$968$	−281.587	−	123.228i	−0.290896	−	0.127302i
$969$	−552.324			−0.569994
$970$	214.069	+	29.6221i	0.220689	+	0.0305383i
$971$			163.084i			0.167955i	0.996468	+	0.0839775i	$0.0267624\pi$
$971$			163.084i			0.167955i	−0.996468	+	0.0839775i	$0.973238\pi$
$972$	353.903	−	1254.28i	0.364098	−	1.29041i
$973$	−1054.50			−1.08376
$974$	194.853	−	1408.13i	0.200055	−	1.44572i
$975$		−	150.727i		−	0.154591i
$976$	−1359.95	−	833.818i	−1.39339	−	0.854321i
$977$	−342.925			−0.350998			−0.175499	−	0.984480i	$-0.556154\pi$
$977$	−342.925			−0.350998			−0.175499	+	0.984480i	$0.556154\pi$
$978$	−1232.71	−	170.579i	−1.26044	−	0.174416i
$979$		−	52.2689i		−	0.0533901i
$980$	−233.099	−	65.7704i	−0.237856	−	0.0671127i
$981$	207.158			0.211171
$982$	210.086	−	1518.22i	0.213937	−	1.54604i
$983$			1330.96i			1.35397i	0.735995	+	0.676986i	$0.236714\pi$
$983$			1330.96i			1.35397i	−0.735995	+	0.676986i	$0.763286\pi$
$984$	−351.270	+	802.683i	−0.356981	+	0.815735i
$985$	553.400			0.561828
$986$	252.978	+	35.0063i	0.256570	+	0.0355034i
$987$			773.786i			0.783977i
$988$	−34.8375	+	123.469i	−0.0352606	+	0.124968i
$989$	−92.9339			−0.0939675
$990$	−43.3686	+	313.410i	−0.0438067	+	0.316575i
$991$			883.450i			0.891473i	0.895164	+	0.445736i	$0.147058\pi$
$991$			883.450i			0.891473i	−0.895164	+	0.445736i	$0.852942\pi$
$992$	−212.376	+	258.625i	−0.214088	+	0.260711i
$993$	−727.873			−0.733004
$994$	−985.449	−	136.363i	−0.991398	−	0.137186i
$995$			191.384i			0.192345i
$996$	470.805	+	132.841i	0.472696	+	0.133374i
$997$	85.0157			0.0852715			0.0426358	−	0.999091i	$-0.486424\pi$
$997$	85.0157			0.0852715			0.0426358	+	0.999091i	$0.486424\pi$
$998$	83.9357	−	606.574i	0.0841039	−	0.607789i
$999$			75.9010i			0.0759769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.b.a.191.5	✓	72
4.3	odd	2	inner	380.3.b.a.191.6	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.b.a.191.5	✓	72	1.1	even	1	trivial
380.3.b.a.191.6	yes	72	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98112 - 0.274141i) q^{2} +4.09700i q^{3} +(3.84969 + 1.08622i) q^{4} -2.23607 q^{5} +(1.12316 - 8.11666i) q^{6} +4.68200i q^{7} +(-7.32894 - 3.20729i) q^{8} -7.78542 q^{9} +O(q^{10})\)	\(q+(-1.98112 - 0.274141i) q^{2} +4.09700i q^{3} +(3.84969 + 1.08622i) q^{4} -2.23607 q^{5} +(1.12316 - 8.11666i) q^{6} +4.68200i q^{7} +(-7.32894 - 3.20729i) q^{8} -7.78542 q^{9} +(4.42992 + 0.612999i) q^{10} -9.08728i q^{11} +(-4.45022 + 15.7722i) q^{12} -7.35790 q^{13} +(1.28353 - 9.27563i) q^{14} -9.16117i q^{15} +(13.6403 + 8.36319i) q^{16} -30.9280 q^{17} +(15.4239 + 2.13430i) q^{18} -4.35890i q^{19} +(-8.60818 - 2.42885i) q^{20} -19.1822 q^{21} +(-2.49120 + 18.0030i) q^{22} -1.71049i q^{23} +(13.1403 - 30.0267i) q^{24} +5.00000 q^{25} +(14.5769 + 2.01710i) q^{26} +4.97615i q^{27} +(-5.08566 + 18.0243i) q^{28} +4.12877 q^{29} +(-2.51146 + 18.1494i) q^{30} -10.4578i q^{31} +(-24.7304 - 20.3079i) q^{32} +37.2306 q^{33} +(61.2721 + 8.47863i) q^{34} -10.4693i q^{35} +(-29.9715 - 8.45664i) q^{36} +15.2530 q^{37} +(-1.19495 + 8.63551i) q^{38} -30.1453i q^{39} +(16.3880 + 7.17171i) q^{40} -26.7323 q^{41} +(38.0022 + 5.25863i) q^{42} -54.3319i q^{43} +(9.87074 - 34.9832i) q^{44} +17.4087 q^{45} +(-0.468915 + 3.38868i) q^{46} -40.3388i q^{47} +(-34.2640 + 55.8842i) q^{48} +27.0788 q^{49} +(-9.90561 - 1.37071i) q^{50} -126.712i q^{51} +(-28.3257 - 7.99226i) q^{52} +7.18411 q^{53} +(1.36417 - 9.85836i) q^{54} +20.3198i q^{55} +(15.0165 - 34.3141i) q^{56} +17.8584 q^{57} +(-8.17960 - 1.13187i) q^{58} -42.0612i q^{59} +(9.95100 - 35.2677i) q^{60} -99.7009 q^{61} +(-2.86692 + 20.7182i) q^{62} -36.4514i q^{63} +(43.4266 + 47.0120i) q^{64} +16.4528 q^{65} +(-73.7584 - 10.2064i) q^{66} +92.4132i q^{67} +(-119.063 - 33.5944i) q^{68} +7.00786 q^{69} +(-2.87006 + 20.7409i) q^{70} -106.241i q^{71} +(57.0588 + 24.9701i) q^{72} -71.5812 q^{73} +(-30.2180 - 4.18147i) q^{74} +20.4850i q^{75} +(4.73470 - 16.7804i) q^{76} +42.5467 q^{77} +(-8.26408 + 59.7216i) q^{78} -3.32756i q^{79} +(-30.5006 - 18.7007i) q^{80} -90.4560 q^{81} +(52.9600 + 7.32844i) q^{82} -29.8503i q^{83} +(-73.8455 - 20.8360i) q^{84} +69.1570 q^{85} +(-14.8946 + 107.638i) q^{86} +16.9156i q^{87} +(-29.1455 + 66.6001i) q^{88} +5.75188 q^{89} +(-34.4888 - 4.77245i) q^{90} -34.4497i q^{91} +(1.85796 - 6.58484i) q^{92} +42.8456 q^{93} +(-11.0585 + 79.9161i) q^{94} +9.74679i q^{95} +(83.2013 - 101.320i) q^{96} +48.3233 q^{97} +(-53.6465 - 7.42343i) q^{98} +70.7483i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

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