LMFDB - Embedded newform 275.3.q.c.149.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(24,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.q (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,18,0,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			149.2
Root			$-0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	275.149
Dual form			275.3.q.c.24.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.224514 + 0.690983i) q^{2} +(-2.35114 + 3.23607i) q^{3} +(2.80902 - 2.04087i) q^{4} +(-2.76393 - 0.898056i) q^{6} +(-0.224514 + 0.163119i) q^{7} +(4.39201 + 3.19098i) q^{8} +(-2.16312 - 6.65740i) q^{9} +(10.3713 + 3.66547i) q^{11} +13.8885i q^{12} +(3.49396 + 10.7533i) q^{13} +(-0.163119 - 0.118513i) q^{14} +(3.07295 - 9.45756i) q^{16} +(-6.26137 + 19.2705i) q^{17} +(4.11450 - 2.98936i) q^{18} +(-16.9721 + 23.3601i) q^{19} -1.11006i q^{21} +(-0.204270 + 7.98936i) q^{22} -27.6180i q^{23} +(-20.6525 + 6.71040i) q^{24} +(-6.64590 + 4.82853i) q^{26} +(-7.60845 - 2.47214i) q^{27} +(-0.297759 + 0.916408i) q^{28} +(-10.2016 - 14.0413i) q^{29} +(10.6180 + 32.6789i) q^{31} +28.9402 q^{32} +(-36.2461 + 24.9443i) q^{33} -14.7214 q^{34} +(-19.6631 - 14.2861i) q^{36} +(7.80021 + 10.7361i) q^{37} +(-19.9519 - 6.48278i) q^{38} +(-43.0132 - 13.9758i) q^{39} +(-10.6140 + 14.6089i) q^{41} +(0.767031 - 0.249224i) q^{42} +34.7931 q^{43} +(36.6140 - 10.8702i) q^{44} +(19.0836 - 6.20063i) q^{46} +(-27.9159 + 38.4230i) q^{47} +(23.3804 + 32.1803i) q^{48} +(-15.1180 + 46.5285i) q^{49} +(-47.6393 - 65.5699i) q^{51} +(31.7606 + 23.0755i) q^{52} +(-39.5406 + 12.8475i) q^{53} -5.81234i q^{54} -1.50658 q^{56} +(-35.6911 - 109.846i) q^{57} +(7.41192 - 10.2016i) q^{58} +(82.3115 - 59.8028i) q^{59} +(48.4164 + 15.7314i) q^{61} +(-20.1967 + 14.6738i) q^{62} +(1.57160 + 1.14183i) q^{63} +(-5.79431 - 17.8330i) q^{64} +(-25.3738 - 19.4451i) q^{66} -40.1803i q^{67} +(21.7403 + 66.9098i) q^{68} +(89.3738 + 64.9339i) q^{69} +(8.70820 - 26.8011i) q^{71} +(11.7432 - 36.1418i) q^{72} +(80.7463 - 58.6656i) q^{73} +(-5.66718 + 7.80021i) q^{74} +100.257i q^{76} +(-2.92641 + 0.868810i) q^{77} -32.8591i q^{78} +(125.172 - 40.6709i) q^{79} +(76.8566 - 55.8396i) q^{81} +(-12.4775 - 4.05418i) q^{82} +(38.7533 - 119.271i) q^{83} +(-2.26548 - 3.11817i) q^{84} +(7.81153 + 24.0414i) q^{86} +69.4242 q^{87} +(33.8545 + 49.1935i) q^{88} -88.9493 q^{89} +(-2.53851 - 1.84433i) q^{91} +(-56.3648 - 77.5795i) q^{92} +(-130.716 - 42.4721i) q^{93} +(-32.8171 - 10.6629i) q^{94} +(-68.0426 + 93.6526i) q^{96} +(45.9533 - 14.9311i) q^{97} -35.5446 q^{98} +(1.96807 - 76.9748i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 18 q^{4} - 40 q^{6} + 14 q^{9} - 2 q^{11} + 30 q^{14} + 38 q^{16} - 100 q^{19} - 40 q^{24} - 80 q^{26} - 180 q^{29} + 76 q^{31} + 240 q^{34} - 126 q^{36} - 40 q^{39} + 170 q^{41} + 38 q^{44} + 260 q^{46}+ \cdots - 266 q^{99}+O(q^{100}) $ 8 * q + 18 * q^4 - 40 * q^6 + 14 * q^9 - 2 * q^11 + 30 * q^14 + 38 * q^16 - 100 * q^19 - 40 * q^24 - 80 * q^26 - 180 * q^29 + 76 * q^31 + 240 * q^34 - 126 * q^36 - 40 * q^39 + 170 * q^41 + 38 * q^44 + 260 * q^46 - 112 * q^49 - 560 * q^51 + 140 * q^56 + 256 * q^59 + 280 * q^61 + 298 * q^64 + 280 * q^66 + 232 * q^69 + 16 * q^71 - 260 * q^74 + 420 * q^79 + 190 * q^81 - 680 * q^84 - 340 * q^86 + 156 * q^89 - 150 * q^91 - 750 * q^94 - 920 * q^96 - 266 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.224514	+	0.690983i	0.112257	+	0.345492i	0.991365	−	0.131131i	$-0.0418609\pi$
$2$	0.224514	+	0.690983i	0.112257	+	0.345492i	−0.879108	+	0.476623i	$0.841861\pi$
$3$	−2.35114	+	3.23607i	−0.783714	+	1.07869i	0.211149	+	0.977454i	$0.432280\pi$
$3$	−2.35114	+	3.23607i	−0.783714	+	1.07869i	−0.994862	+	0.101235i	$0.967720\pi$
$4$	2.80902	−	2.04087i	0.702254	−	0.510218i
$5$		0			0
$5$		0			0
$6$	−2.76393	−	0.898056i	−0.460655	−	0.149676i
$7$	−0.224514	+	0.163119i	−0.0320734	+	0.0233027i	−0.603706	−	0.797207i	$-0.706310\pi$
$7$	−0.224514	+	0.163119i	−0.0320734	+	0.0233027i	0.571633	+	0.820509i	$0.306310\pi$
$8$	4.39201	+	3.19098i	0.549001	+	0.398873i
$9$	−2.16312	−	6.65740i	−0.240347	−	0.739711i
$10$		0			0
$11$	10.3713	+	3.66547i	0.942848	+	0.333224i
$11$	10.3713	+	3.66547i	0.942848	+	0.333224i
$12$			13.8885i			1.15738i
$13$	3.49396	+	10.7533i	0.268766	+	0.827176i	0.990802	+	0.135321i	$0.0432065\pi$
$13$	3.49396	+	10.7533i	0.268766	+	0.827176i	−0.722036	+	0.691855i	$0.756794\pi$
$14$	−0.163119	−	0.118513i	−0.0116514	−	0.00846520i
$15$		0			0
$16$	3.07295	−	9.45756i	0.192059	−	0.591098i
$17$	−6.26137	+	19.2705i	−0.368316	+	1.13356i	0.579563	+	0.814928i	$0.303223\pi$
$17$	−6.26137	+	19.2705i	−0.368316	+	1.13356i	−0.947879	+	0.318632i	$0.896777\pi$
$18$	4.11450	−	2.98936i	0.228583	−	0.166075i
$19$	−16.9721	+	23.3601i	−0.893270	+	1.22948i	0.0792950	+	0.996851i	$0.474733\pi$
$19$	−16.9721	+	23.3601i	−0.893270	+	1.22948i	−0.972565	+	0.232630i	$0.925267\pi$
$20$		0			0
$21$		−	1.11006i		−	0.0528599i
$22$	−0.204270	+	7.98936i	−0.00928498	+	0.363153i
$23$		−	27.6180i		−	1.20078i	−0.799706	−	0.600392i	$-0.795011\pi$
$23$		−	27.6180i		−	1.20078i	0.799706	−	0.600392i	$-0.204989\pi$
$24$	−20.6525	+	6.71040i	−0.860520	+	0.279600i
$25$		0			0
$26$	−6.64590	+	4.82853i	−0.255611	+	0.185713i
$27$	−7.60845	−	2.47214i	−0.281795	−	0.0915606i
$28$	−0.297759	+	0.916408i	−0.0106342	+	0.0327289i
$29$	−10.2016	−	14.0413i	−0.351780	−	0.484184i	0.596055	−	0.802943i	$-0.296734\pi$
$29$	−10.2016	−	14.0413i	−0.351780	−	0.484184i	−0.947836	+	0.318759i	$0.896734\pi$
$30$		0			0
$31$	10.6180	+	32.6789i	0.342517	+	1.05416i	0.962900	+	0.269860i	$0.0869775\pi$
$31$	10.6180	+	32.6789i	0.342517	+	1.05416i	−0.620382	+	0.784300i	$0.713023\pi$
$32$	28.9402			0.904382
$33$	−36.2461	+	24.9443i	−1.09837	+	0.755887i
$34$	−14.7214			−0.432981
$35$		0			0
$36$	−19.6631	−	14.2861i	−0.546198	−	0.396836i
$37$	7.80021	+	10.7361i	0.210816	+	0.290164i	0.901310	−	0.433175i	$-0.142607\pi$
$37$	7.80021	+	10.7361i	0.210816	+	0.290164i	−0.690494	+	0.723339i	$0.742607\pi$
$38$	−19.9519	−	6.48278i	−0.525051	−	0.170599i
$39$	−43.0132	−	13.9758i	−1.10290	−	0.358354i
$40$		0			0
$41$	−10.6140	+	14.6089i	−0.258877	+	0.356314i	−0.918596	−	0.395199i	$-0.870676\pi$
$41$	−10.6140	+	14.6089i	−0.258877	+	0.356314i	0.659718	+	0.751513i	$0.270676\pi$
$42$	0.767031	−	0.249224i	0.0182627	−	0.00593390i
$43$	34.7931			0.809141			0.404571	−	0.914507i	$-0.367421\pi$
$43$	34.7931			0.809141			0.404571	+	0.914507i	$0.367421\pi$
$44$	36.6140	−	10.8702i	0.832136	−	0.247049i
$45$		0			0
$46$	19.0836	−	6.20063i	0.414861	−	0.134796i
$47$	−27.9159	+	38.4230i	−0.593956	+	0.817510i	−0.995138	−	0.0984879i	$-0.968599\pi$
$47$	−27.9159	+	38.4230i	−0.593956	+	0.817510i	0.401182	+	0.915998i	$0.368599\pi$
$48$	23.3804	+	32.1803i	0.487091	+	0.670424i
$49$	−15.1180	+	46.5285i	−0.308531	+	0.949562i
$50$		0			0
$51$	−47.6393	−	65.5699i	−0.934104	−	1.28568i
$52$	31.7606	+	23.0755i	0.610782	+	0.443759i
$53$	−39.5406	+	12.8475i	−0.746049	+	0.242406i	−0.657280	−	0.753646i	$-0.728293\pi$
$53$	−39.5406	+	12.8475i	−0.746049	+	0.242406i	−0.0887689	+	0.996052i	$0.528293\pi$
$54$		−	5.81234i		−	0.107636i
$55$		0			0
$56$	−1.50658			−0.0269032
$57$	−35.6911	−	109.846i	−0.626160	−	1.92712i
$58$	7.41192	−	10.2016i	0.127792	−	0.175890i
$59$	82.3115	−	59.8028i	1.39511	−	1.01361i	0.399828	−	0.916590i	$-0.369070\pi$
$59$	82.3115	−	59.8028i	1.39511	−	1.01361i	0.995283	−	0.0970170i	$-0.0309301\pi$
$60$		0			0
$61$	48.4164	+	15.7314i	0.793712	+	0.257893i	0.677684	−	0.735353i	$-0.262984\pi$
$61$	48.4164	+	15.7314i	0.793712	+	0.257893i	0.116028	+	0.993246i	$0.462984\pi$
$62$	−20.1967	+	14.6738i	−0.325753	+	0.236674i
$63$	1.57160	+	1.14183i	0.0249460	+	0.0181243i
$64$	−5.79431	−	17.8330i	−0.0905361	−	0.278641i
$65$		0			0
$66$	−25.3738	−	19.4451i	−0.384452	−	0.294623i
$67$		−	40.1803i		−	0.599707i	−0.953985	−	0.299853i	$-0.903062\pi$
$67$		−	40.1803i		−	0.599707i	0.953985	−	0.299853i	$-0.0969377\pi$
$68$	21.7403	+	66.9098i	0.319711	+	0.983968i
$69$	89.3738	+	64.9339i	1.29527	+	0.941071i
$70$		0			0
$71$	8.70820	−	26.8011i	0.122651	−	0.377480i	−0.870815	−	0.491611i	$-0.836408\pi$
$71$	8.70820	−	26.8011i	0.122651	−	0.377480i	0.993466	+	0.114131i	$0.0364083\pi$
$72$	11.7432	−	36.1418i	0.163100	−	0.501970i
$73$	80.7463	−	58.6656i	1.10611	−	0.803639i	0.124067	−	0.992274i	$-0.460406\pi$
$73$	80.7463	−	58.6656i	1.10611	−	0.803639i	0.982047	+	0.188635i	$0.0604063\pi$
$74$	−5.66718	+	7.80021i	−0.0765836	+	0.105408i
$75$		0			0
$76$			100.257i			1.31917i
$77$	−2.92641	+	0.868810i	−0.0380054	+	0.0112833i
$78$		−	32.8591i		−	0.421271i
$79$	125.172	−	40.6709i	1.58446	−	0.514822i	0.621258	−	0.783606i	$-0.286622\pi$
$79$	125.172	−	40.6709i	1.58446	−	0.514822i	0.963200	+	0.268784i	$0.0866219\pi$
$80$		0			0
$81$	76.8566	−	55.8396i	0.948847	−	0.689378i
$82$	−12.4775	−	4.05418i	−0.152164	−	0.0494412i
$83$	38.7533	−	119.271i	0.466908	−	1.43699i	−0.389660	−	0.920959i	$-0.627407\pi$
$83$	38.7533	−	119.271i	0.466908	−	1.43699i	0.856567	−	0.516035i	$-0.172593\pi$
$84$	−2.26548	−	3.11817i	−0.0269701	−	0.0371211i
$85$		0			0
$86$	7.81153	+	24.0414i	0.0908317	+	0.279551i
$87$	69.4242			0.797979
$88$	33.8545	+	49.1935i	0.384710	+	0.559017i
$89$	−88.9493			−0.999430			−0.499715	−	0.866190i	$-0.666562\pi$
$89$	−88.9493			−0.999430			−0.499715	+	0.866190i	$0.666562\pi$
$90$		0			0
$91$	−2.53851	−	1.84433i	−0.0278957	−	0.0202674i
$92$	−56.3648	−	77.5795i	−0.612661	−	0.843256i
$93$	−130.716	−	42.4721i	−1.40555	−	0.456690i
$94$	−32.8171	−	10.6629i	−0.349119	−	0.113436i
$95$		0			0
$96$	−68.0426	+	93.6526i	−0.708777	+	0.975548i
$97$	45.9533	−	14.9311i	0.473745	−	0.153929i	−0.0624067	−	0.998051i	$-0.519878\pi$
$97$	45.9533	−	14.9311i	0.473745	−	0.153929i	0.536152	+	0.844122i	$0.319878\pi$
$98$	−35.5446			−0.362700
$99$	1.96807	−	76.9748i	0.0198795	−	0.777524i
$100$		0			0
$101$	36.5836	−	11.8867i	0.362214	−	0.117690i	−0.122256	−	0.992499i	$-0.539013\pi$
$101$	36.5836	−	11.8867i	0.362214	−	0.117690i	0.484469	+	0.874808i	$0.339013\pi$
$102$	34.6120	−	47.6393i	0.339333	−	0.467052i
$103$	−74.1622	−	102.075i	−0.720021	−	0.991024i	−0.999523	−	0.0308788i	$-0.990169\pi$
$103$	−74.1622	−	102.075i	−0.720021	−	0.991024i	0.279502	−	0.960145i	$-0.409831\pi$
$104$	−18.9681	+	58.3777i	−0.182385	+	0.561324i
$105$		0			0
$106$	−17.7548	−	24.4374i	−0.167499	−	0.230542i
$107$	−70.9582	−	51.5542i	−0.663161	−	0.481815i	0.204568	−	0.978852i	$-0.434421\pi$
$107$	−70.9582	−	51.5542i	−0.663161	−	0.481815i	−0.867729	+	0.497038i	$0.834421\pi$
$108$	−26.4176	+	8.58359i	−0.244607	+	0.0794777i
$109$			144.692i			1.32745i	0.747978	+	0.663723i	$0.231025\pi$
$109$			144.692i			1.32745i	−0.747978	+	0.663723i	$0.768975\pi$
$110$		0			0
$111$	−53.0820			−0.478217
$112$	0.852788	+	2.62461i	0.00761418	+	0.0234340i
$113$	−76.1905	+	104.867i	−0.674252	+	0.928029i	−0.999847	−	0.0174806i	$-0.994435\pi$
$113$	−76.1905	+	104.867i	−0.674252	+	0.928029i	0.325595	+	0.945509i	$0.394435\pi$
$114$	67.8885	−	49.3239i	0.595514	−	0.432666i
$115$		0			0
$116$	−57.3131	−	18.6221i	−0.494078	−	0.160536i
$117$	64.0311	−	46.5213i	0.547274	−	0.397618i
$118$	59.8028	+	43.4493i	0.506804	+	0.368214i
$119$	−1.73762	−	5.34785i	−0.0146019	−	0.0449399i
$120$		0			0
$121$	94.1287	+	76.0315i	0.777923	+	0.628360i
$122$			36.9868i			0.303171i
$123$	−22.3204	−	68.6950i	−0.181466	−	0.558496i
$124$	96.5197	+	70.1257i	0.778385	+	0.565530i
$125$		0			0
$126$	−0.436141	+	1.34230i	−0.00346144	+	0.0106532i
$127$	−47.6511	+	146.655i	−0.375205	+	1.15476i	0.568134	+	0.822936i	$0.307665\pi$
$127$	−47.6511	+	146.655i	−0.375205	+	1.15476i	−0.943340	+	0.331828i	$0.892335\pi$
$128$	104.674	−	76.0501i	0.817766	−	0.594141i
$129$	−81.8034	+	112.593i	−0.634135	+	0.872812i
$130$		0			0
$131$		−	128.496i		−	0.980883i	−0.871474	−	0.490442i	$-0.836836\pi$
$131$		−	128.496i		−	0.980883i	0.871474	−	0.490442i	$-0.163164\pi$
$132$	−50.9080	+	144.043i	−0.385667	+	1.09123i
$133$		−	8.01316i		−	0.0602493i
$134$	27.7639	−	9.02105i	0.207194	−	0.0673213i
$135$		0			0
$136$	−88.9919	+	64.6564i	−0.654352	+	0.475415i
$137$	58.9000	+	19.1378i	0.429927	+	0.139692i	0.515984	−	0.856599i	$-0.327427\pi$
$137$	58.9000	+	19.1378i	0.429927	+	0.139692i	−0.0860566	+	0.996290i	$0.527427\pi$
$138$	−24.8025	+	76.3344i	−0.179729	+	0.553148i
$139$	−134.155	−	184.649i	−0.965144	−	1.32841i	−0.944462	−	0.328620i	$-0.893416\pi$
$139$	−134.155	−	184.649i	−0.965144	−	1.32841i	−0.0206817	−	0.999786i	$-0.506584\pi$
$140$		0			0
$141$	−58.7051	−	180.676i	−0.416348	−	1.28139i
$142$	20.4742			0.144185
$143$	−3.17891	+	124.333i	−0.0222301	+	0.869460i
$144$	−69.6099			−0.483402
$145$		0			0
$146$	58.6656	+	42.6231i	0.401819	+	0.291939i
$147$	−115.025	−	158.318i	−0.782482	−	1.07699i
$148$	43.8218	+	14.2386i	0.296094	+	0.0962066i
$149$	74.8460	+	24.3189i	0.502322	+	0.163214i	0.549208	−	0.835686i	$-0.314930\pi$
$149$	74.8460	+	24.3189i	0.502322	+	0.163214i	−0.0468856	+	0.998900i	$0.514930\pi$
$150$		0			0
$151$	41.7852	−	57.5124i	0.276723	−	0.380877i	−0.647922	−	0.761707i	$-0.724362\pi$
$151$	41.7852	−	57.5124i	0.276723	−	0.380877i	0.924645	+	0.380830i	$0.124362\pi$
$152$	−149.084	+	48.4402i	−0.980813	+	0.318686i
$153$	141.835			0.927029
$154$	−1.25735	−	1.82704i	−0.00816464	−	0.0118639i
$155$		0			0
$156$	−149.348	+	48.5260i	−0.957356	+	0.311064i
$157$	126.223	−	173.730i	0.803965	−	1.10656i	−0.188261	−	0.982119i	$-0.560285\pi$
$157$	126.223	−	173.730i	0.803965	−	1.10656i	0.992227	−	0.124444i	$-0.0397148\pi$
$158$	56.2058	+	77.3607i	0.355733	+	0.489625i
$159$	51.3901	−	158.162i	0.323208	−	0.994732i
$160$		0			0
$161$	4.50502	+	6.20063i	0.0279815	+	0.0385133i
$162$	55.8396	+	40.5698i	0.344689	+	0.250431i
$163$	86.7147	−	28.1753i	0.531992	−	0.172855i	−0.0306887	−	0.999529i	$-0.509770\pi$
$163$	86.7147	−	28.1753i	0.531992	−	0.172855i	0.562681	+	0.826674i	$0.309770\pi$
$164$			62.6983i			0.382307i
$165$		0			0
$166$	91.1146			0.548883
$167$	−14.0336	−	43.1910i	−0.0840335	−	0.258629i	0.900207	−	0.435461i	$-0.143415\pi$
$167$	−14.0336	−	43.1910i	−0.0840335	−	0.258629i	−0.984241	+	0.176833i	$0.943415\pi$
$168$	3.54218	−	4.87539i	0.0210844	−	0.0290202i
$169$	33.2984	−	24.1927i	0.197032	−	0.143152i
$170$		0			0
$171$	192.230	+	62.4595i	1.12415	+	0.365260i
$172$	97.7343	−	71.0081i	0.568223	−	0.412838i
$173$	−122.605	−	89.0780i	−0.708701	−	0.514902i	0.174053	−	0.984736i	$-0.444314\pi$
$173$	−122.605	−	89.0780i	−0.708701	−	0.514902i	−0.882754	+	0.469835i	$0.844314\pi$
$174$	15.5867	+	47.9709i	0.0895787	+	0.275695i
$175$		0			0
$176$	66.5370	−	86.8237i	0.378051	−	0.493316i
$177$			406.971i			2.29927i
$178$	−19.9704	−	61.4625i	−0.112193	−	0.345295i
$179$	−137.932	−	100.214i	−0.770570	−	0.559852i	0.131564	−	0.991308i	$-0.458000\pi$
$179$	−137.932	−	100.214i	−0.770570	−	0.559852i	−0.902134	+	0.431456i	$0.858000\pi$
$180$		0			0
$181$	−51.2918	+	157.860i	−0.283380	+	0.872154i	0.703499	+	0.710696i	$0.251620\pi$
$181$	−51.2918	+	157.860i	−0.283380	+	0.872154i	−0.986880	+	0.161458i	$0.948380\pi$
$182$	0.704473	−	2.16814i	0.00387073	−	0.0119129i
$183$	−164.742	+	119.692i	−0.900229	+	0.654054i
$184$	88.1287	−	121.299i	0.478960	−	0.659232i
$185$		0			0
$186$		−	99.8580i		−	0.536871i
$187$	−135.574	+	176.910i	−0.724995	+	0.946042i
$188$			164.904i			0.877147i
$189$	2.11146	−	0.686054i	0.0111717	−	0.00362991i
$190$		0			0
$191$	−9.05573	+	6.57937i	−0.0474122	+	0.0344470i	−0.611239	−	0.791446i	$-0.709329\pi$
$191$	−9.05573	+	6.57937i	−0.0474122	+	0.0344470i	0.563827	+	0.825893i	$0.309329\pi$
$192$	71.3322	+	23.1772i	0.371522	+	0.120715i
$193$	−38.8189	+	119.472i	−0.201134	+	0.619027i	0.798716	+	0.601708i	$0.205513\pi$
$193$	−38.8189	+	119.472i	−0.201134	+	0.619027i	−0.999850	+	0.0173185i	$0.994487\pi$
$194$	20.6343	+	28.4007i	0.106362	+	0.146395i
$195$		0			0
$196$	52.4919	+	161.553i	0.267816	+	0.824252i
$197$	361.517			1.83511			0.917556	−	0.397607i	$-0.130159\pi$
$197$	361.517			1.83511			0.917556	+	0.397607i	$0.130159\pi$
$198$	53.6302	−	15.9220i	0.270859	−	0.0804143i
$199$	−267.692			−1.34519			−0.672593	−	0.740013i	$-0.734819\pi$
$199$	−267.692			−1.34519			−0.672593	+	0.740013i	$0.734819\pi$
$200$		0			0
$201$	130.026	+	94.4696i	0.646897	+	0.469998i
$202$	16.4271	+	22.6099i	0.0813221	+	0.111930i
$203$	4.58082	+	1.48840i	0.0225656	+	0.00733201i
$204$	−267.639	−	86.9613i	−1.31196	−	0.426281i
$205$		0			0
$206$	53.8820	−	74.1622i	0.261563	−	0.360011i
$207$	−183.864	+	59.7411i	−0.888233	+	0.288604i
$208$	112.437			0.540561
$209$	−261.649	+	180.065i	−1.25191	+	0.861554i
$210$		0			0
$211$	−214.971	+	69.8482i	−1.01882	+	0.331034i	−0.770360	−	0.637609i	$-0.779924\pi$
$211$	−214.971	+	69.8482i	−1.01882	+	0.331034i	−0.248458	+	0.968643i	$0.579924\pi$
$212$	−84.8501	+	116.786i	−0.400236	+	0.550878i
$213$	66.2560	+	91.1935i	0.311061	+	0.428138i
$214$	19.6919	−	60.6056i	0.0920184	−	0.283204i
$215$		0			0
$216$	−25.5279	−	35.1361i	−0.118185	−	0.162667i
$217$	−7.71445	−	5.60488i	−0.0355505	−	0.0258289i
$218$	−99.9794	+	32.4853i	−0.458621	+	0.149015i
$219$			399.232i			1.82298i
$220$		0			0
$221$	−229.098			−1.03664
$222$	−11.9177	−	36.6788i	−0.0536832	−	0.165220i
$223$	164.648	−	226.619i	0.738333	−	1.01623i	−0.260379	−	0.965506i	$-0.583848\pi$
$223$	164.648	−	226.619i	0.738333	−	1.01623i	0.998713	−	0.0507223i	$-0.0161523\pi$
$224$	−6.49749	+	4.72070i	−0.0290066	+	0.0210746i
$225$		0			0
$226$	−89.5673	−	29.1022i	−0.396316	−	0.128771i
$227$	70.5247	−	51.2392i	0.310681	−	0.225723i	−0.421507	−	0.906825i	$-0.638499\pi$
$227$	70.5247	−	51.2392i	0.310681	−	0.225723i	0.732189	+	0.681102i	$0.238499\pi$
$228$	−324.438	−	235.718i	−1.42298	−	1.03385i
$229$	−33.1722	−	102.094i	−0.144857	−	0.445823i	0.852136	−	0.523321i	$-0.175307\pi$
$229$	−33.1722	−	102.094i	−0.144857	−	0.445823i	−0.996993	+	0.0774974i	$0.975307\pi$
$230$		0			0
$231$	4.06888	−	11.5128i	0.0176142	−	0.0498388i
$232$		−	94.2229i		−	0.406133i
$233$	−40.7210	−	125.326i	−0.174768	−	0.537881i	0.824855	−	0.565345i	$-0.191257\pi$
$233$	−40.7210	−	125.326i	−0.174768	−	0.537881i	−0.999623	+	0.0274639i	$0.991257\pi$
$234$	46.5213	+	33.7997i	0.198809	+	0.144443i
$235$		0			0
$236$	109.165	−	335.974i	0.462562	−	1.42362i
$237$	−162.684	+	500.689i	−0.686429	+	2.11261i
$238$	3.30515	−	2.40133i	0.0138872	−	0.0100896i
$239$	54.0983	−	74.4599i	0.226353	−	0.311548i	−0.680702	−	0.732560i	$-0.738325\pi$
$239$	54.0983	−	74.4599i	0.226353	−	0.311548i	0.907055	+	0.421013i	$0.138325\pi$
$240$		0			0
$241$			26.5140i			0.110017i	0.998486	+	0.0550083i	$0.0175185\pi$
$241$			26.5140i			0.110017i	−0.998486	+	0.0550083i	$0.982481\pi$
$242$	−31.4033	+	82.1115i	−0.129766	+	0.339304i
$243$			308.000i			1.26749i
$244$	168.108	−	54.6217i	0.688969	−	0.223859i
$245$		0			0
$246$	42.4559	−	30.8460i	0.172585	−	0.125390i
$247$	−310.498	−	100.887i	−1.25708	−	0.408449i
$248$	−57.6434	+	177.408i	−0.232433	+	0.715356i
$249$	294.853	+	405.830i	1.18415	+	1.62984i
$250$		0			0
$251$	−41.7279	−	128.425i	−0.166247	−	0.511655i	0.832879	−	0.553455i	$-0.186691\pi$
$251$	−41.7279	−	128.425i	−0.166247	−	0.511655i	−0.999126	+	0.0417998i	$0.986691\pi$
$252$	6.74498			0.0267658
$253$	101.233	−	286.436i	0.400131	−	1.13216i
$254$	−112.034			−0.441080
$255$		0			0
$256$	15.3713	+	11.1679i	0.0600442	+	0.0436247i
$257$	−143.591	−	197.636i	−0.558720	−	0.769013i	0.432443	−	0.901661i	$-0.357652\pi$
$257$	−143.591	−	197.636i	−0.558720	−	0.769013i	−0.991163	+	0.132649i	$0.957652\pi$
$258$	−96.1657	−	31.2461i	−0.372735	−	0.121109i
$259$	−3.50251	−	1.13804i	−0.0135232	−	0.00439396i
$260$		0			0
$261$	−71.4114	+	98.2893i	−0.273607	+	0.376587i
$262$	88.7883	−	28.8491i	0.338887	−	0.110111i
$263$	1.93304			0.00734998			0.00367499	−	0.999993i	$-0.498830\pi$
$263$	1.93304			0.00734998			0.00367499	+	0.999993i	$0.498830\pi$
$264$	−238.790	−	6.10532i	−0.904508	−	0.0231262i
$265$		0			0
$266$	5.53695	−	1.79907i	0.0208156	−	0.00676340i
$267$	209.132	−	287.846i	0.783267	−	1.07807i
$268$	−82.0029	−	112.867i	−0.305981	−	0.421146i
$269$	56.6149	−	174.243i	0.210464	−	0.647743i	−0.788980	−	0.614419i	$-0.789391\pi$
$269$	56.6149	−	174.243i	0.210464	−	0.647743i	0.999445	−	0.0333242i	$-0.0106094\pi$
$270$		0			0
$271$	298.339	+	410.629i	1.10088	+	1.51524i	0.834208	+	0.551449i	$0.185925\pi$
$271$	298.339	+	410.629i	1.10088	+	1.51524i	0.266675	+	0.963786i	$0.414075\pi$
$272$	163.011	+	118.435i	0.599306	+	0.435421i
$273$	11.9368	−	3.87849i	0.0437245	−	0.0142069i
$274$			44.9956i			0.164217i
$275$		0			0
$276$	383.574			1.38976
$277$	−10.9493	−	33.6985i	−0.0395282	−	0.121655i	0.929345	−	0.369212i	$-0.120372\pi$
$277$	−10.9493	−	33.6985i	−0.0395282	−	0.121655i	−0.968873	+	0.247557i	$0.920372\pi$
$278$	97.4693	−	134.155i	0.350609	−	0.482572i
$279$	194.589	−	141.377i	0.697450	−	0.506727i
$280$		0			0
$281$	−325.066	−	105.620i	−1.15682	−	0.375873i	−0.333110	−	0.942888i	$-0.608098\pi$
$281$	−325.066	−	105.620i	−1.15682	−	0.375873i	−0.823707	+	0.567015i	$0.808098\pi$
$282$	111.664	−	81.1285i	0.395971	−	0.287690i
$283$	334.463	+	243.002i	1.18185	+	0.858664i	0.992379	−	0.123222i	$-0.0393228\pi$
$283$	334.463	+	243.002i	1.18185	+	0.858664i	0.189471	+	0.981886i	$0.439323\pi$
$284$	−30.2361	−	93.0570i	−0.106465	−	0.327666i
$285$		0			0
$286$	−86.6256	+	25.7179i	−0.302887	+	0.0899227i
$287$		−	5.01124i		−	0.0174608i
$288$	−62.6012	−	192.667i	−0.217365	−	0.668981i
$289$	−98.3419	−	71.4496i	−0.340283	−	0.247230i
$290$		0			0
$291$	−59.7245	+	183.813i	−0.205239	+	0.631660i
$292$	107.089	−	329.586i	0.366743	−	1.12872i
$293$	−156.026	+	113.360i	−0.532513	+	0.386893i	−0.821297	−	0.570501i	$-0.806749\pi$
$293$	−156.026	+	113.360i	−0.532513	+	0.386893i	0.288784	+	0.957394i	$0.406749\pi$
$294$	83.5704	−	115.025i	0.284253	−	0.391241i
$295$		0			0
$296$			72.0433i			0.243389i
$297$	−69.8482	−	53.5279i	−0.235179	−	0.180228i
$298$			57.1772i			0.191870i
$299$	296.985	−	96.4962i	0.993260	−	0.322730i
$300$		0			0
$301$	−7.81153	+	5.67541i	−0.0259519	+	0.0188552i
$302$	49.1215	+	15.9605i	0.162654	+	0.0528494i
$303$	−47.5469	+	146.334i	−0.156921	+	0.482952i
$304$	168.776	+	232.300i	0.555183	+	0.764143i
$305$		0			0
$306$	31.8441	+	98.0059i	0.104066	+	0.320281i
$307$	335.115			1.09158			0.545790	−	0.837922i	$-0.316230\pi$
$307$	335.115			1.09158			0.545790	+	0.837922i	$0.316230\pi$
$308$	−6.44722	+	8.41294i	−0.0209325	+	0.0273147i
$309$	504.689			1.63330
$310$		0			0
$311$	−175.687	−	127.644i	−0.564910	−	0.410431i	0.268343	−	0.963323i	$-0.413524\pi$
$311$	−175.687	−	127.644i	−0.564910	−	0.410431i	−0.833253	+	0.552893i	$0.813524\pi$
$312$	−144.318	−	198.636i	−0.462557	−	0.636655i
$313$	565.533	+	183.753i	1.80681	+	0.587069i	0.999993	−	0.00372731i	$-0.00118644\pi$
$313$	565.533	+	183.753i	1.80681	+	0.587069i	0.806821	+	0.590797i	$0.201186\pi$
$314$	148.384	+	48.2127i	0.472559	+	0.153544i
$315$		0			0
$316$	268.607	−	369.706i	0.850022	−	1.16995i
$317$	−68.2814	+	22.1860i	−0.215399	+	0.0699872i	−0.414729	−	0.909945i	$-0.636123\pi$
$317$	−68.2814	+	22.1860i	−0.215399	+	0.0699872i	0.199330	+	0.979932i	$0.436123\pi$
$318$	120.825			0.379954
$319$	−54.3363	−	183.021i	−0.170333	−	0.573733i
$320$		0			0
$321$	333.666	−	108.415i	1.03946	−	0.337740i
$322$	−3.27309	+	4.50502i	−0.0101649	+	0.0139908i
$323$	−343.893	−	473.328i	−1.06468	−	1.46541i
$324$	101.930	−	313.709i	0.314599	−	0.968237i
$325$		0			0
$326$	38.9373	+	53.5926i	0.119440	+	0.164395i
$327$	−468.232	−	340.190i	−1.43190	−	1.04034i
$328$	−93.2333	+	30.2933i	−0.284248	+	0.0923578i
$329$		−	13.1801i		−	0.0400611i
$330$		0			0
$331$	−292.681			−0.884232			−0.442116	−	0.896958i	$-0.645772\pi$
$331$	−292.681			−0.884232			−0.442116	+	0.896958i	$0.645772\pi$
$332$	−134.557	−	414.123i	−0.405292	−	1.24736i
$333$	54.6015	−	75.1525i	0.163968	−	0.225683i
$334$	26.6935	−	19.3940i	0.0799206	−	0.0580657i
$335$		0			0
$336$	−10.4984	−	3.41115i	−0.0312454	−	0.0101522i
$337$	317.132	−	230.410i	0.941046	−	0.683710i	−0.00762639	−	0.999971i	$-0.502428\pi$
$337$	317.132	−	230.410i	0.941046	−	0.683710i	0.948672	+	0.316261i	$0.102428\pi$
$338$	24.1927	+	17.5770i	0.0715760	+	0.0520030i
$339$	−160.223	−	493.115i	−0.472634	−	1.45462i
$340$		0			0
$341$	−9.66061	+	377.844i	−0.0283302	+	1.10805i
$342$			146.851i			0.429389i
$343$	−8.39755	−	25.8450i	−0.0244827	−	0.0753499i
$344$	152.812	+	111.024i	0.444220	+	0.322744i
$345$		0			0
$346$	34.0248	−	104.717i	0.0983375	−	0.302652i
$347$	19.6571	−	60.4984i	0.0566488	−	0.174347i	−0.918729	−	0.394890i	$-0.870783\pi$
$347$	19.6571	−	60.4984i	0.0566488	−	0.174347i	0.975377	+	0.220543i	$0.0707828\pi$
$348$	195.014	−	141.686i	0.560384	−	0.407143i
$349$	−144.289	+	198.596i	−0.413435	+	0.569044i	−0.964052	−	0.265714i	$-0.914392\pi$
$349$	−144.289	+	198.596i	−0.413435	+	0.569044i	0.550617	+	0.834758i	$0.314392\pi$
$350$		0			0
$351$		−	90.4534i		−	0.257702i
$352$	300.149	+	106.080i	0.852695	+	0.301362i
$353$			216.535i			0.613413i	0.951804	+	0.306707i	$0.0992270\pi$
$353$			216.535i			0.613413i	−0.951804	+	0.306707i	$0.900773\pi$
$354$	−281.210	+	91.3706i	−0.794378	+	0.258109i
$355$		0			0
$356$	−249.860	+	181.534i	−0.701854	+	0.509927i
$357$	21.3914	+	6.95048i	0.0599199	+	0.0194691i
$358$	38.2782	−	117.808i	0.106922	−	0.329073i
$359$	401.418	+	552.505i	1.11816	+	1.53901i	0.808818	+	0.588059i	$0.200108\pi$
$359$	401.418	+	552.505i	1.11816	+	1.53901i	0.309339	+	0.950952i	$0.399892\pi$
$360$		0			0
$361$	−146.088	−	449.612i	−0.404675	−	1.24546i
$362$	−120.594			−0.333133
$363$	−467.353	+	125.846i	−1.28747	+	0.346683i
$364$	−10.8948			−0.0299306
$365$		0			0
$366$	−119.692	−	86.9613i	−0.327027	−	0.237599i
$367$	43.3150	+	59.6180i	0.118025	+	0.162447i	0.863942	−	0.503592i	$-0.167988\pi$
$367$	43.3150	+	59.6180i	0.118025	+	0.162447i	−0.745917	+	0.666039i	$0.767988\pi$
$368$	−261.199	−	84.8688i	−0.709781	−	0.230622i
$369$	120.216	+	39.0607i	0.325790	+	0.105855i
$370$		0			0
$371$	6.78175	−	9.33427i	0.0182796	−	0.0251598i
$372$	−453.863	+	147.469i	−1.22006	+	0.396422i
$373$	58.3795			0.156514			0.0782568	−	0.996933i	$-0.475065\pi$
$373$	58.3795			0.156514			0.0782568	+	0.996933i	$0.475065\pi$
$374$	−152.680	−	53.9607i	−0.408235	−	0.144280i
$375$		0			0
$376$	−245.214	+	79.6749i	−0.652165	+	0.211901i
$377$	115.346	−	158.761i	0.305959	−	0.421116i
$378$	0.948103	+	1.30495i	0.00250821	+	0.00345225i
$379$	57.9346	−	178.304i	0.152862	−	0.470460i	−0.845076	−	0.534646i	$-0.820445\pi$
$379$	57.9346	−	178.304i	0.152862	−	0.470460i	0.997938	+	0.0641858i	$0.0204450\pi$
$380$		0			0
$381$	−362.551	−	499.009i	−0.951578	−	1.30973i
$382$	−6.57937	−	4.78019i	−0.0172235	−	0.0125136i
$383$	5.82303	−	1.89202i	0.0152037	−	0.00493999i	−0.301405	−	0.953496i	$-0.597456\pi$
$383$	5.82303	−	1.89202i	0.0152037	−	0.00493999i	0.316609	+	0.948556i	$0.397456\pi$
$384$			517.537i			1.34775i
$385$		0			0
$386$	−91.2686			−0.236447
$387$	−75.2615	−	231.631i	−0.194474	−	0.598530i
$388$	98.6110	−	135.726i	0.254152	−	0.349810i
$389$	−182.923	+	132.901i	−0.470239	+	0.341649i	−0.797534	−	0.603273i	$-0.793863\pi$
$389$	−182.923	+	132.901i	−0.470239	+	0.341649i	0.327295	+	0.944922i	$0.393863\pi$
$390$		0			0
$391$	532.214	+	172.927i	1.36116	+	0.442268i
$392$	−214.870	+	156.112i	−0.548139	+	0.398246i
$393$	415.821	+	302.111i	1.05807	+	0.768731i
$394$	81.1656	+	249.802i	0.206004	+	0.634016i
$395$		0			0
$396$	−151.567	−	220.240i	−0.382746	−	0.556162i
$397$			215.123i			0.541873i	0.962597	+	0.270936i	$0.0873333\pi$
$397$			215.123i			0.541873i	−0.962597	+	0.270936i	$0.912667\pi$
$398$	−60.1006	−	184.971i	−0.151006	−	0.464750i
$399$	25.9311	+	18.8401i	0.0649903	+	0.0472182i
$400$		0			0
$401$	−167.199	+	514.586i	−0.416955	+	1.28326i	0.493535	+	0.869726i	$0.335705\pi$
$401$	−167.199	+	514.586i	−0.416955	+	1.28326i	−0.910490	+	0.413531i	$0.864295\pi$
$402$	−36.0842	+	111.056i	−0.0897617	+	0.276258i
$403$	−314.307	+	228.358i	−0.779919	+	0.566644i
$404$	78.5047	−	108.052i	0.194318	−	0.267456i
$405$		0			0
$406$			3.49943i			0.00861929i
$407$	41.5458	+	139.939i	0.102078	+	0.343830i
$408$		−	440.000i		−	1.07843i
$409$	−348.785	+	113.327i	−0.852774	+	0.277083i	−0.702608	−	0.711578i	$-0.747981\pi$
$409$	−348.785	+	113.327i	−0.852774	+	0.277083i	−0.150167	+	0.988661i	$0.547981\pi$
$410$		0			0
$411$	−200.413	+	145.609i	−0.487624	+	0.354279i
$412$	−416.646	−	135.376i	−1.01128	−	0.328583i
$413$	−8.72511	+	26.8531i	−0.0211262	+	0.0650197i
$414$	−82.5602	−	113.634i	−0.199421	−	0.274479i
$415$		0			0
$416$	101.116	+	311.203i	0.243067	+	0.748083i
$417$	912.952			2.18933
$418$	−183.166	−	140.368i	−0.438195	−	0.335809i
$419$	−164.543			−0.392704			−0.196352	−	0.980533i	$-0.562910\pi$
$419$	−164.543			−0.392704			−0.196352	+	0.980533i	$0.562910\pi$
$420$		0			0
$421$	−97.2887	−	70.6844i	−0.231090	−	0.167896i	0.466215	−	0.884672i	$-0.345617\pi$
$421$	−97.2887	−	70.6844i	−0.231090	−	0.167896i	−0.697304	+	0.716775i	$0.745617\pi$
$422$	−96.5278	−	132.859i	−0.228739	−	0.314832i
$423$	316.183	+	102.734i	0.747476	+	0.242870i
$424$	−214.659	−	69.7470i	−0.506271	−	0.164498i
$425$		0			0
$426$	−48.1378	+	66.2560i	−0.112999	+	0.155530i
$427$	−13.4363	+	4.36570i	−0.0314666	+	0.0102241i
$428$	−304.538			−0.711538
$429$	−394.875	−	302.611i	−0.920455	−	0.705387i
$430$		0			0
$431$	514.135	−	167.052i	1.19289	−	0.387593i	0.355748	−	0.934582i	$-0.384226\pi$
$431$	514.135	−	167.052i	1.19289	−	0.387593i	0.837140	+	0.546989i	$0.184226\pi$
$432$	−46.7608	+	64.3607i	−0.108243	+	0.148983i
$433$	−125.414	−	172.618i	−0.289641	−	0.398656i	0.639257	−	0.768993i	$-0.279242\pi$
$433$	−125.414	−	172.618i	−0.289641	−	0.398656i	−0.928897	+	0.370337i	$0.879242\pi$
$434$	2.14087	−	6.58893i	0.00493289	−	0.0151819i
$435$		0			0
$436$	295.297	+	406.441i	0.677286	+	0.932205i
$437$	645.161	+	468.737i	1.47634	+	1.07262i
$438$	−275.862	+	89.6331i	−0.629823	+	0.204642i
$439$			29.8597i			0.0680175i	0.999422	+	0.0340087i	$0.0108274\pi$
$439$			29.8597i			0.0680175i	−0.999422	+	0.0340087i	$0.989173\pi$
$440$		0			0
$441$	342.461			0.776555
$442$	−51.4358	−	158.303i	−0.116371	−	0.358152i
$443$	−33.6580	+	46.3262i	−0.0759774	+	0.104574i	−0.845314	−	0.534269i	$-0.820587\pi$
$443$	−33.6580	+	46.3262i	−0.0759774	+	0.104574i	0.769337	+	0.638843i	$0.220587\pi$
$444$	−149.108	+	108.334i	−0.335830	+	0.243994i
$445$		0			0
$446$	193.556	+	62.8901i	0.433981	+	0.141009i
$447$	−254.671	+	185.029i	−0.569734	+	0.413936i
$448$	4.20981	+	3.05861i	0.00939690	+	0.00682725i
$449$	−183.771	−	565.590i	−0.409291	−	1.25967i	−0.917259	−	0.398291i	$-0.869603\pi$
$449$	−183.771	−	565.590i	−0.409291	−	1.25967i	0.507968	−	0.861376i	$-0.330397\pi$
$450$		0			0
$451$	−163.629	+	112.608i	−0.362814	+	0.249686i
$452$			450.069i			0.995728i
$453$	87.8712	+	270.440i	0.193976	+	0.596997i
$454$	51.2392	+	37.2274i	0.112862	+	0.0819988i
$455$		0			0
$456$	193.761	−	596.335i	0.424914	−	1.30775i
$457$	−146.831	+	451.899i	−0.321293	+	0.988837i	0.651794	+	0.758396i	$0.274017\pi$
$457$	−146.831	+	451.899i	−0.321293	+	0.988837i	−0.973086	+	0.230441i	$0.925983\pi$
$458$	63.0973	−	45.8429i	0.137767	−	0.100094i
$459$	95.2786	−	131.140i	0.207579	−	0.285708i
$460$		0			0
$461$		−	290.362i		−	0.629853i	−0.949116	−	0.314927i	$-0.898020\pi$
$461$		−	290.362i		−	0.629853i	0.949116	−	0.314927i	$-0.101980\pi$
$462$	8.86865	+	0.226751i	0.0191962	+	0.000490803i
$463$			86.1358i			0.186039i	0.995664	+	0.0930193i	$0.0296518\pi$
$463$			86.1358i			0.186039i	−0.995664	+	0.0930193i	$0.970348\pi$
$464$	−164.146	+	53.3342i	−0.353763	+	0.114944i
$465$		0			0
$466$	77.4559	−	56.2750i	0.166214	−	0.120762i
$467$	−214.877	−	69.8177i	−0.460122	−	0.149503i	0.0697786	−	0.997563i	$-0.477771\pi$
$467$	−214.877	−	69.8177i	−0.460122	−	0.149503i	−0.529900	+	0.848060i	$0.677771\pi$
$468$	84.9204	−	261.358i	0.181454	−	0.558458i
$469$	6.55418	+	9.02105i	0.0139748	+	0.0192346i
$470$		0			0
$471$	265.437	+	816.930i	0.563559	+	1.73446i
$472$	552.343			1.17022
$473$	360.850	+	127.533i	0.762897	+	0.269626i
$474$	−382.492			−0.806946
$475$		0			0
$476$	−15.7953	−	11.4759i	−0.0331833	−	0.0241091i
$477$	171.062	+	235.447i	0.358621	+	0.493599i
$478$	63.5964	+	20.6637i	0.133047	+	0.0432295i
$479$	−79.9888	−	25.9899i	−0.166991	−	0.0542587i	0.224328	−	0.974514i	$-0.427981\pi$
$479$	−79.9888	−	25.9899i	−0.166991	−	0.0542587i	−0.391319	+	0.920255i	$0.627981\pi$
$480$		0			0
$481$	−88.1945	+	121.389i	−0.183356	+	0.252369i
$482$	−18.3207	+	5.95277i	−0.0380098	+	0.0123501i
$483$	−30.6576			−0.0634733
$484$	419.580	+	21.4694i	0.866900	+	0.0443583i
$485$		0			0
$486$	−212.823	+	69.1503i	−0.437907	+	0.142285i
$487$	−388.945	+	535.336i	−0.798654	+	1.09925i	0.194322	+	0.980938i	$0.437749\pi$
$487$	−388.945	+	535.336i	−0.798654	+	1.09925i	−0.992976	+	0.118315i	$0.962251\pi$
$488$	162.447	+	223.589i	0.332882	+	0.458173i
$489$	−112.701	+	346.859i	−0.230473	+	0.709323i
$490$		0			0
$491$	−438.057	−	602.934i	−0.892174	−	1.22797i	−0.972898	−	0.231235i	$-0.925723\pi$
$491$	−438.057	−	602.934i	−0.892174	−	1.22797i	0.0807242	−	0.996736i	$-0.474277\pi$
$492$	−202.896	−	147.413i	−0.412390	−	0.299619i
$493$	334.460	−	108.673i	0.678417	−	0.220431i
$494$		−	237.200i		−	0.480161i
$495$		0			0
$496$	341.692			0.688895
$497$	2.41665	+	7.43769i	0.00486248	+	0.0149652i
$498$	−214.223	+	294.853i	−0.430167	+	0.592074i
$499$	224.927	−	163.419i	0.450756	−	0.327493i	−0.339138	−	0.940736i	$-0.610136\pi$
$499$	224.927	−	163.419i	0.450756	−	0.327493i	0.789894	+	0.613243i	$0.210136\pi$
$500$		0			0
$501$	172.764	+	56.1344i	0.344838	+	0.112045i
$502$	79.3713	−	57.6666i	0.158110	−	0.114874i
$503$	217.971	+	158.365i	0.433342	+	0.314842i	0.782984	−	0.622042i	$-0.213697\pi$
$503$	217.971	+	158.365i	0.433342	+	0.314842i	−0.349642	+	0.936884i	$0.613697\pi$
$504$	3.25891	+	10.0299i	0.00646609	+	0.0199006i
$505$		0			0
$506$	220.650	+	5.64152i	0.436068	+	0.0111493i
$507$			164.636i			0.324726i
$508$	165.451	+	509.206i	0.325691	+	1.00237i
$509$	424.177	+	308.183i	0.833354	+	0.605467i	0.920506	−	0.390728i	$-0.127777\pi$
$509$	424.177	+	308.183i	0.833354	+	0.605467i	−0.0871522	+	0.996195i	$0.527777\pi$
$510$		0			0
$511$	−8.55920	+	26.3425i	−0.0167499	+	0.0515509i
$512$	155.662	−	479.078i	0.304027	−	0.935699i
$513$	186.881	−	135.777i	0.364291	−	0.264673i
$514$	104.325	−	143.591i	0.202967	−	0.279360i
$515$		0			0
$516$			483.225i			0.936483i
$517$	−430.363	+	296.172i	−0.832424	+	0.572867i
$518$		−	2.67568i		−	0.00516541i
$519$	576.525	−	187.324i	1.11084	−	0.360933i
$520$		0			0
$521$	308.640	−	224.240i	0.592400	−	0.430404i	−0.250773	−	0.968046i	$-0.580685\pi$
$521$	308.640	−	224.240i	0.592400	−	0.430404i	0.843173	+	0.537642i	$0.180685\pi$
$522$	−83.9491	−	27.2767i	−0.160822	−	0.0522543i
$523$	−197.390	+	607.503i	−0.377418	+	1.16157i	0.564414	+	0.825492i	$0.309102\pi$
$523$	−197.390	+	607.503i	−0.377418	+	1.16157i	−0.941832	+	0.336083i	$0.890898\pi$
$524$	−262.243	−	360.947i	−0.500464	−	0.688829i
$525$		0			0
$526$	0.433995	+	1.33570i	0.000825086	+	0.00253935i
$527$	−696.223			−1.32111
$528$	124.529	+	419.453i	0.235851	+	0.794418i
$529$	−233.756			−0.441882
$530$		0			0
$531$	−576.181	−	418.620i	−1.08509	−	0.788361i
$532$	−16.3538	−	22.5091i	−0.0307402	−	0.0423103i
$533$	−194.178	−	63.0923i	−0.364312	−	0.118372i
$534$	245.850	+	79.8814i	0.460393	+	0.149591i
$535$		0			0
$536$	128.215	−	176.473i	0.239207	−	0.329240i
$537$	648.596	−	210.741i	1.20781	−	0.392442i
$538$	133.110			0.247416
$539$	−327.343	+	427.148i	−0.607315	+	0.792482i
$540$		0			0
$541$	117.236	−	38.0923i	0.216703	−	0.0704109i	−0.198654	−	0.980070i	$-0.563657\pi$
$541$	117.236	−	38.0923i	0.216703	−	0.0704109i	0.415356	+	0.909659i	$0.363657\pi$
$542$	−216.756	+	298.339i	−0.399919	+	0.550442i
$543$	−390.251	−	537.135i	−0.718695	−	0.989198i
$544$	−181.205	+	557.693i	−0.333098	+	1.02517i
$545$		0			0
$546$	5.35995	+	7.37733i	0.00981675	+	0.0135116i
$547$	274.640	+	199.538i	0.502085	+	0.364786i	0.809813	−	0.586688i	$-0.199569\pi$
$547$	274.640	+	199.538i	0.502085	+	0.364786i	−0.307728	+	0.951474i	$0.599569\pi$
$548$	204.509	−	66.4489i	0.373191	−	0.121257i
$549$		−	356.356i		−	0.649100i
$550$		0			0
$551$	501.151			0.909530
$552$	185.328	+	570.381i	0.335739	+	1.03330i
$553$	−21.4687	+	29.5492i	−0.0388223	+	0.0534343i
$554$	20.8268	−	15.1316i	0.0375936	−	0.0273133i
$555$		0			0
$556$	−753.687	−	244.888i	−1.35555	−	0.440446i
$557$	−427.248	+	310.414i	−0.767052	+	0.557296i	−0.901065	−	0.433684i	$-0.857213\pi$
$557$	−427.248	+	310.414i	−0.767052	+	0.557296i	0.134013	+	0.990980i	$0.457213\pi$
$558$	141.377	+	102.716i	0.253364	+	0.184079i
$559$	121.565	+	374.140i	0.217469	+	0.669302i
$560$		0			0
$561$	−253.738	−	854.667i	−0.452297	−	1.52347i
$562$		−	248.328i		−	0.441865i
$563$	−79.3087	−	244.087i	−0.140868	−	0.433547i	0.855589	−	0.517657i	$-0.173195\pi$
$563$	−79.3087	−	244.087i	−0.140868	−	0.433547i	−0.996457	+	0.0841094i	$0.973195\pi$
$564$	−533.639	−	387.712i	−0.946169	−	0.687432i
$565$		0			0
$566$	−92.8185	+	285.666i	−0.163990	+	0.504710i
$567$	−8.14689	+	25.0735i	−0.0143684	+	0.0442214i
$568$	123.768	−	89.9230i	0.217902	−	0.158315i
$569$	−146.337	+	201.415i	−0.257182	+	0.353981i	−0.918010	−	0.396556i	$-0.870205\pi$
$569$	−146.337	+	201.415i	−0.257182	+	0.353981i	0.660828	+	0.750537i	$0.270205\pi$
$570$		0			0
$571$		−	393.435i		−	0.689028i	−0.938781	−	0.344514i	$-0.888044\pi$
$571$		−	393.435i		−	0.689028i	0.938781	−	0.344514i	$-0.111956\pi$
$572$	244.818	+	355.741i	0.428003	+	0.621924i
$573$		−	44.7740i		−	0.0781396i
$574$	3.46268	−	1.12509i	0.00603254	−	0.00196009i
$575$		0			0
$576$	−106.188	+	77.1500i	−0.184354	+	0.133941i
$577$	−236.436	−	76.8228i	−0.409768	−	0.133142i	0.0968772	−	0.995296i	$-0.469115\pi$
$577$	−236.436	−	76.8228i	−0.409768	−	0.133142i	−0.506645	+	0.862155i	$0.669115\pi$
$578$	27.2913	−	83.9940i	0.0472168	−	0.145318i
$579$	−295.351	−	406.516i	−0.510106	−	0.702101i
$580$		0			0
$581$	10.7546	+	33.0993i	0.0185105	+	0.0569695i
$582$	−140.421			−0.241273
$583$	−457.181	−	11.6891i	−0.784186	−	0.0200499i
$584$	541.840			0.927808
$585$		0			0
$586$	−113.360	−	82.3607i	−0.193447	−	0.140547i
$587$	−224.472	−	308.959i	−0.382406	−	0.526336i	0.573814	−	0.818986i	$-0.305463\pi$
$587$	−224.472	−	308.959i	−0.382406	−	0.526336i	−0.956220	+	0.292649i	$0.905463\pi$
$588$	−646.213	−	209.967i	−1.09900	−	0.357088i
$589$	−943.596	−	306.593i	−1.60203	−	0.520531i
$590$		0			0
$591$	−849.978	+	1169.89i	−1.43820	+	1.97952i
$592$	125.507	−	40.7796i	0.212005	−	0.0688845i
$593$	467.858			0.788968			0.394484	−	0.918903i	$-0.370923\pi$
$593$	467.858			0.788968			0.394484	+	0.918903i	$0.370923\pi$
$594$	21.3050	−	60.2817i	0.0358669	−	0.101484i
$595$		0			0
$596$	259.875	−	84.4386i	0.436033	−	0.141676i
$597$	629.382	−	866.269i	1.05424	−	1.45104i
$598$	133.354	+	183.547i	0.223001	+	0.306934i
$599$	−180.089	+	554.257i	−0.300649	+	0.925304i	0.680616	+	0.732641i	$0.261712\pi$
$599$	−180.089	+	554.257i	−0.300649	+	0.925304i	−0.981265	+	0.192663i	$0.938288\pi$
$600$		0			0
$601$	439.974	+	605.572i	0.732070	+	1.00761i	0.999036	+	0.0439019i	$0.0139789\pi$
$601$	439.974	+	605.572i	0.732070	+	1.00761i	−0.266966	+	0.963706i	$0.586021\pi$
$602$	−5.67541	−	4.12343i	−0.00942759	−	0.00684954i
$603$	−267.496	+	86.9149i	−0.443609	+	0.144137i
$604$		−	246.832i		−	0.408662i
$605$		0			0
$606$	−111.790			−0.184471
$607$	232.370	+	715.161i	0.382817	+	1.17819i	0.938052	+	0.346496i	$0.112628\pi$
$607$	232.370	+	715.161i	0.382817	+	1.17819i	−0.555235	+	0.831694i	$0.687372\pi$
$608$	−491.178	+	676.048i	−0.807858	+	1.11192i
$609$	−15.5867	+	11.3244i	−0.0255939	+	0.0185951i
$610$		0			0
$611$	−510.710	−	165.940i	−0.835860	−	0.271587i
$612$	398.418	−	289.468i	0.651010	−	0.472987i
$613$	−811.379	−	589.502i	−1.32362	−	0.961666i	−0.999880	−	0.0155207i	$-0.995059\pi$
$613$	−811.379	−	589.502i	−1.32362	−	0.961666i	−0.323741	−	0.946146i	$-0.604941\pi$
$614$	75.2380	+	231.559i	0.122537	+	0.377131i
$615$		0			0
$616$	−15.6252	−	5.52231i	−0.0253656	−	0.00896480i
$617$		−	436.456i		−	0.707384i	−0.935362	−	0.353692i	$-0.884926\pi$
$617$		−	436.456i		−	0.707384i	0.935362	−	0.353692i	$-0.115074\pi$
$618$	113.310	+	348.731i	0.183349	+	0.564290i
$619$	102.839	+	74.7172i	0.166138	+	0.120706i	0.667748	−	0.744388i	$-0.267259\pi$
$619$	102.839	+	74.7172i	0.166138	+	0.120706i	−0.501610	+	0.865094i	$0.667259\pi$
$620$		0			0
$621$	−68.2755	+	210.130i	−0.109945	+	0.338374i
$622$	48.7557	−	150.055i	0.0783853	−	0.241245i
$623$	19.9704	−	14.5093i	0.0320552	−	0.0232894i
$624$	−264.354	+	363.853i	−0.423645	+	0.583097i
$625$		0			0
$626$			432.028i			0.690141i
$627$	32.4729	−	1270.07i	0.0517908	−	2.02563i
$628$		−	745.616i		−	1.18729i
$629$	−255.729	+	83.0915i	−0.406565	+	0.132101i
$630$		0			0
$631$	182.154	−	132.343i	0.288675	−	0.209735i	−0.434017	−	0.900905i	$-0.642904\pi$
$631$	182.154	−	132.343i	0.288675	−	0.209735i	0.722692	+	0.691170i	$0.242904\pi$
$632$	679.538	+	220.795i	1.07522	+	0.349360i
$633$	279.393	−	859.882i	0.441379	−	1.35842i
$634$	−30.6602	−	42.2002i	−0.0483600	−	0.0665618i
$635$		0			0
$636$	−178.433	−	549.162i	−0.280556	−	0.863462i
$637$	−553.156			−0.868377
$638$	114.265	−	78.6362i	0.179099	−	0.123254i
$639$	−197.262			−0.308705
$640$		0			0
$641$	852.241	+	619.190i	1.32955	+	0.965975i	0.999760	+	0.0219202i	$0.00697799\pi$
$641$	852.241	+	619.190i	1.32955	+	0.965975i	0.329790	+	0.944054i	$0.393022\pi$
$642$	149.825	+	206.217i	0.233373	+	0.321210i
$643$	−799.805	−	259.872i	−1.24386	−	0.404156i	−0.388146	−	0.921598i	$-0.626884\pi$
$643$	−799.805	−	259.872i	−1.24386	−	0.404156i	−0.855718	+	0.517442i	$0.826884\pi$
$644$	25.3094	+	8.22352i	0.0393003	+	0.0127694i
$645$		0			0
$646$	249.853	−	343.893i	0.386769	−	0.532342i
$647$	61.1738	−	19.8766i	0.0945499	−	0.0307211i	−0.261360	−	0.965241i	$-0.584171\pi$
$647$	61.1738	−	19.8766i	0.0945499	−	0.0307211i	0.355910	+	0.934520i	$0.384171\pi$
$648$	515.738			0.795892
$649$	1072.88	−	318.524i	1.65314	−	0.490792i
$650$		0			0
$651$	36.2755	−	11.7866i	0.0557228	−	0.0181054i
$652$	186.081	−	256.118i	0.285400	−	0.392820i
$653$	628.461	+	865.002i	0.962421	+	1.32466i	0.945784	+	0.324797i	$0.105296\pi$
$653$	628.461	+	865.002i	0.962421	+	1.32466i	0.0166374	+	0.999862i	$0.494704\pi$
$654$	129.941	−	399.918i	0.198687	−	0.611495i
$655$		0			0
$656$	105.548	+	145.275i	0.160897	+	0.221455i
$657$	−565.224	−	410.659i	−0.860311	−	0.625052i
$658$	9.10724	−	2.95912i	0.0138408	−	0.00449714i
$659$			283.355i			0.429978i	0.976617	+	0.214989i	$0.0689715\pi$
$659$			283.355i			0.429978i	−0.976617	+	0.214989i	$0.931028\pi$
$660$		0			0
$661$	−845.155			−1.27860			−0.639300	−	0.768957i	$-0.720776\pi$
$661$	−845.155			−1.27860			−0.639300	+	0.768957i	$0.720776\pi$
$662$	−65.7109	−	202.237i	−0.0992612	−	0.305495i
$663$	538.642	−	741.378i	0.812432	−	1.11822i
$664$	550.795	−	400.176i	0.829511	−	0.602675i
$665$		0			0
$666$	64.1879	+	20.8559i	0.0963782	+	0.0313152i
$667$	−387.794	+	281.749i	−0.581400	+	0.422412i
$668$	−127.568	−	92.6834i	−0.190970	−	0.138748i
$669$	346.243	+	1065.63i	0.517553	+	1.59286i
$670$		0			0
$671$	444.479	+	340.625i	0.662413	+	0.507637i
$672$		−	32.1253i		−	0.0478056i
$673$	−137.135	−	422.060i	−0.203767	−	0.627132i	−0.999762	−	0.0218275i	$-0.993052\pi$
$673$	−137.135	−	422.060i	−0.203767	−	0.627132i	0.795994	−	0.605304i	$-0.206948\pi$
$674$	230.410	+	167.403i	0.341855	+	0.248372i
$675$		0			0
$676$	44.1616	−	135.915i	0.0653278	−	0.201058i
$677$	297.173	−	914.604i	0.438955	−	1.35097i	−0.450023	−	0.893017i	$-0.648584\pi$
$677$	297.173	−	914.604i	0.438955	−	1.35097i	0.888979	−	0.457949i	$-0.151416\pi$
$678$	304.762	−	221.423i	0.449502	−	0.326582i
$679$	−7.88160	+	10.8481i	−0.0116077	+	0.0159766i
$680$		0			0
$681$			348.693i			0.512031i
$682$	−263.253	+	78.1559i	−0.386001	+	0.114598i
$683$		−	488.033i		−	0.714542i	−0.934001	−	0.357271i	$-0.883707\pi$
$683$		−	488.033i		−	0.714542i	0.934001	−	0.357271i	$-0.116293\pi$
$684$	667.450	−	216.868i	0.975804	−	0.317058i
$685$		0			0
$686$	15.9731	−	11.6051i	0.0232844	−	0.0169171i
$687$	408.374	+	132.689i	0.594431	+	0.193142i
$688$	106.917	−	329.058i	0.155403	−	0.478281i
$689$	−276.306	−	380.303i	−0.401025	−	0.551964i
$690$		0			0
$691$	−153.473	−	472.340i	−0.222102	−	0.683560i	−0.998573	−	0.0534066i	$-0.982992\pi$
$691$	−153.473	−	472.340i	−0.222102	−	0.683560i	0.776471	−	0.630153i	$-0.217008\pi$
$692$	−526.197			−0.760400
$693$	12.1142	+	17.6030i	0.0174808	+	0.0254011i
$694$	46.2167			0.0665947
$695$		0			0
$696$	304.912	+	221.531i	0.438092	+	0.318292i
$697$	−215.062	−	296.008i	−0.308555	−	0.424689i
$698$	−169.622	−	55.1134i	−0.243011	−	0.0789590i
$699$	501.305	+	162.884i	0.717174	+	0.233024i
$700$		0			0
$701$	294.515	−	405.366i	0.420136	−	0.578268i	−0.545518	−	0.838099i	$-0.683667\pi$
$701$	294.515	−	405.366i	0.420136	−	0.578268i	0.965654	+	0.259831i	$0.0836670\pi$
$702$	62.5018	−	20.3081i	0.0890339	−	0.0289289i
$703$	−383.182			−0.545067
$704$	5.27184	−	206.191i	0.00748840	−	0.292885i
$705$		0			0
$706$	−149.622	+	48.6151i	−0.211929	+	0.0688599i
$707$	−6.27458	+	8.63621i	−0.00887493	+	0.0122153i
$708$	830.574	+	1143.19i	1.17313	+	1.61467i
$709$	0.643159	−	1.97944i	0.000907135	−	0.00279188i	−0.950602	−	0.310413i	$-0.899533\pi$
$709$	0.643159	−	1.97944i	0.000907135	−	0.00279188i	0.951509	+	0.307621i	$0.0995328\pi$
$710$		0			0
$711$	−541.525	−	745.345i	−0.761638	−	1.04831i
$712$	−390.666	−	283.836i	−0.548689	−	0.398646i
$713$	902.528	−	293.249i	1.26582	−	0.411289i
$714$			16.3416i			0.0228873i
$715$		0			0
$716$	−591.976			−0.826783
$717$	113.765	+	350.132i	0.158668	+	0.488329i
$718$	−291.647	+	401.418i	−0.406194	+	0.559078i
$719$	568.638	−	413.140i	0.790874	−	0.574603i	−0.117349	−	0.993091i	$-0.537440\pi$
$719$	568.638	−	413.140i	0.790874	−	0.574603i	0.908223	+	0.418487i	$0.137440\pi$
$720$		0			0
$721$	33.3009	+	10.8201i	0.0461871	+	0.0150071i
$722$	277.875	−	201.888i	0.384869	−	0.279624i
$723$	−85.8012	−	62.3382i	−0.118674	−	0.0862216i
$724$	178.092	+	548.111i	0.245984	+	0.757060i
$725$		0			0
$726$	−191.885	−	294.679i	−0.264304	−	0.405894i
$727$		−	1163.47i		−	1.60037i	−0.599754	−	0.800184i	$-0.704735\pi$
$727$		−	1163.47i		−	1.60037i	0.599754	−	0.800184i	$-0.295265\pi$
$728$	−5.26392	−	16.2007i	−0.00723065	−	0.0222537i
$729$	−304.999	−	221.595i	−0.418381	−	0.303971i
$730$		0			0
$731$	−217.852	+	670.480i	−0.298019	+	0.917209i
$732$	−218.487	+	672.433i	−0.298479	+	0.918625i
$733$	−1058.23	+	768.849i	−1.44370	+	1.04891i	−0.456443	+	0.889752i	$0.650877\pi$
$733$	−1058.23	+	768.849i	−1.44370	+	1.04891i	−0.987254	+	0.159155i	$0.949123\pi$
$734$	−31.4702	+	43.3150i	−0.0428750	+	0.0590123i
$735$		0			0
$736$		−	799.272i		−	1.08597i
$737$	147.280	−	416.723i	0.199837	−	0.565432i
$738$			91.8371i			0.124441i
$739$	1085.92	−	352.838i	1.46945	−	0.477453i	0.538508	−	0.842621i	$-0.318988\pi$
$739$	1085.92	−	352.838i	1.46945	−	0.477453i	0.930942	+	0.365167i	$0.118988\pi$
$740$		0			0
$741$	1056.50	−	767.594i	1.42578	−	1.03589i
$742$	7.97242	+	2.59040i	0.0107445	+	0.00349110i
$743$	176.414	−	542.947i	0.237435	−	0.730749i	−0.759354	−	0.650677i	$-0.774485\pi$
$743$	176.414	−	542.947i	0.237435	−	0.730749i	0.996789	−	0.0800717i	$-0.0255149\pi$
$744$	−438.577	−	603.650i	−0.589486	−	0.811357i
$745$		0			0
$746$	13.1070	+	40.3393i	0.0175697	+	0.0540741i
$747$	−877.859			−1.17518
$748$	−19.7800	+	773.632i	−0.0264438	+	1.03427i
$749$	24.3406			0.0324974
$750$		0			0
$751$	496.597	+	360.799i	0.661247	+	0.480424i	0.867084	−	0.498162i	$-0.165992\pi$
$751$	496.597	+	360.799i	0.661247	+	0.480424i	−0.205837	+	0.978586i	$0.565992\pi$
$752$	277.604	+	382.089i	0.369154	+	0.508097i
$753$	513.702	+	166.912i	0.682207	+	0.221662i
$754$	135.598	+	44.0584i	0.179838	+	0.0584329i
$755$		0			0
$756$	4.53097	−	6.23634i	0.00599335	−	0.00824913i
$757$	−775.528	+	251.984i	−1.02448	+	0.332872i	−0.772604	−	0.634888i	$-0.781046\pi$
$757$	−775.528	+	251.984i	−1.02448	+	0.332872i	−0.251872	+	0.967761i	$0.581046\pi$
$758$	136.212			0.179700
$759$	688.912	+	1001.05i	0.907657	+	1.31890i
$760$		0			0
$761$	−488.577	+	158.748i	−0.642020	+	0.208605i	−0.611892	−	0.790941i	$-0.709591\pi$
$761$	−488.577	+	158.748i	−0.642020	+	0.208605i	−0.0301278	+	0.999546i	$0.509591\pi$
$762$	263.409	−	362.551i	0.345681	−	0.475789i
$763$	−23.6019	−	32.4853i	−0.0309331	−	0.0425757i
$764$	−12.0100	+	36.9631i	−0.0157200	+	0.0483811i
$765$		0			0
$766$	2.61470	+	3.59883i	0.00341345	+	0.00469821i
$767$	930.670	+	676.171i	1.21339	+	0.881579i
$768$	−72.2803	+	23.4853i	−0.0941150	+	0.0305798i
$769$		−	501.416i		−	0.652036i	−0.945364	−	0.326018i	$-0.894293\pi$
$769$		−	501.416i		−	0.652036i	0.945364	−	0.326018i	$-0.105707\pi$
$770$		0			0
$771$	977.167			1.26740
$772$	134.784	+	414.823i	0.174591	+	0.537336i
$773$	−264.185	+	363.619i	−0.341765	+	0.470400i	−0.944956	−	0.327197i	$-0.893896\pi$
$773$	−264.185	+	363.619i	−0.341765	+	0.470400i	0.603191	+	0.797597i	$0.293896\pi$
$774$	143.156	−	104.009i	0.184956	−	0.134378i
$775$		0			0
$776$	249.472	+	81.0584i	0.321485	+	0.104457i
$777$	11.9177	−	8.65869i	0.0153380	−	0.0111437i
$778$	−132.901	−	96.5585i	−0.170824	−	0.124111i
$779$	−161.124	−	495.888i	−0.206834	−	0.636569i
$780$		0			0
$781$	188.554	−	246.043i	0.241427	−	0.315036i
$782$			406.575i			0.519917i
$783$	42.9065	+	132.053i	0.0547976	+	0.168650i
$784$	393.590	+	285.960i	0.502028	+	0.364744i
$785$		0			0
$786$	−115.396	+	355.153i	−0.146815	+	0.451849i
$787$	177.854	−	547.379i	0.225990	−	0.695526i	−0.772200	−	0.635380i	$-0.780843\pi$
$787$	177.854	−	547.379i	0.225990	−	0.695526i	0.998190	−	0.0601458i	$-0.0191566\pi$
$788$	1015.51	−	737.809i	1.28872	−	0.936306i
$789$	−4.54486	+	6.25546i	−0.00576028	+	0.00792834i
$790$		0			0
$791$		−	35.9723i		−	0.0454770i
$792$	254.269	−	331.794i	0.321047	−	0.418932i
$793$			575.601i			0.725852i
$794$	−148.647	+	48.2982i	−0.187212	+	0.0608290i
$795$		0			0
$796$	−751.951	+	546.325i	−0.944662	+	0.686337i
$797$	−23.7562	−	7.71885i	−0.0298070	−	0.00968488i	0.294076	−	0.955782i	$-0.404988\pi$
$797$	−23.7562	−	7.71885i	−0.0298070	−	0.00968488i	−0.323883	+	0.946097i	$0.604988\pi$
$798$	−7.19626	+	22.1478i	−0.00901787	+	0.0277542i
$799$	−565.639	−	778.535i	−0.707933	−	0.974386i
$800$		0			0
$801$	192.408	+	592.171i	0.240210	+	0.739289i
$802$	−393.109			−0.490160
$803$	1052.48	−	312.467i	1.31069	−	0.389125i
$804$	558.046			0.694088
$805$		0			0
$806$	−228.358	−	165.911i	−0.283322	−	0.205846i
$807$	430.752	+	592.879i	0.533769	+	0.734671i
$808$	198.606	+	64.5310i	0.245799	+	0.0798651i
$809$	711.977	+	231.335i	0.880070	+	0.285952i	0.713987	−	0.700159i	$-0.246888\pi$
$809$	711.977	+	231.335i	0.880070	+	0.285952i	0.166084	+	0.986112i	$0.446888\pi$
$810$		0			0
$811$	138.201	−	190.218i	0.170409	−	0.234547i	−0.715268	−	0.698851i	$-0.753695\pi$
$811$	138.201	−	190.218i	0.170409	−	0.234547i	0.885676	+	0.464303i	$0.153695\pi$
$812$	15.9052	−	5.16792i	0.0195877	−	0.00636443i
$813$	−2030.26			−2.49725
$814$	−87.3676	+	60.1256i	−0.107331	+	0.0738644i
$815$		0			0
$816$	−766.525	+	249.059i	−0.939369	+	0.305219i
$817$	−590.513	+	812.771i	−0.722782	+	0.994824i
$818$	−156.614	−	215.561i	−0.191460	−	0.263522i
$819$	−6.78736	+	20.8894i	−0.00828738	+	0.0255059i
$820$		0			0
$821$	−90.2423	−	124.208i	−0.109918	−	0.151288i	0.750514	−	0.660854i	$-0.229806\pi$
$821$	−90.2423	−	124.208i	−0.109918	−	0.151288i	−0.860432	+	0.509566i	$0.829806\pi$
$822$	−145.609	−	105.791i	−0.177140	−	0.128699i
$823$	−1229.43	+	399.465i	−1.49384	+	0.485377i	−0.938214	−	0.346057i	$-0.887520\pi$
$823$	−1229.43	+	399.465i	−1.49384	+	0.485377i	−0.555624	+	0.831434i	$0.687520\pi$
$824$		−	684.967i		−	0.831270i
$825$		0			0
$826$	−20.5140			−0.0248353
$827$	−193.083	−	594.248i	−0.233474	−	0.718559i	−0.997320	−	0.0731605i	$-0.976691\pi$
$827$	−193.083	−	594.248i	−0.233474	−	0.718559i	0.763846	−	0.645398i	$-0.223309\pi$
$828$	−394.554	+	543.057i	−0.476514	+	0.655866i
$829$	−1192.01	+	866.043i	−1.43788	+	1.04468i	−0.449405	+	0.893328i	$0.648364\pi$
$829$	−1192.01	+	866.043i	−1.43788	+	1.04468i	−0.988479	+	0.151355i	$0.951636\pi$
$830$		0			0
$831$	134.794	+	43.7973i	0.162207	+	0.0527043i
$832$	171.519	−	124.616i	0.206152	−	0.149779i
$833$	−801.969	−	582.664i	−0.962748	−	0.699477i
$834$	204.971	+	630.835i	0.245768	+	0.756396i
$835$		0			0
$836$	−367.489	+	1039.80i	−0.439580	+	1.24378i
$837$		−	274.885i		−	0.328417i
$838$	−36.9422	−	113.696i	−0.0440838	−	0.135676i
$839$	−1083.63	−	787.303i	−1.29157	−	0.938383i	−0.291737	−	0.956498i	$-0.594233\pi$
$839$	−1083.63	−	787.303i	−1.29157	−	0.938383i	−0.999836	+	0.0181155i	$0.994233\pi$
$840$		0			0
$841$	166.797	−	513.350i	0.198332	−	0.610404i
$842$	26.9990	−	83.0945i	0.0320654	−	0.0986870i
$843$	1106.07	−	803.607i	1.31206	−	0.953270i
$844$	−461.305	+	634.932i	−0.546570	+	0.752289i
$845$		0			0
$846$			241.542i			0.285511i
$847$	−33.5354	−	1.71597i	−0.0395931	−	0.00202594i
$848$			413.438i			0.487544i
$849$	−1572.74	+	511.015i	−1.85246	+	0.601902i
$850$		0			0
$851$	296.509	−	215.426i	0.348424	−	0.253145i
$852$	372.228	+	120.944i	0.436888	+	0.141953i
$853$	−359.583	+	1106.68i	−0.421551	+	1.29740i	0.484708	+	0.874676i	$0.338926\pi$
$853$	−359.583	+	1106.68i	−0.421551	+	1.29740i	−0.906259	+	0.422724i	$0.861074\pi$
$854$	−6.03326	−	8.30406i	−0.00706470	−	0.00972373i
$855$		0			0
$856$	−147.141	−	452.853i	−0.171894	−	0.529034i
$857$	1069.27			1.24769			0.623844	−	0.781549i	$-0.285570\pi$
$857$	1069.27			1.24769			0.623844	+	0.781549i	$0.285570\pi$
$858$	120.444	−	340.793i	0.140378	−	0.397194i
$859$	−998.288			−1.16215			−0.581076	−	0.813849i	$-0.697368\pi$
$859$	−998.288			−1.16215			−0.581076	+	0.813849i	$0.697368\pi$
$860$		0			0
$861$	16.2167	+	11.7821i	0.0188347	+	0.0136842i
$862$	230.861	+	317.753i	0.267820	+	0.368623i
$863$	669.085	+	217.399i	0.775301	+	0.251911i	0.669833	−	0.742512i	$-0.266366\pi$
$863$	669.085	+	217.399i	0.775301	+	0.251911i	0.105468	+	0.994423i	$0.466366\pi$
$864$	−220.190	−	71.5442i	−0.254850	−	0.0828058i
$865$		0			0
$866$	91.1189	−	125.414i	0.105218	−	0.144820i
$867$	462.431	−	150.253i	0.533370	−	0.173302i
$868$	−33.1089			−0.0381438
$869$	1447.28	+	37.0036i	1.66545	+	0.0425818i
$870$		0			0
$871$	432.071	−	140.388i	0.496063	−	0.161181i
$872$	−461.708	+	635.487i	−0.529482	+	0.728770i
$873$	−198.805	−	273.631i	−0.227726	−	0.313438i
$874$	−179.042	+	551.033i	−0.204853	+	0.630473i
$875$		0			0
$876$	814.780	+	1121.45i	0.930114	+	1.28019i
$877$	273.042	+	198.377i	0.311336	+	0.226199i	0.732470	−	0.680800i	$-0.238368\pi$
$877$	273.042	+	198.377i	0.311336	+	0.226199i	−0.421133	+	0.906999i	$0.638368\pi$
$878$	−20.6325	+	6.70391i	−0.0234995	+	0.00763544i
$879$		−	771.436i		−	0.877629i
$880$		0			0
$881$	−1011.82			−1.14849			−0.574246	−	0.818682i	$-0.694705\pi$
$881$	−1011.82			−1.14849			−0.574246	+	0.818682i	$0.694705\pi$
$882$	76.8873	+	236.635i	0.0871738	+	0.268293i
$883$	189.317	−	260.572i	0.214402	−	0.295099i	−0.688247	−	0.725476i	$-0.741620\pi$
$883$	189.317	−	260.572i	0.214402	−	0.295099i	0.902649	+	0.430377i	$0.141620\pi$
$884$	−643.541	+	467.560i	−0.727988	+	0.528914i
$885$		0			0
$886$	−39.5673	−	12.8562i	−0.0446584	−	0.0145104i
$887$	−602.240	+	437.553i	−0.678963	+	0.493296i	−0.873014	−	0.487696i	$-0.837837\pi$
$887$	−602.240	+	437.553i	−0.678963	+	0.493296i	0.194050	+	0.980992i	$0.437837\pi$
$888$	−233.137	−	169.384i	−0.262542	−	0.190748i
$889$	−13.2239	−	40.6989i	−0.0148750	−	0.0457805i
$890$		0			0
$891$	1001.78	−	297.415i	1.12434	−	0.333799i
$892$		−	972.603i		−	1.09036i
$893$	−423.773	−	1304.24i	−0.474550	−	1.46052i
$894$	−185.029	−	134.432i	−0.206968	−	0.150371i
$895$		0			0
$896$	−11.0956	+	34.1486i	−0.0123834	+	0.0381123i
$897$	−385.985	+	1187.94i	−0.430306	+	1.32435i
$898$	349.554	−	253.966i	0.389258	−	0.282813i
$899$	350.535	−	482.470i	0.389916	−	0.536674i
$900$		0			0
$901$		−	842.411i		−	0.934973i
$902$	−114.547	−	87.7829i	−0.126993	−	0.0973203i
$903$		−	38.6223i		−	0.0427711i
$904$	−669.259	+	217.456i	−0.740331	+	0.240548i
$905$		0			0
$906$	−167.141	+	121.435i	−0.184482	+	0.134034i
$907$	534.971	+	173.823i	0.589825	+	0.191646i	0.588697	−	0.808354i	$-0.299641\pi$
$907$	534.971	+	173.823i	0.589825	+	0.191646i	0.00112787	+	0.999999i	$0.499641\pi$
$908$	93.5325	−	287.863i	0.103009	−	0.317030i
$909$	−158.269	−	217.839i	−0.174114	−	0.239647i
$910$		0			0
$911$	−21.9218	−	67.4684i	−0.0240634	−	0.0740597i	0.938304	−	0.345813i	$-0.112397\pi$
$911$	−21.9218	−	67.4684i	−0.0240634	−	0.0740597i	−0.962367	+	0.271753i	$0.912397\pi$
$912$	−1148.55			−1.25938
$913$	839.106	−	1094.94i	0.919064	−	1.19928i
$914$	−345.220			−0.377702
$915$		0			0
$916$	−301.541	−	219.082i	−0.329193	−	0.239173i
$917$	20.9601	+	28.8491i	0.0228572	+	0.0314603i
$918$	112.007	+	36.3932i	0.122012	+	0.0396440i
$919$	−64.4021	−	20.9255i	−0.0700784	−	0.0227699i	0.273768	−	0.961796i	$-0.411730\pi$
$919$	−64.4021	−	20.9255i	−0.0700784	−	0.0227699i	−0.343846	+	0.939026i	$0.611730\pi$
$920$		0			0
$921$	−787.902	+	1084.45i	−0.855486	+	1.17748i
$922$	200.635	−	65.1904i	0.217609	−	0.0707054i
$923$	318.626			0.345207
$924$	−12.0665	−	40.6436i	−0.0130590	−	0.0439866i
$925$		0			0
$926$	−59.5184	+	19.3387i	−0.0642747	+	0.0208841i
$927$	−519.135	+	714.528i	−0.560016	+	0.770796i
$928$	−295.237	−	406.359i	−0.318144	−	0.437887i
$929$	−385.947	+	1187.82i	−0.415443	+	1.27860i	0.496411	+	0.868088i	$0.334651\pi$
$929$	−385.947	+	1187.82i	−0.415443	+	1.27860i	−0.911854	+	0.410515i	$0.865349\pi$
$930$		0			0
$931$	−830.328	−	1142.85i	−0.891866	−	1.22755i
$932$	−370.160	−	268.937i	−0.397168	−	0.288559i
$933$	826.129	−	268.426i	0.885455	−	0.287702i
$934$		−	164.151i		−	0.175751i
$935$		0			0
$936$	429.674			0.459053
$937$	167.401	+	515.209i	0.178657	+	0.549849i	0.999782	−	0.0208996i	$-0.00665305\pi$
$937$	167.401	+	515.209i	0.178657	+	0.549849i	−0.821125	+	0.570749i	$0.806653\pi$
$938$	−4.76189	+	6.55418i	−0.00507664	+	0.00698739i
$939$	−1924.28	+	1398.07i	−2.04929	+	1.48890i
$940$		0			0
$941$	−561.217	−	182.350i	−0.596405	−	0.193784i	−0.00476834	−	0.999989i	$-0.501518\pi$
$941$	−561.217	−	182.350i	−0.596405	−	0.193784i	−0.591636	+	0.806205i	$0.701518\pi$
$942$	−504.890	+	366.824i	−0.535977	+	0.389410i
$943$	403.468	+	293.137i	0.427856	+	0.310856i
$944$	−312.650	−	962.238i	−0.331197	−	1.01932i
$945$		0			0
$946$	−7.10716	+	277.974i	−0.00751286	+	0.293842i
$947$			527.364i			0.556878i	0.960454	+	0.278439i	$0.0898171\pi$
$947$			527.364i			0.556878i	−0.960454	+	0.278439i	$0.910183\pi$
$948$	564.860	+	1738.46i	0.595844	+	1.83382i
$949$	912.973	+	663.313i	0.962036	+	0.698960i
$950$		0			0
$951$	88.7438	−	273.125i	0.0933163	−	0.287198i
$952$	9.43324	−	29.0325i	0.00990886	−	0.0304963i
$953$	−1429.23	+	1038.40i	−1.49972	+	1.08961i	−0.529223	+	0.848483i	$0.677517\pi$
$953$	−1429.23	+	1038.40i	−1.49972	+	1.08961i	−0.970494	+	0.241125i	$0.922483\pi$
$954$	−124.284	+	171.062i	−0.130277	+	0.179310i
$955$		0			0
$956$		−	319.567i		−	0.334275i
$957$	720.021	+	254.472i	0.752373	+	0.265906i
$958$		−	61.1060i		−	0.0637849i
$959$	−16.3456	+	5.31101i	−0.0170444	+	0.00553807i
$960$		0			0
$961$	−177.706	+	129.111i	−0.184917	+	0.134350i
$962$	−103.679	−	33.6873i	−0.107774	−	0.0350180i
$963$	−189.725	+	583.915i	−0.197015	+	0.606350i
$964$	54.1117	+	74.4783i	0.0561325	+	0.0772597i
$965$		0			0
$966$	−6.88307	−	21.1839i	−0.00712533	−	0.0219295i
$967$	−1457.23			−1.50696			−0.753481	−	0.657470i	$-0.771627\pi$
$967$	−1457.23			−1.50696			−0.753481	+	0.657470i	$0.771627\pi$
$968$	170.799	+	634.294i	0.176445	+	0.655263i
$969$	2340.26			2.41513
$970$		0			0
$971$	−151.983	−	110.422i	−0.156522	−	0.113720i	0.506768	−	0.862083i	$-0.330840\pi$
$971$	−151.983	−	110.422i	−0.156522	−	0.113720i	−0.663290	+	0.748363i	$0.730840\pi$
$972$	628.588	+	865.177i	0.646696	+	0.890100i
$973$	60.2393	+	19.5729i	0.0619109	+	0.0201161i
$974$	−457.232	−	148.564i	−0.469437	−	0.152529i
$975$		0			0
$976$	297.562	−	409.559i	0.304879	−	0.419631i
$977$	1197.75	−	389.172i	1.22595	−	0.398334i	0.376702	−	0.926335i	$-0.377058\pi$
$977$	1197.75	−	389.172i	1.22595	−	0.398334i	0.849244	+	0.528001i	$0.177058\pi$
$978$	−264.977			−0.270937
$979$	−922.522	−	326.041i	−0.942310	−	0.333035i
$980$		0			0
$981$	963.269	−	312.985i	0.981926	−	0.319047i
$982$	318.267	−	438.057i	0.324101	−	0.446087i
$983$	612.344	+	842.819i	0.622934	+	0.857395i	0.997562	−	0.0697799i	$-0.0222297\pi$
$983$	612.344	+	842.819i	0.622934	+	0.857395i	−0.374628	+	0.927175i	$0.622230\pi$
$984$	121.173	−	372.933i	0.123144	−	0.378997i
$985$		0			0
$986$	150.182	+	206.708i	0.152314	+	0.209643i
$987$	42.6518	+	30.9883i	0.0432135	+	0.0313965i
$988$	−1078.09	+	350.293i	−1.09119	+	0.354548i
$989$		−	960.916i		−	0.971604i
$990$		0			0
$991$	−664.312			−0.670345			−0.335173	−	0.942157i	$-0.608795\pi$
$991$	−664.312			−0.670345			−0.335173	+	0.942157i	$0.608795\pi$
$992$	307.288	+	945.736i	0.309767	+	0.953363i
$993$	688.134	−	947.135i	0.692985	−	0.953811i
$994$	−4.59675	+	3.33973i	−0.00462449	+	0.00335989i
$995$		0			0
$996$	1656.49	+	538.227i	1.66315	+	0.540389i
$997$	−159.697	+	116.026i	−0.160177	+	0.116375i	−0.664987	−	0.746855i	$-0.731563\pi$
$997$	−159.697	+	116.026i	−0.160177	+	0.116375i	0.504809	+	0.863231i	$0.331563\pi$
$998$	163.419	+	118.731i	0.163747	+	0.118969i
$999$	−32.8065	−	100.968i	−0.0328393	−	0.101069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.q.c.149.2		8
5.2	odd	4		55.3.i.a.6.1	✓	4
5.3	odd	4		275.3.x.d.226.1		4
5.4	even	2	inner	275.3.q.c.149.1		8
11.2	odd	10	inner	275.3.q.c.24.1		8
55.2	even	20		55.3.i.a.46.1	yes	4
55.13	even	20		275.3.x.d.101.1		4
55.24	odd	10	inner	275.3.q.c.24.2		8
55.47	odd	20		605.3.c.a.241.3		4
55.52	even	20		605.3.c.a.241.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.a.6.1	✓	4	5.2	odd	4
55.3.i.a.46.1	yes	4	55.2	even	20
275.3.q.c.24.1		8	11.2	odd	10	inner
275.3.q.c.24.2		8	55.24	odd	10	inner
275.3.q.c.149.1		8	5.4	even	2	inner
275.3.q.c.149.2		8	1.1	even	1	trivial
275.3.x.d.101.1		4	55.13	even	20
275.3.x.d.226.1		4	5.3	odd	4
605.3.c.a.241.2		4	55.52	even	20
605.3.c.a.241.3		4	55.47	odd	20

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.q (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.224514 + 0.690983i) q^{2} +(-2.35114 + 3.23607i) q^{3} +(2.80902 - 2.04087i) q^{4} +(-2.76393 - 0.898056i) q^{6} +(-0.224514 + 0.163119i) q^{7} +(4.39201 + 3.19098i) q^{8} +(-2.16312 - 6.65740i) q^{9} +(10.3713 + 3.66547i) q^{11} +13.8885i q^{12} +(3.49396 + 10.7533i) q^{13} +(-0.163119 - 0.118513i) q^{14} +(3.07295 - 9.45756i) q^{16} +(-6.26137 + 19.2705i) q^{17} +(4.11450 - 2.98936i) q^{18} +(-16.9721 + 23.3601i) q^{19} -1.11006i q^{21} +(-0.204270 + 7.98936i) q^{22} -27.6180i q^{23} +(-20.6525 + 6.71040i) q^{24} +(-6.64590 + 4.82853i) q^{26} +(-7.60845 - 2.47214i) q^{27} +(-0.297759 + 0.916408i) q^{28} +(-10.2016 - 14.0413i) q^{29} +(10.6180 + 32.6789i) q^{31} +28.9402 q^{32} +(-36.2461 + 24.9443i) q^{33} -14.7214 q^{34} +(-19.6631 - 14.2861i) q^{36} +(7.80021 + 10.7361i) q^{37} +(-19.9519 - 6.48278i) q^{38} +(-43.0132 - 13.9758i) q^{39} +(-10.6140 + 14.6089i) q^{41} +(0.767031 - 0.249224i) q^{42} +34.7931 q^{43} +(36.6140 - 10.8702i) q^{44} +(19.0836 - 6.20063i) q^{46} +(-27.9159 + 38.4230i) q^{47} +(23.3804 + 32.1803i) q^{48} +(-15.1180 + 46.5285i) q^{49} +(-47.6393 - 65.5699i) q^{51} +(31.7606 + 23.0755i) q^{52} +(-39.5406 + 12.8475i) q^{53} -5.81234i q^{54} -1.50658 q^{56} +(-35.6911 - 109.846i) q^{57} +(7.41192 - 10.2016i) q^{58} +(82.3115 - 59.8028i) q^{59} +(48.4164 + 15.7314i) q^{61} +(-20.1967 + 14.6738i) q^{62} +(1.57160 + 1.14183i) q^{63} +(-5.79431 - 17.8330i) q^{64} +(-25.3738 - 19.4451i) q^{66} -40.1803i q^{67} +(21.7403 + 66.9098i) q^{68} +(89.3738 + 64.9339i) q^{69} +(8.70820 - 26.8011i) q^{71} +(11.7432 - 36.1418i) q^{72} +(80.7463 - 58.6656i) q^{73} +(-5.66718 + 7.80021i) q^{74} +100.257i q^{76} +(-2.92641 + 0.868810i) q^{77} -32.8591i q^{78} +(125.172 - 40.6709i) q^{79} +(76.8566 - 55.8396i) q^{81} +(-12.4775 - 4.05418i) q^{82} +(38.7533 - 119.271i) q^{83} +(-2.26548 - 3.11817i) q^{84} +(7.81153 + 24.0414i) q^{86} +69.4242 q^{87} +(33.8545 + 49.1935i) q^{88} -88.9493 q^{89} +(-2.53851 - 1.84433i) q^{91} +(-56.3648 - 77.5795i) q^{92} +(-130.716 - 42.4721i) q^{93} +(-32.8171 - 10.6629i) q^{94} +(-68.0426 + 93.6526i) q^{96} +(45.9533 - 14.9311i) q^{97} -35.5446 q^{98} +(1.96807 - 76.9748i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 18 q^{4} - 40 q^{6} + 14 q^{9} - 2 q^{11} + 30 q^{14} + 38 q^{16} - 100 q^{19} - 40 q^{24} - 80 q^{26} - 180 q^{29} + 76 q^{31} + 240 q^{34} - 126 q^{36} - 40 q^{39} + 170 q^{41} + 38 q^{44} + 260 q^{46}+ \cdots - 266 q^{99}+O(q^{100}) \) 8 * q + 18 * q^4 - 40 * q^6 + 14 * q^9 - 2 * q^11 + 30 * q^14 + 38 * q^16 - 100 * q^19 - 40 * q^24 - 80 * q^26 - 180 * q^29 + 76 * q^31 + 240 * q^34 - 126 * q^36 - 40 * q^39 + 170 * q^41 + 38 * q^44 + 260 * q^46 - 112 * q^49 - 560 * q^51 + 140 * q^56 + 256 * q^59 + 280 * q^61 + 298 * q^64 + 280 * q^66 + 232 * q^69 + 16 * q^71 - 260 * q^74 + 420 * q^79 + 190 * q^81 - 680 * q^84 - 340 * q^86 + 156 * q^89 - 150 * q^91 - 750 * q^94 - 920 * q^96 - 266 * q^99

Introduction

L-functions

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