LMFDB - Embedded newform 368.2.j.c.277.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(93,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("368.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.j (of order $4$, degree $2$, 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.221124989353984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} + 12 x^{8} - 8 x^{7} - 14 x^{6} - 16 x^{5} + 48 x^{4} + 16 x^{3} + \cdots + 64 $ x^12 - 2x^11 - 2x^10 + 2x^9 + 12x^8 - 8x^7 - 14x^6 - 16x^5 + 48x^4 + 16x^3 - 32x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.2
Root			$1.35092 + 0.418349i$ of defining polynomial
Character	$\chi$	$=$	368.277
Dual form			368.2.j.c.93.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.730558 - 1.21090i) q^{2} +(1.49351 - 1.49351i) q^{3} +(-0.932570 + 1.76927i) q^{4} +(-1.17219 - 1.17219i) q^{5} +(-2.89958 - 0.717397i) q^{6} -0.836699i q^{7} +(2.82371 - 0.163301i) q^{8} -1.46112i q^{9} +O(q^{10})$	\(q+(-0.730558 - 1.21090i) q^{2} +(1.49351 - 1.49351i) q^{3} +(-0.932570 + 1.76927i) q^{4} +(-1.17219 - 1.17219i) q^{5} +(-2.89958 - 0.717397i) q^{6} -0.836699i q^{7} +(2.82371 - 0.163301i) q^{8} -1.46112i q^{9} +(-0.563056 + 2.27576i) q^{10} +(-2.72996 - 2.72996i) q^{11} +(1.24961 + 4.03521i) q^{12} +(3.86087 - 3.86087i) q^{13} +(-1.01316 + 0.611257i) q^{14} -3.50135 q^{15} +(-2.26063 - 3.29994i) q^{16} -6.79704 q^{17} +(-1.76927 + 1.06743i) q^{18} +(-2.46112 + 2.46112i) q^{19} +(3.16707 - 0.980771i) q^{20} +(-1.24961 - 1.24961i) q^{21} +(-1.31132 + 5.30011i) q^{22} +1.00000i q^{23} +(3.97333 - 4.46112i) q^{24} -2.25193i q^{25} +(-7.49573 - 1.85455i) q^{26} +(2.29833 + 2.29833i) q^{27} +(1.48034 + 0.780280i) q^{28} +(3.58194 - 3.58194i) q^{29} +(2.55794 + 4.23979i) q^{30} +5.64220 q^{31} +(-2.34438 + 5.14819i) q^{32} -8.15441 q^{33} +(4.96563 + 8.23056i) q^{34} +(-0.980771 + 0.980771i) q^{35} +(2.58511 + 1.36259i) q^{36} +(5.17185 + 5.17185i) q^{37} +(4.77816 + 1.18218i) q^{38} -11.5325i q^{39} +(-3.50135 - 3.11851i) q^{40} +2.36368i q^{41} +(-0.600245 + 2.42608i) q^{42} +(-4.86479 - 4.86479i) q^{43} +(7.37591 - 2.28415i) q^{44} +(-1.71271 + 1.71271i) q^{45} +(1.21090 - 0.730558i) q^{46} -6.69829 q^{47} +(-8.30473 - 1.55222i) q^{48} +6.29994 q^{49} +(-2.72687 + 1.64517i) q^{50} +(-10.1514 + 10.1514i) q^{51} +(3.23038 + 10.4315i) q^{52} +(5.97511 + 5.97511i) q^{53} +(1.10399 - 4.46212i) q^{54} +6.40007i q^{55} +(-0.136634 - 2.36259i) q^{56} +7.35138i q^{57} +(-6.95419 - 1.72057i) q^{58} +(-2.79082 - 2.79082i) q^{59} +(3.26525 - 6.19483i) q^{60} +(8.82336 - 8.82336i) q^{61} +(-4.12195 - 6.83215i) q^{62} -1.22251 q^{63} +(7.94667 - 0.922232i) q^{64} -9.05136 q^{65} +(5.95727 + 9.87420i) q^{66} +(0.659190 - 0.659190i) q^{67} +(6.33872 - 12.0258i) q^{68} +(1.49351 + 1.49351i) q^{69} +(1.90413 + 0.471108i) q^{70} -12.0202i q^{71} +(-0.238602 - 4.12577i) q^{72} +9.63409i q^{73} +(2.48427 - 10.0409i) q^{74} +(-3.36327 - 3.36327i) q^{75} +(-2.05921 - 6.64954i) q^{76} +(-2.28415 + 2.28415i) q^{77} +(-13.9647 + 8.42513i) q^{78} -0.450884 q^{79} +(-1.21827 + 6.51804i) q^{80} +11.2485 q^{81} +(2.86219 - 1.72680i) q^{82} +(9.95642 - 9.95642i) q^{83} +(3.37626 - 1.04555i) q^{84} +(7.96744 + 7.96744i) q^{85} +(-2.33678 + 9.44481i) q^{86} -10.6993i q^{87} +(-8.15441 - 7.26280i) q^{88} -4.51731i q^{89} +(3.32515 + 0.822690i) q^{90} +(-3.23038 - 3.23038i) q^{91} +(-1.76927 - 0.932570i) q^{92} +(8.42665 - 8.42665i) q^{93} +(4.89349 + 8.11097i) q^{94} +5.76980 q^{95} +(4.18750 + 11.1902i) q^{96} -2.31130 q^{97} +(-4.60247 - 7.62861i) q^{98} +(-3.98879 + 3.98879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26} + 14 q^{27} + 12 q^{28} + 2 q^{29} - 30 q^{30} + 20 q^{31} - 8 q^{32} - 36 q^{33} + 10 q^{34} + 4 q^{35} + 4 q^{36} - 4 q^{37} + 24 q^{38} - 14 q^{42} + 20 q^{43} + 4 q^{44} - 20 q^{45} - 2 q^{46} - 16 q^{47} - 12 q^{48} + 52 q^{49} + 6 q^{50} - 4 q^{51} - 16 q^{53} + 16 q^{54} + 28 q^{56} + 14 q^{58} + 8 q^{59} + 48 q^{60} + 12 q^{61} - 44 q^{62} - 4 q^{63} + 24 q^{64} - 52 q^{65} + 34 q^{66} - 4 q^{67} - 16 q^{68} + 2 q^{69} + 28 q^{70} + 8 q^{72} - 26 q^{74} - 46 q^{75} - 8 q^{76} - 12 q^{77} - 44 q^{78} - 4 q^{79} + 4 q^{80} + 48 q^{81} - 6 q^{82} + 28 q^{83} + 12 q^{84} - 8 q^{85} + 44 q^{86} - 36 q^{88} + 4 q^{90} - 4 q^{92} - 14 q^{93} + 48 q^{95} + 32 q^{96} + 36 q^{97} - 2 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8 - 6 * q^10 - 4 * q^11 - 8 * q^12 + 18 * q^13 - 2 * q^14 + 8 * q^16 - 8 * q^17 - 4 * q^18 - 8 * q^19 - 32 * q^20 + 8 * q^21 - 34 * q^22 + 12 * q^24 - 14 * q^26 + 14 * q^27 + 12 * q^28 + 2 * q^29 - 30 * q^30 + 20 * q^31 - 8 * q^32 - 36 * q^33 + 10 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 24 * q^38 - 14 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 2 * q^46 - 16 * q^47 - 12 * q^48 + 52 * q^49 + 6 * q^50 - 4 * q^51 - 16 * q^53 + 16 * q^54 + 28 * q^56 + 14 * q^58 + 8 * q^59 + 48 * q^60 + 12 * q^61 - 44 * q^62 - 4 * q^63 + 24 * q^64 - 52 * q^65 + 34 * q^66 - 4 * q^67 - 16 * q^68 + 2 * q^69 + 28 * q^70 + 8 * q^72 - 26 * q^74 - 46 * q^75 - 8 * q^76 - 12 * q^77 - 44 * q^78 - 4 * q^79 + 4 * q^80 + 48 * q^81 - 6 * q^82 + 28 * q^83 + 12 * q^84 - 8 * q^85 + 44 * q^86 - 36 * q^88 + 4 * q^90 - 4 * q^92 - 14 * q^93 + 48 * q^95 + 32 * q^96 + 36 * q^97 - 2 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.730558	−	1.21090i	−0.516582	−	0.856237i
$2$	−0.730558	−	1.21090i	−0.516582	−	0.856237i
$3$	1.49351	−	1.49351i	0.862276	−	0.862276i	−0.129326	−	0.991602i	$-0.541282\pi$
$3$	1.49351	−	1.49351i	0.862276	−	0.862276i	0.991602	+	0.129326i	$0.0412815\pi$
$4$	−0.932570	+	1.76927i	−0.466285	+	0.884634i
$5$	−1.17219	−	1.17219i	−0.524220	−	0.524220i	0.394623	−	0.918843i	$-0.370875\pi$
$5$	−1.17219	−	1.17219i	−0.524220	−	0.524220i	−0.918843	+	0.394623i	$0.870875\pi$
$6$	−2.89958	−	0.717397i	−1.18375	−	0.292876i
$7$		−	0.836699i		−	0.316242i	−0.987420	−	0.158121i	$-0.949456\pi$
$7$		−	0.836699i		−	0.316242i	0.987420	−	0.158121i	$-0.0505437\pi$
$8$	2.82371	−	0.163301i	0.998332	−	0.0577358i
$9$		−	1.46112i		−	0.487039i
$10$	−0.563056	+	2.27576i	−0.178054	+	0.719660i
$11$	−2.72996	−	2.72996i	−0.823113	−	0.823113i	0.163440	−	0.986553i	$-0.447741\pi$
$11$	−2.72996	−	2.72996i	−0.823113	−	0.823113i	−0.986553	+	0.163440i	$0.947741\pi$
$12$	1.24961	+	4.03521i	0.360732	+	1.16487i
$13$	3.86087	−	3.86087i	1.07081	−	1.07081i	0.0735190	−	0.997294i	$-0.476577\pi$
$13$	3.86087	−	3.86087i	1.07081	−	1.07081i	0.997294	−	0.0735190i	$-0.0234229\pi$
$14$	−1.01316	+	0.611257i	−0.270779	+	0.163365i
$15$	−3.50135			−0.904044
$16$	−2.26063	−	3.29994i	−0.565156	−	0.824984i
$17$	−6.79704			−1.64852			−0.824262	−	0.566208i	$-0.808410\pi$
$17$	−6.79704			−1.64852			−0.824262	+	0.566208i	$0.808410\pi$
$18$	−1.76927	+	1.06743i	−0.417021	+	0.251596i
$19$	−2.46112	+	2.46112i	−0.564619	+	0.564619i	−0.930616	−	0.365997i	$-0.880728\pi$
$19$	−2.46112	+	2.46112i	−0.564619	+	0.564619i	0.365997	+	0.930616i	$0.380728\pi$
$20$	3.16707	−	0.980771i	0.708179	−	0.219307i
$21$	−1.24961	−	1.24961i	−0.272688	−	0.272688i
$22$	−1.31132	+	5.30011i	−0.279575	+	1.12999i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	3.97333	−	4.46112i	0.811053	−	0.910621i
$25$		−	2.25193i		−	0.450387i
$26$	−7.49573	−	1.85455i	−1.47003	−	0.363707i
$27$	2.29833	+	2.29833i	0.442314	+	0.442314i
$28$	1.48034	+	0.780280i	0.279759	+	0.147459i
$29$	3.58194	−	3.58194i	0.665149	−	0.665149i	−0.291440	−	0.956589i	$-0.594134\pi$
$29$	3.58194	−	3.58194i	0.665149	−	0.665149i	0.956589	+	0.291440i	$0.0941343\pi$
$30$	2.55794	+	4.23979i	0.467013	+	0.774077i
$31$	5.64220			1.01337			0.506684	−	0.862132i	$-0.330871\pi$
$31$	5.64220			1.01337			0.506684	+	0.862132i	$0.330871\pi$
$32$	−2.34438	+	5.14819i	−0.414432	+	0.910080i
$33$	−8.15441			−1.41950
$34$	4.96563	+	8.23056i	0.851599	+	1.41153i
$35$	−0.980771	+	0.980771i	−0.165781	+	0.165781i
$36$	2.58511	+	1.36259i	0.430851	+	0.227099i
$37$	5.17185	+	5.17185i	0.850246	+	0.850246i	0.990163	−	0.139917i	$-0.0446836\pi$
$37$	5.17185	+	5.17185i	0.850246	+	0.850246i	−0.139917	+	0.990163i	$0.544684\pi$
$38$	4.77816	+	1.18218i	0.775120	+	0.191776i
$39$		−	11.5325i		−	1.84667i
$40$	−3.50135	−	3.11851i	−0.553612	−	0.493079i
$41$			2.36368i			0.369145i	0.982819	+	0.184572i	$0.0590900\pi$
$41$			2.36368i			0.369145i	−0.982819	+	0.184572i	$0.940910\pi$
$42$	−0.600245	+	2.42608i	−0.0926199	+	0.374352i
$43$	−4.86479	−	4.86479i	−0.741874	−	0.741874i	0.231064	−	0.972938i	$-0.425779\pi$
$43$	−4.86479	−	4.86479i	−0.741874	−	0.741874i	−0.972938	+	0.231064i	$0.925779\pi$
$44$	7.37591	−	2.28415i	1.11196	−	0.344349i
$45$	−1.71271	+	1.71271i	−0.255315	+	0.255315i
$46$	1.21090	−	0.730558i	0.178538	−	0.107715i
$47$	−6.69829			−0.977045			−0.488523	−	0.872551i	$-0.662464\pi$
$47$	−6.69829			−0.977045			−0.488523	+	0.872551i	$0.662464\pi$
$48$	−8.30473	−	1.55222i	−1.19868	−	0.224043i
$49$	6.29994			0.899991
$50$	−2.72687	+	1.64517i	−0.385638	+	0.232662i
$51$	−10.1514	+	10.1514i	−1.42148	+	1.42148i
$52$	3.23038	+	10.4315i	0.447974	+	1.44658i
$53$	5.97511	+	5.97511i	0.820744	+	0.820744i	0.986215	−	0.165471i	$-0.0529143\pi$
$53$	5.97511	+	5.97511i	0.820744	+	0.820744i	−0.165471	+	0.986215i	$0.552914\pi$
$54$	1.10399	−	4.46212i	0.150234	−	0.607218i
$55$			6.40007i			0.862985i
$56$	−0.136634	−	2.36259i	−0.0182585	−	0.315715i
$57$			7.35138i			0.973714i
$58$	−6.95419	−	1.72057i	−0.913130	−	0.225921i
$59$	−2.79082	−	2.79082i	−0.363334	−	0.363334i	0.501705	−	0.865039i	$-0.332706\pi$
$59$	−2.79082	−	2.79082i	−0.363334	−	0.363334i	−0.865039	+	0.501705i	$0.832706\pi$
$60$	3.26525	−	6.19483i	0.421542	−	0.799749i
$61$	8.82336	−	8.82336i	1.12972	−	1.12972i	0.139493	−	0.990223i	$-0.455453\pi$
$61$	8.82336	−	8.82336i	1.12972	−	1.12972i	0.990223	−	0.139493i	$-0.0445472\pi$
$62$	−4.12195	−	6.83215i	−0.523488	−	0.867684i
$63$	−1.22251			−0.154022
$64$	7.94667	−	0.922232i	0.993333	−	0.115279i
$65$	−9.05136			−1.12268
$66$	5.95727	+	9.87420i	0.733289	+	1.21543i
$67$	0.659190	−	0.659190i	0.0805329	−	0.0805329i	−0.665693	−	0.746226i	$-0.731864\pi$
$67$	0.659190	−	0.659190i	0.0805329	−	0.0805329i	0.746226	+	0.665693i	$0.231864\pi$
$68$	6.33872	−	12.0258i	0.768683	−	1.45834i
$69$	1.49351	+	1.49351i	0.179797	+	0.179797i
$70$	1.90413	+	0.471108i	0.227587	+	0.0563082i
$71$		−	12.0202i		−	1.42654i	−0.700889	−	0.713270i	$-0.747213\pi$
$71$		−	12.0202i		−	1.42654i	0.700889	−	0.713270i	$-0.252787\pi$
$72$	−0.238602	−	4.12577i	−0.0281196	−	0.486226i
$73$			9.63409i			1.12758i	0.825917	+	0.563792i	$0.190658\pi$
$73$			9.63409i			1.12758i	−0.825917	+	0.563792i	$0.809342\pi$
$74$	2.48427	−	10.0409i	0.288790	−	1.16723i
$75$	−3.36327	−	3.36327i	−0.388358	−	0.388358i
$76$	−2.05921	−	6.64954i	−0.236208	−	0.762754i
$77$	−2.28415	+	2.28415i	−0.260303	+	0.260303i
$78$	−13.9647	+	8.42513i	−1.58119	+	0.953958i
$79$	−0.450884			−0.0507284			−0.0253642	−	0.999678i	$-0.508075\pi$
$79$	−0.450884			−0.0507284			−0.0253642	+	0.999678i	$0.508075\pi$
$80$	−1.21827	+	6.51804i	−0.136207	+	0.728739i
$81$	11.2485			1.24983
$82$	2.86219	−	1.72680i	0.316076	−	0.190694i
$83$	9.95642	−	9.95642i	1.09286	−	1.09286i	0.0976374	−	0.995222i	$-0.468871\pi$
$83$	9.95642	−	9.95642i	1.09286	−	1.09286i	0.995222	−	0.0976374i	$-0.0311286\pi$
$84$	3.37626	−	1.04555i	0.368380	−	0.114079i
$85$	7.96744	+	7.96744i	0.864190	+	0.864190i
$86$	−2.33678	+	9.44481i	−0.251981	+	1.01846i
$87$		−	10.6993i		−	1.14708i
$88$	−8.15441	−	7.26280i	−0.869263	−	0.774217i
$89$		−	4.51731i		−	0.478834i	−0.970917	−	0.239417i	$-0.923044\pi$
$89$		−	4.51731i		−	0.478834i	0.970917	−	0.239417i	$-0.0769563\pi$
$90$	3.32515	+	0.822690i	0.350502	+	0.0867192i
$91$	−3.23038	−	3.23038i	−0.338636	−	0.338636i
$92$	−1.76927	−	0.932570i	−0.184459	−	0.0972272i
$93$	8.42665	−	8.42665i	0.873803	−	0.873803i
$94$	4.89349	+	8.11097i	0.504724	+	0.836583i
$95$	5.76980			0.591969
$96$	4.18750	+	11.1902i	0.427385	+	1.14209i
$97$	−2.31130			−0.234677			−0.117338	−	0.993092i	$-0.537436\pi$
$97$	−2.31130			−0.234677			−0.117338	+	0.993092i	$0.537436\pi$
$98$	−4.60247	−	7.62861i	−0.464919	−	0.770606i
$99$	−3.98879	+	3.98879i	−0.400888	+	0.400888i
$100$	3.98428	+	2.10009i	0.398428	+	0.210009i
$101$	7.96205	+	7.96205i	0.792254	+	0.792254i	0.981860	−	0.189607i	$-0.0607212\pi$
$101$	7.96205	+	7.96205i	0.792254	+	0.792254i	−0.189607	+	0.981860i	$0.560721\pi$
$102$	19.7086	+	4.87618i	1.95144	+	0.482814i
$103$			6.45810i			0.636335i	0.948034	+	0.318168i	$0.103068\pi$
$103$			6.45810i			0.636335i	−0.948034	+	0.318168i	$0.896932\pi$
$104$	10.2715	−	11.5325i	1.00720	−	1.13085i
$105$			2.92957i			0.285897i
$106$	2.87011	−	11.6004i	0.278770	−	1.12673i
$107$	6.95392	+	6.95392i	0.672261	+	0.672261i	0.958237	−	0.285976i	$-0.0923177\pi$
$107$	6.95392	+	6.95392i	0.672261	+	0.672261i	−0.285976	+	0.958237i	$0.592318\pi$
$108$	−6.20972	+	1.92301i	−0.597531	+	0.185042i
$109$	0.633853	−	0.633853i	0.0607121	−	0.0607121i	−0.676099	−	0.736811i	$-0.736331\pi$
$109$	0.633853	−	0.633853i	0.0607121	−	0.0607121i	0.736811	+	0.676099i	$0.236331\pi$
$110$	7.74986	−	4.67562i	0.738920	−	0.445803i
$111$	15.4484			1.46629
$112$	−2.76105	+	1.89146i	−0.260895	+	0.178726i
$113$	16.0801			1.51269			0.756344	−	0.654174i	$-0.226984\pi$
$113$	16.0801			1.51269			0.756344	+	0.654174i	$0.226984\pi$
$114$	8.90180	−	5.37061i	0.833730	−	0.503003i
$115$	1.17219	−	1.17219i	0.109307	−	0.109307i
$116$	2.99700	+	9.67782i	0.278265	+	0.898563i
$117$	−5.64118	−	5.64118i	−0.521527	−	0.521527i
$118$	−1.34055	+	5.41826i	−0.123408	+	0.498792i
$119$			5.68707i			0.521333i
$120$	−9.88679	+	0.571775i	−0.902536	+	0.0521957i
$121$			3.90535i			0.355031i
$122$	−17.1302	−	4.23826i	−1.55090	−	0.383714i
$123$	3.53017	+	3.53017i	0.318305	+	0.318305i
$124$	−5.26175	+	9.98256i	−0.472519	+	0.896461i
$125$	−8.50066	+	8.50066i	−0.760322	+	0.760322i
$126$	0.893117	+	1.48034i	0.0795652	+	0.131880i
$127$	−10.2233			−0.907167			−0.453584	−	0.891214i	$-0.649855\pi$
$127$	−10.2233			−0.907167			−0.453584	+	0.891214i	$0.649855\pi$
$128$	−6.92223	−	8.94889i	−0.611845	−	0.790978i
$129$	−14.5312			−1.27940
$130$	6.61254	+	10.9603i	0.579958	+	0.961283i
$131$	2.58700	−	2.58700i	0.226027	−	0.226027i	−0.585003	−	0.811031i	$-0.698907\pi$
$131$	2.58700	−	2.58700i	0.226027	−	0.226027i	0.811031	+	0.585003i	$0.198907\pi$
$132$	7.60457	−	14.4274i	0.661892	−	1.25574i
$133$	2.05921	+	2.05921i	0.178556	+	0.178556i
$134$	−1.27979	−	0.316638i	−0.110557	−	0.0273534i
$135$		−	5.38817i		−	0.463740i
$136$	−19.1929	+	1.10997i	−1.64577	+	0.0951789i
$137$		−	6.34039i		−	0.541696i	−0.962622	−	0.270848i	$-0.912696\pi$
$137$		−	6.34039i		−	0.541696i	0.962622	−	0.270848i	$-0.0873041\pi$
$138$	0.717397	−	2.89958i	0.0610689	−	0.246829i
$139$	3.12169	+	3.12169i	0.264779	+	0.264779i	0.826992	−	0.562213i	$-0.190050\pi$
$139$	3.12169	+	3.12169i	0.264779	+	0.264779i	−0.562213	+	0.826992i	$0.690050\pi$
$140$	−0.820610	−	2.64989i	−0.0693542	−	0.223956i
$141$	−10.0039	+	10.0039i	−0.842482	+	0.842482i
$142$	−14.5553	+	8.78148i	−1.22146	+	0.736926i
$143$	−21.0800			−1.76280
$144$	−4.82159	+	3.30303i	−0.401799	+	0.275253i
$145$	−8.39744			−0.697369
$146$	11.6659	−	7.03826i	0.965480	−	0.582490i
$147$	9.40899	−	9.40899i	0.776040	−	0.776040i
$148$	−13.9735	+	4.32728i	−1.14861	+	0.355700i
$149$	−0.737198	−	0.737198i	−0.0603936	−	0.0603936i	0.676265	−	0.736659i	$-0.263597\pi$
$149$	−0.737198	−	0.737198i	−0.0603936	−	0.0603936i	−0.736659	+	0.676265i	$0.763597\pi$
$150$	−1.61553	+	6.52967i	−0.131908	+	0.533145i
$151$			6.67706i			0.543372i	0.962386	+	0.271686i	$0.0875812\pi$
$151$			6.67706i			0.543372i	−0.962386	+	0.271686i	$0.912419\pi$
$152$	−6.54757	+	7.35138i	−0.531078	+	0.596276i
$153$			9.93126i			0.802895i
$154$	4.43459	+	1.09718i	0.357350	+	0.0884133i
$155$	−6.61374	−	6.61374i	−0.531228	−	0.531228i
$156$	20.4040	+	10.7548i	1.63363	+	0.861076i
$157$	−5.42215	+	5.42215i	−0.432734	+	0.432734i	−0.889558	−	0.456823i	$-0.848987\pi$
$157$	−5.42215	+	5.42215i	−0.432734	+	0.432734i	0.456823	+	0.889558i	$0.348987\pi$
$158$	0.329397	+	0.545976i	0.0262054	+	0.0434355i
$159$	17.8477			1.41542
$160$	8.78273	−	3.28660i	0.694336	−	0.259829i
$161$	0.836699			0.0659411
$162$	−8.21767	−	13.6208i	−0.645641	−	1.07015i
$163$	−9.76189	+	9.76189i	−0.764611	+	0.764611i	−0.977152	−	0.212541i	$-0.931826\pi$
$163$	−9.76189	+	9.76189i	−0.764611	+	0.764611i	0.212541	+	0.977152i	$0.431826\pi$
$164$	−4.18199	−	2.20430i	−0.326558	−	0.172127i
$165$	9.55854	+	9.55854i	0.744131	+	0.744131i
$166$	−19.3300	−	4.78252i	−1.50030	−	0.371195i
$167$		−	14.1160i		−	1.09233i	−0.837679	−	0.546164i	$-0.816088\pi$
$167$		−	14.1160i		−	1.09233i	0.837679	−	0.546164i	$-0.183912\pi$
$168$	−3.73261	−	3.32448i	−0.287977	−	0.256489i
$169$		−	16.8126i		−	1.29328i
$170$	3.82712	−	15.4685i	0.293526	−	1.18638i
$171$	3.59598	+	3.59598i	0.274991	+	0.274991i
$172$	13.1439	−	4.07037i	1.00221	−	0.310363i
$173$	4.39793	−	4.39793i	0.334369	−	0.334369i	−0.519874	−	0.854243i	$-0.674021\pi$
$173$	4.39793	−	4.39793i	0.334369	−	0.334369i	0.854243	+	0.519874i	$0.174021\pi$
$174$	−12.9558	+	7.81645i	−0.982176	+	0.592563i
$175$	−1.88419			−0.142431
$176$	−2.83727	+	15.1801i	−0.213868	+	1.14424i
$177$	−8.33620			−0.626587
$178$	−5.47002	+	3.30016i	−0.409996	+	0.247357i
$179$	−16.5709	+	16.5709i	−1.23857	+	1.23857i	−0.277981	+	0.960587i	$0.589665\pi$
$179$	−16.5709	+	16.5709i	−1.23857	+	1.23857i	−0.960587	+	0.277981i	$0.910335\pi$
$180$	−1.43302	−	4.62746i	−0.106811	−	0.344911i
$181$	12.5305	+	12.5305i	0.931383	+	0.931383i	0.997792	−	0.0664091i	$-0.0211542\pi$
$181$	12.5305	+	12.5305i	0.931383	+	0.931383i	−0.0664091	+	0.997792i	$0.521154\pi$
$182$	−1.55170	+	6.27166i	−0.115020	+	0.464887i
$183$		−	26.3555i		−	1.94825i
$184$	0.163301	+	2.82371i	0.0120387	+	0.208167i
$185$		−	12.1248i		−	0.891432i
$186$	−16.3600	−	4.04770i	−1.19957	−	0.296792i
$187$	18.5556	+	18.5556i	1.35692	+	1.35692i
$188$	6.24662	−	11.8511i	0.455582	−	0.864328i
$189$	1.92301	−	1.92301i	0.139878	−	0.139878i
$190$	−4.21517	−	6.98666i	−0.305801	−	0.506866i
$191$	−10.8473			−0.784884			−0.392442	−	0.919777i	$-0.628370\pi$
$191$	−10.8473			−0.784884			−0.392442	+	0.919777i	$0.628370\pi$
$192$	10.4910	−	13.2457i	0.757125	−	0.955929i
$193$	−21.4782			−1.54603			−0.773016	−	0.634386i	$-0.781253\pi$
$193$	−21.4782			−1.54603			−0.773016	+	0.634386i	$0.781253\pi$
$194$	1.68854	+	2.79875i	0.121230	+	0.200939i
$195$	−13.5183	+	13.5183i	−0.968062	+	0.968062i
$196$	−5.87513	+	11.1463i	−0.419652	+	0.796163i
$197$	9.43218	+	9.43218i	0.672015	+	0.672015i	0.958180	−	0.286166i	$-0.0923807\pi$
$197$	9.43218	+	9.43218i	0.672015	+	0.672015i	−0.286166	+	0.958180i	$0.592381\pi$
$198$	7.74407	+	1.91599i	0.550347	+	0.136164i
$199$		−	4.79264i		−	0.339741i	−0.985466	−	0.169870i	$-0.945665\pi$
$199$		−	4.79264i		−	0.339741i	0.985466	−	0.169870i	$-0.0543349\pi$
$200$	−0.367744	−	6.35881i	−0.0260034	−	0.449635i
$201$		−	1.96901i		−	0.138883i
$202$	3.82453	−	15.4580i	0.269093	−	1.08762i
$203$	−2.99700	−	2.99700i	−0.210348	−	0.210348i
$204$	−8.49368	−	27.4275i	−0.594676	−	1.92031i
$205$	2.77069	−	2.77069i	0.193513	−	0.193513i
$206$	7.82013	−	4.71802i	0.544854	−	0.328720i
$207$	1.46112			0.101555
$208$	−21.4686	−	4.01264i	−1.48858	−	0.278227i
$209$	13.4375			0.929490
$210$	3.54743	−	2.14022i	0.244796	−	0.147689i
$211$	−8.19831	+	8.19831i	−0.564395	+	0.564395i	−0.930553	−	0.366158i	$-0.880673\pi$
$211$	−8.19831	+	8.19831i	−0.564395	+	0.564395i	0.366158	+	0.930553i	$0.380673\pi$
$212$	−16.1438	+	4.99936i	−1.10876	+	0.343358i
$213$	−17.9523	−	17.9523i	−1.23007	−	1.23007i
$214$	3.34028	−	13.5008i	0.228337	−	0.922894i
$215$			11.4049i			0.777811i
$216$	6.86514	+	6.11450i	0.467114	+	0.416039i
$217$		−	4.72082i		−	0.320470i
$218$	−1.23060	−	0.304468i	−0.0833467	−	0.0206212i
$219$	14.3886	+	14.3886i	0.972289	+	0.972289i
$220$	−11.3234	−	5.96851i	−0.763426	−	0.402397i
$221$	−26.2425	+	26.2425i	−1.76526	+	1.76526i
$222$	−11.2859	−	18.7065i	−0.757461	−	1.25550i
$223$	16.3356			1.09391			0.546957	−	0.837160i	$-0.315786\pi$
$223$	16.3356			1.09391			0.546957	+	0.837160i	$0.315786\pi$
$224$	4.30748	+	1.96154i	0.287806	+	0.131061i
$225$	−3.29034			−0.219356
$226$	−11.7474	−	19.4714i	−0.781428	−	1.29522i
$227$	−9.62449	+	9.62449i	−0.638800	+	0.638800i	−0.950259	−	0.311459i	$-0.899182\pi$
$227$	−9.62449	+	9.62449i	−0.638800	+	0.638800i	0.311459	+	0.950259i	$0.399182\pi$
$228$	−13.0066	−	6.85568i	−0.861381	−	0.454028i
$229$	−12.3271	−	12.3271i	−0.814598	−	0.814598i	0.170721	−	0.985319i	$-0.445390\pi$
$229$	−12.3271	−	12.3271i	−0.814598	−	0.814598i	−0.985319	+	0.170721i	$0.945390\pi$
$230$	−2.27576	−	0.563056i	−0.150059	−	0.0371268i
$231$			6.82279i			0.448906i
$232$	9.52942	−	10.6993i	0.625637	−	0.702443i
$233$			19.1034i			1.25151i	0.780021	+	0.625753i	$0.215208\pi$
$233$			19.1034i			1.25151i	−0.780021	+	0.625753i	$0.784792\pi$
$234$	−2.70971	+	10.9521i	−0.177139	+	0.715963i
$235$	7.85167	+	7.85167i	0.512187	+	0.512187i
$236$	7.54034	−	2.33507i	0.490834	−	0.152000i
$237$	−0.673397	+	0.673397i	−0.0437418	+	0.0437418i
$238$	6.88649	−	4.15474i	0.446385	−	0.269312i
$239$	−12.2178			−0.790301			−0.395150	−	0.918616i	$-0.629308\pi$
$239$	−12.2178			−0.790301			−0.395150	+	0.918616i	$0.629308\pi$
$240$	7.91524	+	11.5542i	0.510926	+	0.745822i
$241$	19.9907			1.28771			0.643857	−	0.765145i	$-0.277333\pi$
$241$	19.9907			1.28771			0.643857	+	0.765145i	$0.277333\pi$
$242$	4.72899	−	2.85308i	0.303991	−	0.183403i
$243$	9.90468	−	9.90468i	0.635386	−	0.635386i
$244$	7.38249	+	23.8393i	0.472616	+	1.52616i
$245$	−7.38473	−	7.38473i	−0.471793	−	0.471793i
$246$	1.69570	−	6.85368i	0.108114	−	0.436975i
$247$			19.0041i			1.20920i
$248$	15.9319	−	0.921379i	1.01168	−	0.0585076i
$249$		−	29.7399i		−	1.88469i
$250$	16.5037	+	4.08325i	1.04378	+	0.258247i
$251$	19.3743	+	19.3743i	1.22289	+	1.22289i	0.966599	+	0.256295i	$0.0825018\pi$
$251$	19.3743	+	19.3743i	1.22289	+	1.22289i	0.256295	+	0.966599i	$0.417498\pi$
$252$	1.14008	−	2.16296i	0.0718183	−	0.136253i
$253$	2.72996	−	2.72996i	0.171631	−	0.171631i
$254$	7.46868	+	12.3794i	0.468627	+	0.776750i
$255$	23.7988			1.49034
$256$	−5.77915	+	14.9198i	−0.361197	+	0.932490i
$257$	−7.75151			−0.483526			−0.241763	−	0.970335i	$-0.577726\pi$
$257$	−7.75151			−0.483526			−0.241763	+	0.970335i	$0.577726\pi$
$258$	10.6159	+	17.5959i	0.660916	+	1.09547i
$259$	4.32728	−	4.32728i	0.268884	−	0.268884i
$260$	8.44103	−	16.0143i	0.523490	−	0.993164i
$261$	−5.23363	−	5.23363i	−0.323953	−	0.323953i
$262$	−5.02256	−	1.24265i	−0.310295	−	0.0767713i
$263$		−	1.13315i		−	0.0698730i	−0.999390	−	0.0349365i	$-0.988877\pi$
$263$		−	1.13315i		−	0.0698730i	0.999390	−	0.0349365i	$-0.0111229\pi$
$264$	−23.0257	+	1.33163i	−1.41713	+	0.0819560i
$265$		−	14.0079i		−	0.860501i
$266$	0.989132	−	3.99788i	0.0606476	−	0.245126i
$267$	−6.74663	−	6.74663i	−0.412887	−	0.412887i
$268$	0.551543	+	1.78102i	0.0336909	+	0.108793i
$269$	15.6240	−	15.6240i	0.952610	−	0.952610i	−0.0463164	−	0.998927i	$-0.514748\pi$
$269$	15.6240	−	15.6240i	0.952610	−	0.952610i	0.998927	+	0.0463164i	$0.0147482\pi$
$270$	−6.52455	+	3.93637i	−0.397071	+	0.239560i
$271$	−22.6570			−1.37631			−0.688157	−	0.725562i	$-0.741580\pi$
$271$	−22.6570			−1.37631			−0.688157	+	0.725562i	$0.741580\pi$
$272$	15.3656	+	22.4298i	0.931674	+	1.36001i
$273$	−9.64919			−0.583996
$274$	−7.67759	+	4.63202i	−0.463820	+	0.279831i
$275$	−6.14769	+	6.14769i	−0.370719	+	0.370719i
$276$	−4.03521	+	1.24961i	−0.242891	+	0.0752179i
$277$	−5.88800	−	5.88800i	−0.353776	−	0.353776i	0.507737	−	0.861512i	$-0.330482\pi$
$277$	−5.88800	−	5.88800i	−0.353776	−	0.353776i	−0.861512	+	0.507737i	$0.830482\pi$
$278$	1.49949	−	6.06065i	0.0899334	−	0.363493i
$279$		−	8.24390i		−	0.493550i
$280$	−2.60925	+	2.92957i	−0.155933	+	0.175075i
$281$			23.4422i			1.39844i	0.714905	+	0.699221i	$0.246470\pi$
$281$			23.4422i			1.39844i	−0.714905	+	0.699221i	$0.753530\pi$
$282$	19.4222	+	4.80533i	1.15658	+	0.286153i
$283$	7.69603	+	7.69603i	0.457482	+	0.457482i	0.897828	−	0.440346i	$-0.145144\pi$
$283$	7.69603	+	7.69603i	0.457482	+	0.457482i	−0.440346	+	0.897828i	$0.645144\pi$
$284$	21.2670	+	11.2097i	1.26197	+	0.665175i
$285$	8.61722	−	8.61722i	0.510440	−	0.510440i
$286$	15.4002	+	25.5259i	0.910632	+	1.50938i
$287$	1.97769			0.116739
$288$	7.52210	+	3.42542i	0.443244	+	0.201845i
$289$	29.1998			1.71763
$290$	6.13481	+	10.1685i	0.360249	+	0.597114i
$291$	−3.45193	+	3.45193i	−0.202356	+	0.202356i
$292$	−17.0453	−	8.98446i	−0.997500	−	0.525776i
$293$	−12.6311	−	12.6311i	−0.737917	−	0.737917i	0.234257	−	0.972175i	$-0.424734\pi$
$293$	−12.6311	−	12.6311i	−0.737917	−	0.737917i	−0.972175	+	0.234257i	$0.924734\pi$
$294$	−18.2672	−	4.51956i	−1.06536	−	0.263586i
$295$			6.54275i			0.380933i
$296$	15.4484	+	13.7592i	0.897917	+	0.799738i
$297$		−	12.5487i		−	0.728149i
$298$	−0.354109	+	1.43124i	−0.0205130	+	0.0829095i
$299$	3.86087	+	3.86087i	0.223280	+	0.223280i
$300$	9.08703	−	2.81405i	0.524640	−	0.162469i
$301$	−4.07037	+	4.07037i	−0.234612	+	0.234612i
$302$	8.08527	−	4.87798i	0.465255	−	0.280696i
$303$	23.7827			1.36628
$304$	13.6852	+	2.55786i	0.784899	+	0.146704i
$305$	−20.6853			−1.18444
$306$	12.0258	−	7.25536i	0.687469	−	0.414762i
$307$	2.53791	−	2.53791i	0.144846	−	0.144846i	−0.630965	−	0.775811i	$-0.717341\pi$
$307$	2.53791	−	2.53791i	0.144846	−	0.144846i	0.775811	+	0.630965i	$0.217341\pi$
$308$	−1.91115	−	6.17141i	−0.108898	−	0.351649i
$309$	9.64521	+	9.64521i	0.548697	+	0.548697i
$310$	−3.17687	+	12.8403i	−0.180434	+	0.729280i
$311$		−	3.69293i		−	0.209407i	−0.994503	−	0.104703i	$-0.966611\pi$
$311$		−	3.69293i		−	0.209407i	0.994503	−	0.104703i	$-0.0333893\pi$
$312$	−1.88327	−	32.5643i	−0.106619	−	1.84359i
$313$			8.94100i			0.505375i	0.967548	+	0.252688i	$0.0813145\pi$
$313$			8.94100i			0.505375i	−0.967548	+	0.252688i	$0.918686\pi$
$314$	10.5269	+	2.60450i	0.594066	+	0.146980i
$315$	1.43302	+	1.43302i	0.0807415	+	0.0807415i
$316$	0.420481	−	0.797734i	0.0236539	−	0.0448761i
$317$	7.21914	−	7.21914i	0.405467	−	0.405467i	−0.474687	−	0.880155i	$-0.657439\pi$
$317$	7.21914	−	7.21914i	0.405467	−	0.405467i	0.880155	+	0.474687i	$0.157439\pi$
$318$	−13.0388	−	21.6118i	−0.731179	−	1.21193i
$319$	−19.5571			−1.09499
$320$	−10.3960	−	8.23398i	−0.581157	−	0.460294i
$321$	20.7714			1.15935
$322$	−0.611257	−	1.01316i	−0.0340640	−	0.0564612i
$323$	16.7283	−	16.7283i	0.930788	−	0.930788i
$324$	−10.4900	+	19.9016i	−0.582778	+	1.10564i
$325$	−8.69442	−	8.69442i	−0.482280	−	0.482280i
$326$	18.9523	+	4.68907i	1.04967	+	0.259704i
$327$		−	1.89332i		−	0.104701i
$328$	0.385992	+	6.67434i	0.0213129	+	0.368529i
$329$			5.60445i			0.308983i
$330$	4.59139	−	18.5575i	0.252748	−	1.02156i
$331$	−3.11018	−	3.11018i	−0.170951	−	0.170951i	0.616446	−	0.787397i	$-0.288572\pi$
$331$	−3.11018	−	3.11018i	−0.170951	−	0.170951i	−0.787397	+	0.616446i	$0.788572\pi$
$332$	8.33053	+	26.9007i	0.457197	+	1.47637i
$333$	7.55666	−	7.55666i	0.414103	−	0.414103i
$334$	−17.0931	+	10.3125i	−0.935292	+	0.564277i
$335$	−1.54539			−0.0844339
$336$	−1.29874	+	6.94855i	−0.0708519	+	0.379075i
$337$	−21.0292			−1.14553			−0.572767	−	0.819719i	$-0.694130\pi$
$337$	−21.0292			−1.14553			−0.572767	+	0.819719i	$0.694130\pi$
$338$	−20.3585	+	12.2826i	−1.10735	+	0.668086i
$339$	24.0157	−	24.0157i	1.30435	−	1.30435i
$340$	−21.5267	+	6.66634i	−1.16745	+	0.361533i
$341$	−15.4030	−	15.4030i	−0.834117	−	0.834117i
$342$	1.72731	−	6.98144i	0.0934021	−	0.377513i
$343$		−	11.1280i		−	0.600858i
$344$	−14.5312	−	12.9423i	−0.783469	−	0.697804i
$345$		−	3.50135i		−	0.188506i
$346$	−8.53841	−	2.11252i	−0.459028	−	0.113570i
$347$	−12.0073	−	12.0073i	−0.644587	−	0.644587i	0.307093	−	0.951680i	$-0.400644\pi$
$347$	−12.0073	−	12.0073i	−0.644587	−	0.644587i	−0.951680	+	0.307093i	$0.900644\pi$
$348$	18.9299	+	9.97784i	1.01475	+	0.534868i
$349$	21.5509	−	21.5509i	1.15359	−	1.15359i	0.167764	−	0.985827i	$-0.446345\pi$
$349$	21.5509	−	21.5509i	1.15359	−	1.15359i	0.985827	−	0.167764i	$-0.0536547\pi$
$350$	1.37651	+	2.28157i	0.0735775	+	0.121955i
$351$	17.7471			0.947271
$352$	20.4544	−	7.65428i	1.09022	−	0.407974i
$353$	−29.4769			−1.56890			−0.784449	−	0.620194i	$-0.787054\pi$
$353$	−29.4769			−1.56890			−0.784449	+	0.620194i	$0.787054\pi$
$354$	6.09008	+	10.0943i	0.323684	+	0.536508i
$355$	−14.0900	+	14.0900i	−0.747821	+	0.747821i
$356$	7.99234	+	4.21271i	0.423593	+	0.223273i
$357$	8.49368	+	8.49368i	0.449533	+	0.449533i
$358$	32.1718	+	7.95975i	1.70033	+	0.420686i
$359$		−	4.71258i		−	0.248721i	−0.992237	−	0.124360i	$-0.960312\pi$
$359$		−	4.71258i		−	0.248721i	0.992237	−	0.124360i	$-0.0396879\pi$
$360$	−4.55650	+	5.11588i	−0.240149	+	0.269630i
$361$			6.88582i			0.362411i
$362$	6.01895	−	24.3274i	0.316349	−	1.27862i
$363$	5.83265	+	5.83265i	0.306135	+	0.306135i
$364$	8.72798	−	2.70286i	0.457470	−	0.141668i
$365$	11.2930	−	11.2930i	0.591102	−	0.591102i
$366$	−31.9139	+	19.2542i	−1.66817	+	1.00643i
$367$	−18.9186			−0.987543			−0.493771	−	0.869592i	$-0.664382\pi$
$367$	−18.9186			−0.987543			−0.493771	+	0.869592i	$0.664382\pi$
$368$	3.29994	−	2.26063i	0.172021	−	0.117843i
$369$	3.45361			0.179788
$370$	−14.6819	+	8.85786i	−0.763278	+	0.460498i
$371$	4.99936	−	4.99936i	0.259554	−	0.259554i
$372$	7.05057	+	22.7675i	0.365555	+	1.18044i
$373$	−8.86810	−	8.86810i	−0.459173	−	0.459173i	0.439211	−	0.898384i	$-0.355258\pi$
$373$	−8.86810	−	8.86810i	−0.459173	−	0.459173i	−0.898384	+	0.439211i	$0.855258\pi$
$374$	8.91310	−	36.0250i	0.460886	−	1.86281i
$375$			25.3915i			1.31121i
$376$	−18.9140	+	1.09384i	−0.975415	+	0.0564105i
$377$		−	27.6588i		−	1.42450i
$378$	−3.73345	−	0.923708i	−0.192028	−	0.0475104i
$379$	−15.0162	−	15.0162i	−0.771329	−	0.771329i	0.207010	−	0.978339i	$-0.433627\pi$
$379$	−15.0162	−	15.0162i	−0.771329	−	0.771329i	−0.978339	+	0.207010i	$0.933627\pi$
$380$	−5.38074	+	10.2083i	−0.276026	+	0.523676i
$381$	−15.2685	+	15.2685i	−0.782228	+	0.782228i
$382$	7.92459	+	13.1350i	0.405457	+	0.672047i
$383$	4.91525			0.251158			0.125579	−	0.992084i	$-0.459921\pi$
$383$	4.91525			0.251158			0.125579	+	0.992084i	$0.459921\pi$
$384$	−23.7036	−	3.02683i	−1.20962	−	0.154462i
$385$	5.35493			0.272912
$386$	15.6910	+	26.0080i	0.798653	+	1.32377i
$387$	−7.10803	+	7.10803i	−0.361321	+	0.361321i
$388$	2.15545	−	4.08930i	0.109426	−	0.207603i
$389$	18.3420	+	18.3420i	0.929976	+	0.929976i	0.997704	−	0.0677278i	$-0.0215749\pi$
$389$	18.3420	+	18.3420i	0.929976	+	0.929976i	−0.0677278	+	0.997704i	$0.521575\pi$
$390$	26.2452	+	6.49342i	1.32898	+	0.328807i
$391$		−	6.79704i		−	0.343741i
$392$	17.7892	−	1.02879i	0.898490	−	0.0519617i
$393$		−	7.72740i		−	0.389796i
$394$	4.53070	−	18.3122i	0.228253	−	0.922555i
$395$	0.528522	+	0.528522i	0.0265928	+	0.0265928i
$396$	−3.33741	−	10.7771i	−0.167711	−	0.541567i
$397$	6.88943	−	6.88943i	0.345771	−	0.345771i	−0.512761	−	0.858532i	$-0.671377\pi$
$397$	6.88943	−	6.88943i	0.345771	−	0.345771i	0.858532	+	0.512761i	$0.171377\pi$
$398$	−5.80341	+	3.50130i	−0.290899	+	0.175504i
$399$	6.15089			0.307930
$400$	−7.43124	+	5.09078i	−0.371562	+	0.254539i
$401$	−26.2566			−1.31119			−0.655595	−	0.755113i	$-0.727582\pi$
$401$	−26.2566			−1.31119			−0.655595	+	0.755113i	$0.727582\pi$
$402$	−2.38428	+	1.43847i	−0.118917	+	0.0717445i
$403$	21.7838	−	21.7838i	1.08513	−	1.08513i
$404$	−21.5122	+	6.66184i	−1.07027	+	0.331439i
$405$	−13.1854	−	13.1854i	−0.655187	−	0.655187i
$406$	−1.43959	+	5.81856i	−0.0714459	+	0.288770i
$407$		−	28.2378i		−	1.39970i
$408$	−27.0069	+	30.3224i	−1.33704	+	1.50118i
$409$		−	18.0934i		−	0.894661i	−0.894369	−	0.447331i	$-0.852375\pi$
$409$		−	18.0934i		−	0.894661i	0.894369	−	0.447331i	$-0.147625\pi$
$410$	−5.37918	−	1.33088i	−0.265659	−	0.0657277i
$411$	−9.46940	−	9.46940i	−0.467091	−	0.467091i
$412$	−11.4261	−	6.02263i	−0.562924	−	0.296714i
$413$	−2.33507	+	2.33507i	−0.114901	+	0.114901i
$414$	−1.06743	−	1.76927i	−0.0524613	−	0.0869548i
$415$	−23.3417			−1.14580
$416$	10.8251	+	28.9279i	0.530746	+	1.41830i
$417$	9.32453			0.456624
$418$	−9.81686	−	16.2715i	−0.480158	−	0.795865i
$419$	24.3611	−	24.3611i	1.19012	−	1.19012i	0.213082	−	0.977034i	$-0.431650\pi$
$419$	24.3611	−	24.3611i	1.19012	−	1.19012i	0.977034	−	0.213082i	$-0.0683500\pi$
$420$	−5.18320	−	2.73203i	−0.252914	−	0.133310i
$421$	4.33767	+	4.33767i	0.211405	+	0.211405i	0.804864	−	0.593459i	$-0.202238\pi$
$421$	4.33767	+	4.33767i	0.211405	+	0.211405i	−0.593459	+	0.804864i	$0.702238\pi$
$422$	15.9167	+	3.93801i	0.774813	+	0.191700i
$423$			9.78697i			0.475859i
$424$	17.8477	+	15.8962i	0.866761	+	0.771989i
$425$			15.3065i			0.742474i
$426$	−8.62329	+	34.8537i	−0.417800	+	1.68867i
$427$	−7.38249	−	7.38249i	−0.357264	−	0.357264i
$428$	−18.7884	+	5.81834i	−0.908171	+	0.281240i
$429$	−31.4831	+	31.4831i	−1.52002	+	1.52002i
$430$	13.8103	−	8.33197i	0.665991	−	0.401803i
$431$	20.7331			0.998680			0.499340	−	0.866406i	$-0.333576\pi$
$431$	20.7331			0.998680			0.499340	+	0.866406i	$0.333576\pi$
$432$	2.38868	−	12.7800i	0.114925	−	0.614879i
$433$	30.4936			1.46543			0.732715	−	0.680536i	$-0.238253\pi$
$433$	30.4936			1.46543			0.732715	+	0.680536i	$0.238253\pi$
$434$	−5.71645	+	3.44883i	−0.274398	+	0.165549i
$435$	−12.5416	+	12.5416i	−0.601324	+	0.601324i
$436$	0.530344	+	1.71257i	0.0253989	+	0.0820171i
$437$	−2.46112	−	2.46112i	−0.117731	−	0.117731i
$438$	6.91147	−	27.9348i	0.330243	−	1.33478i
$439$			31.4837i			1.50264i	0.659941	+	0.751318i	$0.270581\pi$
$439$			31.4837i			1.50264i	−0.659941	+	0.751318i	$0.729419\pi$
$440$	1.04514	+	18.0719i	0.0498251	+	0.861546i
$441$		−	9.20494i		−	0.438330i
$442$	50.9488	+	12.6054i	2.42339	+	0.599580i
$443$	28.3756	+	28.3756i	1.34817	+	1.34817i	0.887653	+	0.460514i	$0.152335\pi$
$443$	28.3756	+	28.3756i	1.34817	+	1.34817i	0.460514	+	0.887653i	$0.347665\pi$
$444$	−14.4067	+	27.3323i	−0.683711	+	1.29713i
$445$	−5.29515	+	5.29515i	−0.251014	+	0.251014i
$446$	−11.9341	−	19.7809i	−0.565097	−	0.936651i
$447$	−2.20202			−0.104152
$448$	−0.771630	−	6.64896i	−0.0364561	−	0.314134i
$449$	−29.4415			−1.38943			−0.694715	−	0.719285i	$-0.744470\pi$
$449$	−29.4415			−1.38943			−0.694715	+	0.719285i	$0.744470\pi$
$450$	2.40378	+	3.98428i	0.113315	+	0.187821i
$451$	6.45275	−	6.45275i	0.303848	−	0.303848i
$452$	−14.9958	+	28.4500i	−0.705344	+	1.33818i
$453$	9.97223	+	9.97223i	0.468536	+	0.468536i
$454$	18.6856	+	4.62307i	0.876957	+	0.216972i
$455$			7.57326i			0.355040i
$456$	1.20049	+	20.7582i	0.0562181	+	0.972090i
$457$		−	15.9355i		−	0.745429i	−0.927946	−	0.372714i	$-0.878427\pi$
$457$		−	15.9355i		−	0.745429i	0.927946	−	0.372714i	$-0.121573\pi$
$458$	−5.92126	+	23.9326i	−0.276682	+	1.11830i
$459$	−15.6219	−	15.6219i	−0.729166	−	0.729166i
$460$	0.980771	+	3.16707i	0.0457287	+	0.147666i
$461$	5.77259	−	5.77259i	0.268856	−	0.268856i	−0.559783	−	0.828639i	$-0.689115\pi$
$461$	5.77259	−	5.77259i	0.268856	−	0.268856i	0.828639	+	0.559783i	$0.189115\pi$
$462$	8.26173	−	4.98444i	0.384370	−	0.231897i
$463$	36.6695			1.70418			0.852088	−	0.523398i	$-0.175336\pi$
$463$	36.6695			1.70418			0.852088	+	0.523398i	$0.175336\pi$
$464$	−19.9176	−	3.72275i	−0.924651	−	0.172824i
$465$	−19.7553			−0.916130
$466$	23.1324	−	13.9562i	1.07159	−	0.646506i
$467$	−5.89270	+	5.89270i	−0.272682	+	0.272682i	−0.830179	−	0.557497i	$-0.811762\pi$
$467$	−5.89270	+	5.89270i	−0.272682	+	0.272682i	0.557497	+	0.830179i	$0.311762\pi$
$468$	15.2416	−	4.71997i	0.704541	−	0.218181i
$469$	−0.551543	−	0.551543i	−0.0254679	−	0.0254679i
$470$	3.77151	−	15.2437i	0.173967	−	0.703140i
$471$			16.1960i			0.746273i
$472$	−8.33620	−	7.42471i	−0.383705	−	0.341750i
$473$			26.5614i			1.22129i
$474$	1.30737	+	0.323463i	0.0600497	+	0.0148571i
$475$	5.54227	+	5.54227i	0.254297	+	0.254297i
$476$	−10.0620	−	5.30360i	−0.461189	−	0.243090i
$477$	8.73032	−	8.73032i	0.399734	−	0.399734i
$478$	8.92578	+	14.7945i	0.408256	+	0.676685i
$479$	−5.57265			−0.254621			−0.127311	−	0.991863i	$-0.540634\pi$
$479$	−5.57265			−0.254621			−0.127311	+	0.991863i	$0.540634\pi$
$480$	8.20850	−	18.0256i	0.374665	−	0.822753i
$481$	39.9356			1.82091
$482$	−14.6044	−	24.2068i	−0.665211	−	1.10259i
$483$	1.24961	−	1.24961i	0.0568594	−	0.0568594i
$484$	−6.90961	−	3.64201i	−0.314073	−	0.165546i
$485$	2.70928	+	2.70928i	0.123022	+	0.123022i
$486$	−19.2295	−	4.75766i	−0.872270	−	0.215812i
$487$			36.5900i			1.65805i	0.559211	+	0.829026i	$0.311104\pi$
$487$			36.5900i			1.65805i	−0.559211	+	0.829026i	$0.688896\pi$
$488$	23.4737	−	26.3555i	1.06261	−	1.19306i
$489$			29.1589i			1.31861i
$490$	−3.54722	+	14.3372i	−0.160247	+	0.647687i
$491$	−16.4267	−	16.4267i	−0.741325	−	0.741325i	0.231508	−	0.972833i	$-0.425634\pi$
$491$	−16.4267	−	16.4267i	−0.741325	−	0.741325i	−0.972833	+	0.231508i	$0.925634\pi$
$492$	−9.53795	+	2.95369i	−0.430004	+	0.133162i
$493$	−24.3466	+	24.3466i	−1.09652	+	1.09652i
$494$	23.0121	−	13.8836i	1.03536	−	0.624652i
$495$	9.35124			0.420307
$496$	−12.7549	−	18.6189i	−0.572712	−	0.836013i
$497$	−10.0573			−0.451132
$498$	−36.0122	+	21.7267i	−1.61374	+	0.973599i
$499$	18.9659	−	18.9659i	0.849032	−	0.849032i	−0.140980	−	0.990012i	$-0.545025\pi$
$499$	18.9659	−	18.9659i	0.849032	−	0.849032i	0.990012	+	0.140980i	$0.0450255\pi$
$500$	−7.11249	−	22.9674i	−0.318080	−	1.02713i
$501$	−21.0823	−	21.0823i	−0.941887	−	0.941887i
$502$	9.30633	−	37.6144i	0.415362	−	1.67881i
$503$			5.19328i			0.231557i	0.993275	+	0.115778i	$0.0369362\pi$
$503$			5.19328i			0.231557i	−0.993275	+	0.115778i	$0.963064\pi$
$504$	−3.45202	+	0.199638i	−0.153765	+	0.00889259i
$505$		−	18.6661i		−	0.830630i
$506$	−5.30011	−	1.31132i	−0.235618	−	0.0582953i
$507$	−25.1098	−	25.1098i	−1.11516	−	1.11516i
$508$	9.53390	−	18.0877i	0.422999	−	0.802511i
$509$	−20.7004	+	20.7004i	−0.917527	+	0.917527i	−0.996849	−	0.0793216i	$-0.974725\pi$
$509$	−20.7004	+	20.7004i	−0.917527	+	0.917527i	0.0793216	+	0.996849i	$0.474725\pi$
$510$	−17.3864	−	28.8180i	−0.769883	−	1.27608i
$511$	8.06083			0.356590
$512$	22.2885	−	3.90182i	0.985020	−	0.172438i
$513$	−11.3129			−0.499478
$514$	5.66292	+	9.38632i	0.249781	+	0.414013i
$515$	7.57013	−	7.57013i	0.333580	−	0.333580i
$516$	13.5514	−	25.7096i	0.596565	−	1.13180i
$517$	18.2860	+	18.2860i	0.804219	+	0.804219i
$518$	−8.40123	−	2.07858i	−0.369129	−	0.0913277i
$519$		−	13.1367i		−	0.576636i
$520$	−25.5584	+	1.47810i	−1.12081	+	0.0648190i
$521$			33.5302i			1.46898i	0.678617	+	0.734492i	$0.262580\pi$
$521$			33.5302i			1.46898i	−0.678617	+	0.734492i	$0.737420\pi$
$522$	−2.51395	+	10.1609i	−0.110032	+	0.444730i
$523$	−21.0872	−	21.0872i	−0.922081	−	0.922081i	0.0750956	−	0.997176i	$-0.476074\pi$
$523$	−21.0872	−	21.0872i	−0.922081	−	0.922081i	−0.997176	+	0.0750956i	$0.976074\pi$
$524$	2.16454	+	6.98966i	0.0945583	+	0.305345i
$525$	−2.81405	+	2.81405i	−0.122815	+	0.122815i
$526$	−1.37213	+	0.827832i	−0.0598279	+	0.0360952i
$527$	−38.3503			−1.67056
$528$	18.4341	+	26.9090i	0.802240	+	1.17107i
$529$	−1.00000			−0.0434783
$530$	−16.9623	+	10.2336i	−0.736793	+	0.444520i
$531$	−4.07771	+	4.07771i	−0.176957	+	0.176957i
$532$	−5.56366	+	1.72294i	−0.241215	+	0.0746989i
$533$	9.12586	+	9.12586i	0.395285	+	0.395285i
$534$	−3.24071	+	13.0983i	−0.140239	+	0.566819i
$535$		−	16.3027i		−	0.704826i
$536$	1.75371	−	1.96901i	0.0757489	−	0.0850481i
$537$			49.4975i			2.13597i
$538$	−30.3333	−	7.50489i	−1.30776	−	0.323559i
$539$	−17.1986	−	17.1986i	−0.740795	−	0.740795i
$540$	9.53312	+	5.02485i	0.410240	+	0.216235i
$541$	22.3269	−	22.3269i	0.959908	−	0.959908i	−0.0393184	−	0.999227i	$-0.512519\pi$
$541$	22.3269	−	22.3269i	0.959908	−	0.959908i	0.999227	+	0.0393184i	$0.0125187\pi$
$542$	16.5522	+	27.4354i	0.710979	+	1.17845i
$543$	37.4287			1.60622
$544$	15.9349	−	34.9925i	0.683202	−	1.50029i
$545$	−1.48599			−0.0636530
$546$	7.04929	+	11.6842i	0.301682	+	0.500039i
$547$	−19.5447	+	19.5447i	−0.835671	+	0.835671i	−0.988286	−	0.152615i	$-0.951231\pi$
$547$	−19.5447	+	19.5447i	−0.835671	+	0.835671i	0.152615	+	0.988286i	$0.451231\pi$
$548$	11.2179	+	5.91286i	0.479203	+	0.252585i
$549$	−12.8920	−	12.8920i	−0.550215	−	0.550215i
$550$	11.9355	+	2.95301i	0.508931	+	0.125917i
$551$			17.6311i			0.751111i
$552$	4.46112	+	3.97333i	0.189878	+	0.169116i
$553$			0.377254i			0.0160425i
$554$	−2.82827	+	11.4313i	−0.120162	+	0.485671i
$555$	−18.1084	−	18.1084i	−0.768660	−	0.768660i
$556$	−8.43432	+	2.61192i	−0.357695	+	0.110770i
$557$	1.06994	−	1.06994i	0.0453347	−	0.0453347i	−0.684076	−	0.729411i	$-0.739794\pi$
$557$	1.06994	−	1.06994i	0.0453347	−	0.0453347i	0.729411	+	0.684076i	$0.239794\pi$
$558$	−9.98256	+	6.02265i	−0.422596	+	0.254959i
$559$	−37.5647			−1.58882
$560$	5.45364	+	1.01933i	0.230458	+	0.0430744i
$561$	55.4259			2.34008
$562$	28.3862	−	17.1259i	1.19740	−	0.722411i
$563$	26.6686	−	26.6686i	1.12395	−	1.12395i	0.132806	−	0.991142i	$-0.457601\pi$
$563$	26.6686	−	26.6686i	1.12395	−	1.12395i	0.991142	−	0.132806i	$-0.0423986\pi$
$564$	−8.37027	−	27.0290i	−0.352452	−	1.13813i
$565$	−18.8489	−	18.8489i	−0.792981	−	0.792981i
$566$	3.69675	−	14.9415i	0.155386	−	0.628040i
$567$		−	9.41159i		−	0.395250i
$568$	−1.96292	−	33.9417i	−0.0823624	−	1.42416i
$569$		−	24.6342i		−	1.03272i	−0.856372	−	0.516359i	$-0.827287\pi$
$569$		−	24.6342i		−	1.03272i	0.856372	−	0.516359i	$-0.172713\pi$
$570$	−16.7300	−	4.13924i	−0.700743	−	0.173374i
$571$	−21.7399	−	21.7399i	−0.909788	−	0.909788i	0.0864666	−	0.996255i	$-0.472442\pi$
$571$	−21.7399	−	21.7399i	−0.909788	−	0.909788i	−0.996255	+	0.0864666i	$0.972442\pi$
$572$	19.6586	−	37.2962i	0.821968	−	1.55943i
$573$	−16.2005	+	16.2005i	−0.676786	+	0.676786i
$574$	−1.44482	−	2.39479i	−0.0603054	−	0.0999565i
$575$	2.25193			0.0939121
$576$	−1.34749	−	11.6110i	−0.0561453	−	0.483792i
$577$	8.82926			0.367567			0.183784	−	0.982967i	$-0.441165\pi$
$577$	8.82926			0.367567			0.183784	+	0.982967i	$0.441165\pi$
$578$	−21.3321	−	35.3581i	−0.887299	−	1.47070i
$579$	−32.0778	+	32.0778i	−1.33311	+	1.33311i
$580$	7.83120	−	14.8573i	0.325173	−	0.616917i
$581$	−8.33053	−	8.33053i	−0.345608	−	0.345608i
$582$	6.70179	+	1.65812i	0.277798	+	0.0687312i
$583$		−	32.6236i		−	1.35113i
$584$	1.57326	+	27.2039i	0.0651020	+	1.12570i
$585$			13.2251i			0.546790i
$586$	−6.06729	+	24.5228i	−0.250637	+	1.01303i
$587$	5.40195	+	5.40195i	0.222962	+	0.222962i	0.809745	−	0.586782i	$-0.199606\pi$
$587$	5.40195	+	5.40195i	0.222962	+	0.222962i	−0.586782	+	0.809745i	$0.699606\pi$
$588$	7.87249	+	25.4216i	0.324656	+	1.04837i
$589$	−13.8861	+	13.8861i	−0.572167	+	0.572167i
$590$	7.92263	−	4.77986i	0.326169	−	0.196784i
$591$	28.1740			1.15892
$592$	5.37515	−	28.7584i	0.220917	−	1.18196i
$593$	21.9879			0.902933			0.451467	−	0.892288i	$-0.350901\pi$
$593$	21.9879			0.902933			0.451467	+	0.892288i	$0.350901\pi$
$594$	−15.1953	+	9.16755i	−0.623469	+	0.376149i
$595$	6.66634	−	6.66634i	0.273293	−	0.273293i
$596$	1.99179	−	0.616812i	0.0815869	−	0.0252656i
$597$	−7.15783	−	7.15783i	−0.292950	−	0.292950i
$598$	1.85455	−	7.49573i	0.0758381	−	0.306523i
$599$			40.5578i			1.65715i	0.559881	+	0.828573i	$0.310847\pi$
$599$			40.5578i			1.65715i	−0.559881	+	0.828573i	$0.689153\pi$
$600$	−10.0461	−	8.94768i	−0.410132	−	0.365288i
$601$		−	44.8779i		−	1.83061i	−0.402763	−	0.915304i	$-0.631950\pi$
$601$		−	44.8779i		−	1.83061i	0.402763	−	0.915304i	$-0.368050\pi$
$602$	7.90246	+	1.95518i	0.322080	+	0.0796872i
$603$	−0.963153	−	0.963153i	−0.0392226	−	0.0392226i
$604$	−11.8135	−	6.22683i	−0.480685	−	0.253366i
$605$	4.57781	−	4.57781i	0.186115	−	0.186115i
$606$	−17.3747	−	28.7986i	−0.705797	−	1.16986i
$607$	40.6926			1.65166			0.825832	−	0.563917i	$-0.190706\pi$
$607$	40.6926			1.65166			0.825832	+	0.563917i	$0.190706\pi$
$608$	−6.90049	−	18.4401i	−0.279852	−	0.747844i
$609$	−8.95208			−0.362757
$610$	15.1118	+	25.0479i	0.611861	+	1.01416i
$611$	−25.8612	+	25.8612i	−1.04623	+	1.04623i
$612$	−17.5711	−	9.26160i	−0.710269	−	0.374378i
$613$	−8.45521	−	8.45521i	−0.341503	−	0.341503i	0.515429	−	0.856932i	$-0.327632\pi$
$613$	−8.45521	−	8.45521i	−0.341503	−	0.341503i	−0.856932	+	0.515429i	$0.827632\pi$
$614$	−4.92724	−	1.21907i	−0.198847	−	0.0491977i
$615$		−	8.27607i		−	0.333723i
$616$	−6.07678	+	6.82279i	−0.244840	+	0.274898i
$617$			11.7202i			0.471836i	0.971773	+	0.235918i	$0.0758096\pi$
$617$			11.7202i			0.471836i	−0.971773	+	0.235918i	$0.924190\pi$
$618$	4.63302	−	18.7258i	0.186368	−	0.753262i
$619$	−27.5714	−	27.5714i	−1.10819	−	1.10819i	−0.993389	−	0.114798i	$-0.963378\pi$
$619$	−27.5714	−	27.5714i	−1.10819	−	1.10819i	−0.114798	−	0.993389i	$-0.536622\pi$
$620$	17.8693	−	5.53370i	0.717646	−	0.222239i
$621$	−2.29833	+	2.29833i	−0.0922289	+	0.0922289i
$622$	−4.47178	+	2.69790i	−0.179302	+	0.108176i
$623$	−3.77963			−0.151428
$624$	−38.0564	+	26.0706i	−1.52347	+	1.04366i
$625$	8.66913			0.346765
$626$	10.8267	−	6.53192i	0.432721	−	0.261068i
$627$	20.0690	−	20.0690i	0.801477	−	0.801477i
$628$	−4.53670	−	14.6498i	−0.181034	−	0.584589i
$629$	−35.1532	−	35.1532i	−1.40165	−	1.40165i
$630$	0.688344	−	2.78215i	0.0274243	−	0.110844i
$631$			4.88975i			0.194658i	0.995252	+	0.0973289i	$0.0310299\pi$
$631$			4.88975i			0.194658i	−0.995252	+	0.0973289i	$0.968970\pi$
$632$	−1.27316	+	0.0736300i	−0.0506438	+	0.00292884i
$633$			24.4884i			0.973328i
$634$	−14.0157	−	3.46768i	−0.556634	−	0.137719i
$635$	11.9836	+	11.9836i	0.475555	+	0.475555i
$636$	−16.6442	+	31.5774i	−0.659987	+	1.25213i
$637$	24.3232	−	24.3232i	0.963722	−	0.963722i
$638$	14.2876	+	23.6817i	0.565651	+	0.937569i
$639$	−17.5630			−0.694780
$640$	−2.37564	+	18.6040i	−0.0939053	+	0.735388i
$641$	2.67986			0.105848			0.0529240	−	0.998599i	$-0.483146\pi$
$641$	2.67986			0.105848			0.0529240	+	0.998599i	$0.483146\pi$
$642$	−15.1747	−	25.1522i	−0.598899	−	0.992678i
$643$	−9.23577	+	9.23577i	−0.364223	+	0.364223i	−0.865365	−	0.501142i	$-0.832913\pi$
$643$	−9.23577	+	9.23577i	−0.364223	+	0.364223i	0.501142	+	0.865365i	$0.332913\pi$
$644$	−0.780280	+	1.48034i	−0.0307474	+	0.0583338i
$645$	17.0333	+	17.0333i	0.670687	+	0.670687i
$646$	−32.4773	−	8.03535i	−1.27780	−	0.316147i
$647$			47.5093i			1.86778i	0.357558	+	0.933891i	$0.383610\pi$
$647$			47.5093i			1.86778i	−0.357558	+	0.933891i	$0.616390\pi$
$648$	31.7625	−	1.83689i	1.24775	−	0.0721600i
$649$			15.2376i			0.598129i
$650$	−4.17632	+	16.8799i	−0.163809	+	0.662083i
$651$	−7.05057	−	7.05057i	−0.276334	−	0.276334i
$652$	−8.16776	−	26.3751i	−0.319874	−	1.03293i
$653$	2.88361	−	2.88361i	0.112844	−	0.112844i	−0.648430	−	0.761274i	$-0.724574\pi$
$653$	2.88361	−	2.88361i	0.112844	−	0.112844i	0.761274	+	0.648430i	$0.224574\pi$
$654$	−2.29263	+	1.38318i	−0.0896490	+	0.0540867i
$655$	−6.06492			−0.236976
$656$	7.79999	−	5.34339i	0.304538	−	0.208624i
$657$	14.0765			0.549177
$658$	6.78644	−	4.09437i	0.264563	−	0.159615i
$659$	−6.54919	+	6.54919i	−0.255120	+	0.255120i	−0.823066	−	0.567946i	$-0.807738\pi$
$659$	−6.54919	+	6.54919i	−0.255120	+	0.255120i	0.567946	+	0.823066i	$0.307738\pi$
$660$	−25.8256	+	7.99761i	−1.00526	+	0.311307i
$661$	32.3582	+	32.3582i	1.25859	+	1.25859i	0.951766	+	0.306823i	$0.0992661\pi$
$661$	32.3582	+	32.3582i	1.25859	+	1.25859i	0.306823	+	0.951766i	$0.400734\pi$
$662$	−1.49396	+	6.03829i	−0.0580643	+	0.234685i
$663$			78.3866i			3.04428i
$664$	26.4881	−	29.7399i	1.02794	−	1.15413i
$665$		−	4.82758i		−	0.187206i
$666$	−14.6710	−	3.62980i	−0.568488	−	0.140652i
$667$	3.58194	+	3.58194i	0.138693	+	0.138693i
$668$	24.9750	+	13.1641i	0.966310	+	0.509336i
$669$	24.3974	−	24.3974i	0.943256	−	0.943256i
$670$	1.12900	+	1.87132i	0.0436171	+	0.0722954i
$671$	−48.1748			−1.85977
$672$	9.36282	−	3.50368i	0.361179	−	0.135157i
$673$	−33.4942			−1.29111			−0.645554	−	0.763715i	$-0.723373\pi$
$673$	−33.4942			−1.29111			−0.645554	+	0.763715i	$0.723373\pi$
$674$	15.3630	+	25.4643i	0.591762	+	0.980848i
$675$	5.17569	−	5.17569i	0.199212	−	0.199212i
$676$	29.7461	+	15.6790i	1.14408	+	0.603037i
$677$	0.249260	+	0.249260i	0.00957985	+	0.00957985i	0.711880	−	0.702301i	$-0.247844\pi$
$677$	0.249260	+	0.249260i	0.00957985	+	0.00957985i	−0.702301	+	0.711880i	$0.747844\pi$
$678$	−46.6255	−	11.5358i	−1.79064	−	0.443030i
$679$			1.93386i			0.0742147i
$680$	23.7988	+	21.1966i	0.912643	+	0.812853i
$681$			28.7485i			1.10164i
$682$	−7.39873	+	29.9042i	−0.283312	+	1.14509i
$683$	16.5195	+	16.5195i	0.632101	+	0.632101i	0.948595	−	0.316494i	$-0.102506\pi$
$683$	16.5195	+	16.5195i	0.632101	+	0.632101i	−0.316494	+	0.948595i	$0.602506\pi$
$684$	−9.71575	+	3.00875i	−0.371491	+	0.115042i
$685$	−7.43215	+	7.43215i	−0.283968	+	0.283968i
$686$	−13.4750	+	8.12968i	−0.514477	+	0.310392i
$687$	−36.8212			−1.40482
$688$	−5.05603	+	27.0510i	−0.192759	+	1.03131i
$689$	46.1382			1.75773
$690$	−4.23979	+	2.55794i	−0.161406	+	0.0973790i
$691$	−21.0833	+	21.0833i	−0.802046	+	0.802046i	−0.983415	−	0.181369i	$-0.941947\pi$
$691$	−21.0833	+	21.0833i	−0.802046	+	0.802046i	0.181369	+	0.983415i	$0.441947\pi$
$692$	3.67974	+	11.8825i	0.139883	+	0.451705i
$693$	3.33741	+	3.33741i	0.126778	+	0.126778i
$694$	−5.76766	+	23.3117i	−0.218937	+	0.884902i
$695$		−	7.31845i		−	0.277605i
$696$	−1.74721	−	30.2117i	−0.0662278	−	1.14517i
$697$		−	16.0660i		−	0.608544i
$698$	−41.8401	−	10.3518i	−1.58367	−	0.391823i
$699$	28.5311	+	28.5311i	1.07914	+	1.07914i
$700$	1.75714	−	3.33364i	0.0664136	−	0.126000i
$701$	31.5426	−	31.5426i	1.19135	−	1.19135i	0.214660	−	0.976689i	$-0.431136\pi$
$701$	31.5426	−	31.5426i	1.19135	−	1.19135i	0.976689	−	0.214660i	$-0.0688643\pi$
$702$	−12.9653	−	21.4900i	−0.489344	−	0.811089i
$703$	−25.4570			−0.960130
$704$	−24.2117	−	19.1764i	−0.912514	−	0.722738i
$705$	23.4530			0.883292
$706$	21.5346	+	35.6937i	0.810465	+	1.34335i
$707$	6.66184	−	6.66184i	0.250544	−	0.250544i
$708$	7.77410	−	14.7490i	0.292168	−	0.554301i
$709$	24.2002	+	24.2002i	0.908856	+	0.908856i	0.996180	−	0.0873239i	$-0.0278315\pi$
$709$	24.2002	+	24.2002i	0.908856	+	0.908856i	−0.0873239	+	0.996180i	$0.527831\pi$
$710$	27.3552	+	6.76807i	1.02662	+	0.254001i
$711$			0.658793i			0.0247067i
$712$	−0.737684	−	12.7556i	−0.0276459	−	0.478035i
$713$			5.64220i			0.211302i
$714$	4.07989	−	16.4901i	0.152686	−	0.617128i
$715$	24.7098	+	24.7098i	0.924095	+	0.924095i
$716$	−13.8649	−	44.7719i	−0.518154	−	1.67321i
$717$	−18.2473	+	18.2473i	−0.681457	+	0.681457i
$718$	−5.70648	+	3.44281i	−0.212964	+	0.128485i
$719$	−6.68837			−0.249434			−0.124717	−	0.992192i	$-0.539802\pi$
$719$	−6.68837			−0.249434			−0.124717	+	0.992192i	$0.539802\pi$
$720$	9.52361	+	1.78004i	0.354924	+	0.0663380i
$721$	5.40348			0.201236
$722$	8.33806	−	5.03049i	0.310310	−	0.187215i
$723$	29.8562	−	29.8562i	1.11037	−	1.11037i
$724$	−33.8553	+	10.4842i	−1.25822	+	0.389644i
$725$	−8.06629	−	8.06629i	−0.299574	−	0.299574i
$726$	2.80169	−	11.3239i	0.103980	−	0.420268i
$727$			7.04386i			0.261242i	0.991432	+	0.130621i	$0.0416972\pi$
$727$			7.04386i			0.261242i	−0.991432	+	0.130621i	$0.958303\pi$
$728$	−9.64919	−	8.59414i	−0.357623	−	0.318520i
$729$			4.16008i			0.154077i
$730$	−21.9249	−	5.42453i	−0.811477	−	0.200771i
$731$	33.0662	+	33.0662i	1.22300	+	1.22300i
$732$	46.6299	+	24.5783i	1.72349	+	0.908441i
$733$	−23.9055	+	23.9055i	−0.882968	+	0.882968i	−0.993835	−	0.110867i	$-0.964637\pi$
$733$	−23.9055	+	23.9055i	−0.882968	+	0.882968i	0.110867	+	0.993835i	$0.464637\pi$
$734$	13.8211	+	22.9086i	0.510147	+	0.845571i
$735$	−22.0583			−0.813632
$736$	−5.14819	−	2.34438i	−0.189765	−	0.0864151i
$737$	−3.59912			−0.132575
$738$	−2.52306	−	4.18199i	−0.0928752	−	0.153941i
$739$	33.0329	−	33.0329i	1.21513	−	1.21513i	0.245818	−	0.969316i	$-0.420944\pi$
$739$	33.0329	−	33.0329i	1.21513	−	1.21513i	0.969316	−	0.245818i	$-0.0790564\pi$
$740$	21.4520	+	11.3072i	0.788592	+	0.415662i
$741$	28.3827	+	28.3827i	1.04267	+	1.04267i
$742$	−9.70607	−	2.40142i	−0.356321	−	0.0881588i
$743$		−	20.9205i		−	0.767499i	−0.923437	−	0.383750i	$-0.874633\pi$
$743$		−	20.9205i		−	0.767499i	0.923437	−	0.383750i	$-0.125367\pi$
$744$	22.4183	−	25.1705i	0.821896	−	0.922795i
$745$			1.72827i			0.0633191i
$746$	−4.25974	+	17.2171i	−0.155960	+	0.630361i
$747$	−14.5475	−	14.5475i	−0.532265	−	0.532265i
$748$	−50.1344	+	15.5255i	−1.83309	+	0.567668i
$749$	5.81834	−	5.81834i	0.212597	−	0.212597i
$750$	30.7467	−	18.5500i	1.12271	−	0.677350i
$751$	18.4702			0.673988			0.336994	−	0.941507i	$-0.390590\pi$
$751$	18.4702			0.673988			0.336994	+	0.941507i	$0.390590\pi$
$752$	15.1423	+	22.1039i	0.552183	+	0.806047i
$753$	57.8712			2.10894
$754$	−33.4921	+	20.2064i	−1.21971	+	0.735872i
$755$	7.82680	−	7.82680i	0.284846	−	0.284846i
$756$	1.60898	+	5.19567i	0.0585180	+	0.188965i
$757$	−8.20058	−	8.20058i	−0.298055	−	0.298055i	0.542197	−	0.840252i	$-0.317593\pi$
$757$	−8.20058	−	8.20058i	−0.298055	−	0.298055i	−0.840252	+	0.542197i	$0.817593\pi$
$758$	−7.21294	+	29.1533i	−0.261986	+	1.05890i
$759$		−	8.15441i		−	0.295986i
$760$	16.2922	−	0.942216i	0.590981	−	0.0341778i
$761$			26.1787i			0.948977i	0.880262	+	0.474488i	$0.157367\pi$
$761$			26.1787i			0.948977i	−0.880262	+	0.474488i	$0.842633\pi$
$762$	29.6432	+	7.33414i	1.07386	+	0.265688i
$763$	−0.530344	−	0.530344i	−0.0191997	−	0.0191997i
$764$	10.1159	−	19.1918i	0.365980	−	0.694336i
$765$	11.6413	−	11.6413i	0.420894	−	0.420894i
$766$	−3.59088	−	5.95189i	−0.129744	−	0.215051i
$767$	−21.5500			−0.778124
$768$	13.6517	+	30.9140i	0.492612	+	1.11551i
$769$

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.730558 - 1.21090i) q^{2} +(1.49351 - 1.49351i) q^{3} +(-0.932570 + 1.76927i) q^{4} +(-1.17219 - 1.17219i) q^{5} +(-2.89958 - 0.717397i) q^{6} -0.836699i q^{7} +(2.82371 - 0.163301i) q^{8} -1.46112i q^{9} +O(q^{10})\)	\(q+(-0.730558 - 1.21090i) q^{2} +(1.49351 - 1.49351i) q^{3} +(-0.932570 + 1.76927i) q^{4} +(-1.17219 - 1.17219i) q^{5} +(-2.89958 - 0.717397i) q^{6} -0.836699i q^{7} +(2.82371 - 0.163301i) q^{8} -1.46112i q^{9} +(-0.563056 + 2.27576i) q^{10} +(-2.72996 - 2.72996i) q^{11} +(1.24961 + 4.03521i) q^{12} +(3.86087 - 3.86087i) q^{13} +(-1.01316 + 0.611257i) q^{14} -3.50135 q^{15} +(-2.26063 - 3.29994i) q^{16} -6.79704 q^{17} +(-1.76927 + 1.06743i) q^{18} +(-2.46112 + 2.46112i) q^{19} +(3.16707 - 0.980771i) q^{20} +(-1.24961 - 1.24961i) q^{21} +(-1.31132 + 5.30011i) q^{22} +1.00000i q^{23} +(3.97333 - 4.46112i) q^{24} -2.25193i q^{25} +(-7.49573 - 1.85455i) q^{26} +(2.29833 + 2.29833i) q^{27} +(1.48034 + 0.780280i) q^{28} +(3.58194 - 3.58194i) q^{29} +(2.55794 + 4.23979i) q^{30} +5.64220 q^{31} +(-2.34438 + 5.14819i) q^{32} -8.15441 q^{33} +(4.96563 + 8.23056i) q^{34} +(-0.980771 + 0.980771i) q^{35} +(2.58511 + 1.36259i) q^{36} +(5.17185 + 5.17185i) q^{37} +(4.77816 + 1.18218i) q^{38} -11.5325i q^{39} +(-3.50135 - 3.11851i) q^{40} +2.36368i q^{41} +(-0.600245 + 2.42608i) q^{42} +(-4.86479 - 4.86479i) q^{43} +(7.37591 - 2.28415i) q^{44} +(-1.71271 + 1.71271i) q^{45} +(1.21090 - 0.730558i) q^{46} -6.69829 q^{47} +(-8.30473 - 1.55222i) q^{48} +6.29994 q^{49} +(-2.72687 + 1.64517i) q^{50} +(-10.1514 + 10.1514i) q^{51} +(3.23038 + 10.4315i) q^{52} +(5.97511 + 5.97511i) q^{53} +(1.10399 - 4.46212i) q^{54} +6.40007i q^{55} +(-0.136634 - 2.36259i) q^{56} +7.35138i q^{57} +(-6.95419 - 1.72057i) q^{58} +(-2.79082 - 2.79082i) q^{59} +(3.26525 - 6.19483i) q^{60} +(8.82336 - 8.82336i) q^{61} +(-4.12195 - 6.83215i) q^{62} -1.22251 q^{63} +(7.94667 - 0.922232i) q^{64} -9.05136 q^{65} +(5.95727 + 9.87420i) q^{66} +(0.659190 - 0.659190i) q^{67} +(6.33872 - 12.0258i) q^{68} +(1.49351 + 1.49351i) q^{69} +(1.90413 + 0.471108i) q^{70} -12.0202i q^{71} +(-0.238602 - 4.12577i) q^{72} +9.63409i q^{73} +(2.48427 - 10.0409i) q^{74} +(-3.36327 - 3.36327i) q^{75} +(-2.05921 - 6.64954i) q^{76} +(-2.28415 + 2.28415i) q^{77} +(-13.9647 + 8.42513i) q^{78} -0.450884 q^{79} +(-1.21827 + 6.51804i) q^{80} +11.2485 q^{81} +(2.86219 - 1.72680i) q^{82} +(9.95642 - 9.95642i) q^{83} +(3.37626 - 1.04555i) q^{84} +(7.96744 + 7.96744i) q^{85} +(-2.33678 + 9.44481i) q^{86} -10.6993i q^{87} +(-8.15441 - 7.26280i) q^{88} -4.51731i q^{89} +(3.32515 + 0.822690i) q^{90} +(-3.23038 - 3.23038i) q^{91} +(-1.76927 - 0.932570i) q^{92} +(8.42665 - 8.42665i) q^{93} +(4.89349 + 8.11097i) q^{94} +5.76980 q^{95} +(4.18750 + 11.1902i) q^{96} -2.31130 q^{97} +(-4.60247 - 7.62861i) q^{98} +(-3.98879 + 3.98879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26} + 14 q^{27} + 12 q^{28} + 2 q^{29} - 30 q^{30} + 20 q^{31} - 8 q^{32} - 36 q^{33} + 10 q^{34} + 4 q^{35} + 4 q^{36} - 4 q^{37} + 24 q^{38} - 14 q^{42} + 20 q^{43} + 4 q^{44} - 20 q^{45} - 2 q^{46} - 16 q^{47} - 12 q^{48} + 52 q^{49} + 6 q^{50} - 4 q^{51} - 16 q^{53} + 16 q^{54} + 28 q^{56} + 14 q^{58} + 8 q^{59} + 48 q^{60} + 12 q^{61} - 44 q^{62} - 4 q^{63} + 24 q^{64} - 52 q^{65} + 34 q^{66} - 4 q^{67} - 16 q^{68} + 2 q^{69} + 28 q^{70} + 8 q^{72} - 26 q^{74} - 46 q^{75} - 8 q^{76} - 12 q^{77} - 44 q^{78} - 4 q^{79} + 4 q^{80} + 48 q^{81} - 6 q^{82} + 28 q^{83} + 12 q^{84} - 8 q^{85} + 44 q^{86} - 36 q^{88} + 4 q^{90} - 4 q^{92} - 14 q^{93} + 48 q^{95} + 32 q^{96} + 36 q^{97} - 2 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8 - 6 * q^10 - 4 * q^11 - 8 * q^12 + 18 * q^13 - 2 * q^14 + 8 * q^16 - 8 * q^17 - 4 * q^18 - 8 * q^19 - 32 * q^20 + 8 * q^21 - 34 * q^22 + 12 * q^24 - 14 * q^26 + 14 * q^27 + 12 * q^28 + 2 * q^29 - 30 * q^30 + 20 * q^31 - 8 * q^32 - 36 * q^33 + 10 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 24 * q^38 - 14 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 2 * q^46 - 16 * q^47 - 12 * q^48 + 52 * q^49 + 6 * q^50 - 4 * q^51 - 16 * q^53 + 16 * q^54 + 28 * q^56 + 14 * q^58 + 8 * q^59 + 48 * q^60 + 12 * q^61 - 44 * q^62 - 4 * q^63 + 24 * q^64 - 52 * q^65 + 34 * q^66 - 4 * q^67 - 16 * q^68 + 2 * q^69 + 28 * q^70 + 8 * q^72 - 26 * q^74 - 46 * q^75 - 8 * q^76 - 12 * q^77 - 44 * q^78 - 4 * q^79 + 4 * q^80 + 48 * q^81 - 6 * q^82 + 28 * q^83 + 12 * q^84 - 8 * q^85 + 44 * q^86 - 36 * q^88 + 4 * q^90 - 4 * q^92 - 14 * q^93 + 48 * q^95 + 32 * q^96 + 36 * q^97 - 2 * q^98 + 36 * q^99

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