LMFDB - Embedded newform 368.2.j.c.93.2

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			93.2
Root			$1.35092 - 0.418349i$ of defining polynomial
Character	$\chi$	$=$	368.93
Dual form			368.2.j.c.277.2

$q$-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} +(-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} - 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}+ \cdots + 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

Character values

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

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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	0.991602	−	0.129326i	$-0.0412815\pi$
$3$	1.49351	+	1.49351i	0.862276	+	0.862276i	−0.129326	+	0.991602i	$0.541282\pi$
$4$	−0.932570	−	1.76927i	−0.466285	−	0.884634i
$5$	−1.17219	+	1.17219i	−0.524220	+	0.524220i	−0.918843	−	0.394623i	$-0.870875\pi$
$5$	−1.17219	+	1.17219i	−0.524220	+	0.524220i	0.394623	+	0.918843i	$0.370875\pi$
$6$	−2.89958	+	0.717397i	−1.18375	+	0.292876i
$7$			0.836699i			0.316242i	0.987420	+	0.158121i	$0.0505437\pi$
$7$			0.836699i			0.316242i	−0.987420	+	0.158121i	$0.949456\pi$
$8$	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	−0.986553	−	0.163440i	$-0.947741\pi$
$11$	−2.72996	+	2.72996i	−0.823113	+	0.823113i	0.163440	+	0.986553i	$0.447741\pi$
$12$	1.24961	−	4.03521i	0.360732	−	1.16487i
$13$	3.86087	+	3.86087i	1.07081	+	1.07081i	0.997294	+	0.0735190i	$0.0234229\pi$
$13$	3.86087	+	3.86087i	1.07081	+	1.07081i	0.0735190	+	0.997294i	$0.476577\pi$
$14$	−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	0.365997	−	0.930616i	$-0.380728\pi$
$19$	−2.46112	−	2.46112i	−0.564619	−	0.564619i	−0.930616	+	0.365997i	$0.880728\pi$
$20$	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	0.956589	−	0.291440i	$-0.0941343\pi$
$29$	3.58194	+	3.58194i	0.665149	+	0.665149i	−0.291440	+	0.956589i	$0.594134\pi$
$30$	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	−0.139917	−	0.990163i	$-0.544684\pi$
$37$	5.17185	−	5.17185i	0.850246	−	0.850246i	0.990163	+	0.139917i	$0.0446836\pi$
$38$	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	$-0.940910\pi$
$41$		−	2.36368i		−	0.369145i	0.982819	−	0.184572i	$-0.0590900\pi$
$42$	−0.600245	−	2.42608i	−0.0926199	−	0.374352i
$43$	−4.86479	+	4.86479i	−0.741874	+	0.741874i	−0.972938	−	0.231064i	$-0.925779\pi$
$43$	−4.86479	+	4.86479i	−0.741874	+	0.741874i	0.231064	+	0.972938i	$0.425779\pi$
$44$	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	−0.165471	−	0.986215i	$-0.552914\pi$
$53$	5.97511	−	5.97511i	0.820744	−	0.820744i	0.986215	+	0.165471i	$0.0529143\pi$
$54$	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	−0.865039	−	0.501705i	$-0.832706\pi$
$59$	−2.79082	+	2.79082i	−0.363334	+	0.363334i	0.501705	+	0.865039i	$0.332706\pi$
$60$	3.26525	+	6.19483i	0.421542	+	0.799749i
$61$	8.82336	+	8.82336i	1.12972	+	1.12972i	0.990223	+	0.139493i	$0.0445472\pi$
$61$	8.82336	+	8.82336i	1.12972	+	1.12972i	0.139493	+	0.990223i	$0.455453\pi$
$62$	−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	0.746226	−	0.665693i	$-0.231864\pi$
$67$	0.659190	+	0.659190i	0.0805329	+	0.0805329i	−0.665693	+	0.746226i	$0.731864\pi$
$68$	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	$0.252787\pi$
$71$			12.0202i			1.42654i	−0.700889	+	0.713270i	$0.747213\pi$
$72$	−0.238602	+	4.12577i	−0.0281196	+	0.486226i
$73$		−	9.63409i		−	1.12758i	−0.825917	−	0.563792i	$-0.809342\pi$
$73$		−	9.63409i		−	1.12758i	0.825917	−	0.563792i	$-0.190658\pi$
$74$	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	0.995222	+	0.0976374i	$0.0311286\pi$
$83$	9.95642	+	9.95642i	1.09286	+	1.09286i	0.0976374	+	0.995222i	$0.468871\pi$
$84$	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	$0.0769563\pi$
$89$			4.51731i			0.478834i	−0.970917	+	0.239417i	$0.923044\pi$
$90$	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	−0.189607	−	0.981860i	$-0.560721\pi$
$101$	7.96205	−	7.96205i	0.792254	−	0.792254i	0.981860	+	0.189607i	$0.0607212\pi$
$102$	19.7086	−	4.87618i	1.95144	−	0.482814i
$103$		−	6.45810i		−	0.636335i	−0.948034	−	0.318168i	$-0.896932\pi$
$103$		−	6.45810i		−	0.636335i	0.948034	−	0.318168i	$-0.103068\pi$
$104$	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	−0.285976	−	0.958237i	$-0.592318\pi$
$107$	6.95392	−	6.95392i	0.672261	−	0.672261i	0.958237	+	0.285976i	$0.0923177\pi$
$108$	−6.20972	−	1.92301i	−0.597531	−	0.185042i
$109$	0.633853	+	0.633853i	0.0607121	+	0.0607121i	0.736811	−	0.676099i	$-0.236331\pi$
$109$	0.633853	+	0.633853i	0.0607121	+	0.0607121i	−0.676099	+	0.736811i	$0.736331\pi$
$110$	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	0.811031	−	0.585003i	$-0.198907\pi$
$131$	2.58700	+	2.58700i	0.226027	+	0.226027i	−0.585003	+	0.811031i	$0.698907\pi$
$132$	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	$0.0873041\pi$
$137$			6.34039i			0.541696i	−0.962622	+	0.270848i	$0.912696\pi$
$138$	0.717397	+	2.89958i	0.0610689	+	0.246829i
$139$	3.12169	−	3.12169i	0.264779	−	0.264779i	−0.562213	−	0.826992i	$-0.690050\pi$
$139$	3.12169	−	3.12169i	0.264779	−	0.264779i	0.826992	+	0.562213i	$0.190050\pi$
$140$	−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	−0.736659	−	0.676265i	$-0.763597\pi$
$149$	−0.737198	+	0.737198i	−0.0603936	+	0.0603936i	0.676265	+	0.736659i	$0.263597\pi$
$150$	−1.61553	−	6.52967i	−0.131908	−	0.533145i
$151$		−	6.67706i		−	0.543372i	−0.962386	−	0.271686i	$-0.912419\pi$
$151$		−	6.67706i		−	0.543372i	0.962386	−	0.271686i	$-0.0875812\pi$
$152$	−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	0.456823	−	0.889558i	$-0.348987\pi$
$157$	−5.42215	−	5.42215i	−0.432734	−	0.432734i	−0.889558	+	0.456823i	$0.848987\pi$
$158$	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	0.212541	−	0.977152i	$-0.431826\pi$
$163$	−9.76189	−	9.76189i	−0.764611	−	0.764611i	−0.977152	+	0.212541i	$0.931826\pi$
$164$	−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	$0.183912\pi$
$167$			14.1160i			1.09233i	−0.837679	+	0.546164i	$0.816088\pi$
$168$	−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	0.854243	−	0.519874i	$-0.174021\pi$
$173$	4.39793	+	4.39793i	0.334369	+	0.334369i	−0.519874	+	0.854243i	$0.674021\pi$
$174$	−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	−0.960587	−	0.277981i	$-0.910335\pi$
$179$	−16.5709	−	16.5709i	−1.23857	−	1.23857i	−0.277981	−	0.960587i	$-0.589665\pi$
$180$	−1.43302	+	4.62746i	−0.106811	+	0.344911i
$181$	12.5305	−	12.5305i	0.931383	−	0.931383i	−0.0664091	−	0.997792i	$-0.521154\pi$
$181$	12.5305	−	12.5305i	0.931383	−	0.931383i	0.997792	+	0.0664091i	$0.0211542\pi$
$182$	−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	−0.286166	−	0.958180i	$-0.592381\pi$
$197$	9.43218	−	9.43218i	0.672015	−	0.672015i	0.958180	+	0.286166i	$0.0923807\pi$
$198$	7.74407	−	1.91599i	0.550347	−	0.136164i
$199$			4.79264i			0.339741i	0.985466	+	0.169870i	$0.0543349\pi$
$199$			4.79264i			0.339741i	−0.985466	+	0.169870i	$0.945665\pi$
$200$	−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	0.366158	−	0.930553i	$-0.380673\pi$
$211$	−8.19831	−	8.19831i	−0.564395	−	0.564395i	−0.930553	+	0.366158i	$0.880673\pi$
$212$	−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	0.311459	−	0.950259i	$-0.399182\pi$
$227$	−9.62449	−	9.62449i	−0.638800	−	0.638800i	−0.950259	+	0.311459i	$0.899182\pi$
$228$	−13.0066	+	6.85568i	−0.861381	+	0.454028i
$229$	−12.3271	+	12.3271i	−0.814598	+	0.814598i	−0.985319	−	0.170721i	$-0.945390\pi$
$229$	−12.3271	+	12.3271i	−0.814598	+	0.814598i	0.170721	+	0.985319i	$0.445390\pi$
$230$	−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	$-0.784792\pi$
$233$		−	19.1034i		−	1.25151i	0.780021	−	0.625753i	$-0.215208\pi$
$234$	−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	0.256295	−	0.966599i	$-0.417498\pi$
$251$	19.3743	−	19.3743i	1.22289	−	1.22289i	0.966599	−	0.256295i	$-0.0825018\pi$
$252$	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	$0.0111229\pi$
$263$			1.13315i			0.0698730i	−0.999390	+	0.0349365i	$0.988877\pi$
$264$	−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	0.998927	−	0.0463164i	$-0.0147482\pi$
$269$	15.6240	+	15.6240i	0.952610	+	0.952610i	−0.0463164	+	0.998927i	$0.514748\pi$
$270$	−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	−0.861512	−	0.507737i	$-0.830482\pi$
$277$	−5.88800	+	5.88800i	−0.353776	+	0.353776i	0.507737	+	0.861512i	$0.330482\pi$
$278$	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	$-0.753530\pi$
$281$		−	23.4422i		−	1.39844i	0.714905	−	0.699221i	$-0.246470\pi$
$282$	19.4222	−	4.80533i	1.15658	−	0.286153i
$283$	7.69603	−	7.69603i	0.457482	−	0.457482i	−0.440346	−	0.897828i	$-0.645144\pi$
$283$	7.69603	−	7.69603i	0.457482	−	0.457482i	0.897828	+	0.440346i	$0.145144\pi$
$284$	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	−0.972175	−	0.234257i	$-0.924734\pi$
$293$	−12.6311	+	12.6311i	−0.737917	+	0.737917i	0.234257	+	0.972175i	$0.424734\pi$
$294$	−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	0.775811	−	0.630965i	$-0.217341\pi$
$307$	2.53791	+	2.53791i	0.144846	+	0.144846i	−0.630965	+	0.775811i	$0.717341\pi$
$308$	−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	$0.0333893\pi$
$311$			3.69293i			0.209407i	−0.994503	+	0.104703i	$0.966611\pi$
$312$	−1.88327	+	32.5643i	−0.106619	+	1.84359i
$313$		−	8.94100i		−	0.505375i	−0.967548	−	0.252688i	$-0.918686\pi$
$313$		−	8.94100i		−	0.505375i	0.967548	−	0.252688i	$-0.0813145\pi$
$314$	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	0.880155	−	0.474687i	$-0.157439\pi$
$317$	7.21914	+	7.21914i	0.405467	+	0.405467i	−0.474687	+	0.880155i	$0.657439\pi$
$318$	−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	−0.787397	−	0.616446i	$-0.788572\pi$
$331$	−3.11018	+	3.11018i	−0.170951	+	0.170951i	0.616446	+	0.787397i	$0.288572\pi$
$332$	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	−0.951680	−	0.307093i	$-0.900644\pi$
$347$	−12.0073	+	12.0073i	−0.644587	+	0.644587i	0.307093	+	0.951680i	$0.400644\pi$
$348$	18.9299	−	9.97784i	1.01475	−	0.534868i
$349$	21.5509	+	21.5509i	1.15359	+	1.15359i	0.985827	+	0.167764i	$0.0536547\pi$
$349$	21.5509	+	21.5509i	1.15359	+	1.15359i	0.167764	+	0.985827i	$0.446345\pi$
$350$	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	$0.0396879\pi$
$359$			4.71258i			0.248721i	−0.992237	+	0.124360i	$0.960312\pi$
$360$	−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	−0.898384	−	0.439211i	$-0.855258\pi$
$373$	−8.86810	+	8.86810i	−0.459173	+	0.459173i	0.439211	+	0.898384i	$0.355258\pi$
$374$	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	−0.978339	−	0.207010i	$-0.933627\pi$
$379$	−15.0162	+	15.0162i	−0.771329	+	0.771329i	0.207010	+	0.978339i	$0.433627\pi$
$380$	−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	−0.0677278	−	0.997704i	$-0.521575\pi$
$389$	18.3420	−	18.3420i	0.929976	−	0.929976i	0.997704	+	0.0677278i	$0.0215749\pi$
$390$	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	0.858532	−	0.512761i	$-0.171377\pi$
$397$	6.88943	+	6.88943i	0.345771	+	0.345771i	−0.512761	+	0.858532i	$0.671377\pi$
$398$	−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	$0.147625\pi$
$409$			18.0934i			0.894661i	−0.894369	+	0.447331i	$0.852375\pi$
$410$	−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	0.977034	+	0.213082i	$0.0683500\pi$
$419$	24.3611	+	24.3611i	1.19012	+	1.19012i	0.213082	+	0.977034i	$0.431650\pi$
$420$	−5.18320	+	2.73203i	−0.252914	+	0.133310i
$421$	4.33767	−	4.33767i	0.211405	−	0.211405i	−0.593459	−	0.804864i	$-0.702238\pi$
$421$	4.33767	−	4.33767i	0.211405	−	0.211405i	0.804864	+	0.593459i	$0.202238\pi$
$422$	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	$-0.729419\pi$
$439$		−	31.4837i		−	1.50264i	0.659941	−	0.751318i	$-0.270581\pi$
$440$	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	0.460514	−	0.887653i	$-0.347665\pi$
$443$	28.3756	−	28.3756i	1.34817	−	1.34817i	0.887653	−	0.460514i	$-0.152335\pi$
$444$	−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	$0.121573\pi$
$457$			15.9355i			0.745429i	−0.927946	+	0.372714i	$0.878427\pi$
$458$	−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	0.828639	−	0.559783i	$-0.189115\pi$
$461$	5.77259	+	5.77259i	0.268856	+	0.268856i	−0.559783	+	0.828639i	$0.689115\pi$
$462$	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	0.557497	−	0.830179i	$-0.311762\pi$
$467$	−5.89270	−	5.89270i	−0.272682	−	0.272682i	−0.830179	+	0.557497i	$0.811762\pi$
$468$	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	$-0.688896\pi$
$487$		−	36.5900i		−	1.65805i	0.559211	−	0.829026i	$-0.311104\pi$
$488$	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	−0.972833	−	0.231508i	$-0.925634\pi$
$491$	−16.4267	+	16.4267i	−0.741325	+	0.741325i	0.231508	+	0.972833i	$0.425634\pi$
$492$	−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	0.990012	−	0.140980i	$-0.0450255\pi$
$499$	18.9659	+	18.9659i	0.849032	+	0.849032i	−0.140980	+	0.990012i	$0.545025\pi$
$500$	−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	$-0.963064\pi$
$503$		−	5.19328i		−	0.231557i	0.993275	−	0.115778i	$-0.0369362\pi$
$504$	−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	0.0793216	−	0.996849i	$-0.474725\pi$
$509$	−20.7004	−	20.7004i	−0.917527	−	0.917527i	−0.996849	+	0.0793216i	$0.974725\pi$
$510$	−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	$-0.737420\pi$
$521$		−	33.5302i		−	1.46898i	0.678617	−	0.734492i	$-0.262580\pi$
$522$	−2.51395	−	10.1609i	−0.110032	−	0.444730i
$523$	−21.0872	+	21.0872i	−0.922081	+	0.922081i	−0.997176	−	0.0750956i	$-0.976074\pi$
$523$	−21.0872	+	21.0872i	−0.922081	+	0.922081i	0.0750956	+	0.997176i	$0.476074\pi$
$524$	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	0.999227	−	0.0393184i	$-0.0125187\pi$
$541$	22.3269	+	22.3269i	0.959908	+	0.959908i	−0.0393184	+	0.999227i	$0.512519\pi$
$542$	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	0.152615	−	0.988286i	$-0.451231\pi$
$547$	−19.5447	−	19.5447i	−0.835671	−	0.835671i	−0.988286	+	0.152615i	$0.951231\pi$
$548$	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	0.729411	−	0.684076i	$-0.239794\pi$
$557$	1.06994	+	1.06994i	0.0453347	+	0.0453347i	−0.684076	+	0.729411i	$0.739794\pi$
$558$	−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	0.991142	+	0.132806i	$0.0423986\pi$
$563$	26.6686	+	26.6686i	1.12395	+	1.12395i	0.132806	+	0.991142i	$0.457601\pi$
$564$	−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	$0.172713\pi$
$569$			24.6342i			1.03272i	−0.856372	+	0.516359i	$0.827287\pi$
$570$	−16.7300	+	4.13924i	−0.700743	+	0.173374i
$571$	−21.7399	+	21.7399i	−0.909788	+	0.909788i	−0.996255	−	0.0864666i	$-0.972442\pi$
$571$	−21.7399	+	21.7399i	−0.909788	+	0.909788i	0.0864666	+	0.996255i	$0.472442\pi$
$572$	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	−0.586782	−	0.809745i	$-0.699606\pi$
$587$	5.40195	−	5.40195i	0.222962	−	0.222962i	0.809745	+	0.586782i	$0.199606\pi$
$588$	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	$-0.689153\pi$
$599$		−	40.5578i		−	1.65715i	0.559881	−	0.828573i	$-0.310847\pi$
$600$	−10.0461	+	8.94768i	−0.410132	+	0.365288i
$601$			44.8779i			1.83061i	0.402763	+	0.915304i	$0.368050\pi$
$601$			44.8779i			1.83061i	−0.402763	+	0.915304i	$0.631950\pi$
$602$	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	−0.856932	−	0.515429i	$-0.827632\pi$
$613$	−8.45521	+	8.45521i	−0.341503	+	0.341503i	0.515429	+	0.856932i	$0.327632\pi$
$614$	−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	$-0.924190\pi$
$617$		−	11.7202i		−	0.471836i	0.971773	−	0.235918i	$-0.0758096\pi$
$618$	4.63302	+	18.7258i	0.186368	+	0.753262i
$619$	−27.5714	+	27.5714i	−1.10819	+	1.10819i	−0.114798	+	0.993389i	$0.536622\pi$
$619$	−27.5714	+	27.5714i	−1.10819	+	1.10819i	−0.993389	+	0.114798i	$0.963378\pi$
$620$	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	$-0.968970\pi$
$631$		−	4.88975i		−	0.194658i	0.995252	−	0.0973289i	$-0.0310299\pi$
$632$	−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	0.501142	−	0.865365i	$-0.332913\pi$
$643$	−9.23577	−	9.23577i	−0.364223	−	0.364223i	−0.865365	+	0.501142i	$0.832913\pi$
$644$	−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	$-0.616390\pi$
$647$		−	47.5093i		−	1.86778i	0.357558	−	0.933891i	$-0.383610\pi$
$648$	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	0.761274	−	0.648430i	$-0.224574\pi$
$653$	2.88361	+	2.88361i	0.112844	+	0.112844i	−0.648430	+	0.761274i	$0.724574\pi$
$654$	−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	0.567946	−	0.823066i	$-0.307738\pi$
$659$	−6.54919	−	6.54919i	−0.255120	−	0.255120i	−0.823066	+	0.567946i	$0.807738\pi$
$660$	−25.8256	−	7.99761i	−1.00526	−	0.311307i
$661$	32.3582	−	32.3582i	1.25859	−	1.25859i	0.306823	−	0.951766i	$-0.400734\pi$
$661$	32.3582	−	32.3582i	1.25859	−	1.25859i	0.951766	−	0.306823i	$-0.0992661\pi$
$662$	−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	−0.702301	−	0.711880i	$-0.747844\pi$
$677$	0.249260	−	0.249260i	0.00957985	−	0.00957985i	0.711880	+	0.702301i	$0.247844\pi$
$678$	−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	−0.316494	−	0.948595i	$-0.602506\pi$
$683$	16.5195	−	16.5195i	0.632101	−	0.632101i	0.948595	+	0.316494i	$0.102506\pi$
$684$	−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	0.181369	−	0.983415i	$-0.441947\pi$
$691$	−21.0833	−	21.0833i	−0.802046	−	0.802046i	−0.983415	+	0.181369i	$0.941947\pi$
$692$	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	0.976689	+	0.214660i	$0.0688643\pi$
$701$	31.5426	+	31.5426i	1.19135	+	1.19135i	0.214660	+	0.976689i	$0.431136\pi$
$702$	−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	−0.0873239	−	0.996180i	$-0.527831\pi$
$709$	24.2002	−	24.2002i	0.908856	−	0.908856i	0.996180	+	0.0873239i	$0.0278315\pi$
$710$	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	$-0.958303\pi$
$727$		−	7.04386i		−	0.261242i	0.991432	−	0.130621i	$-0.0416972\pi$
$728$	−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	0.110867	−	0.993835i	$-0.464637\pi$
$733$	−23.9055	−	23.9055i	−0.882968	−	0.882968i	−0.993835	+	0.110867i	$0.964637\pi$
$734$	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	0.969316	+	0.245818i	$0.0790564\pi$
$739$	33.0329	+	33.0329i	1.21513	+	1.21513i	0.245818	+	0.969316i	$0.420944\pi$
$740$	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	$0.125367\pi$
$743$			20.9205i			0.767499i	−0.923437	+	0.383750i	$0.874633\pi$
$744$	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	−0.840252	−	0.542197i	$-0.817593\pi$
$757$	−8.20058	+	8.20058i	−0.298055	+	0.298055i	0.542197	+	0.840252i	$0.317593\pi$
$758$	−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	$-0.842633\pi$
$761$		−	26.1787i		−	0.948977i	0.880262	−	0.474488i	$-0.157367\pi$
$762$	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
$769$	21.6097			0.779266			0.389633	−	0.920970i	$-0.372602\pi$
$769$	21.6097			0.779266			0.389633	+	0.920970i	$0.372602\pi$
$770$	−3.91208	+	6.48430i	−0.140982	+	0.233678i

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26}+ \cdots + 36 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

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