LMFDB - Embedded newform 273.2.l.c.256.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (of order $3$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			256.1
Root			$-1.35774 + 2.35168i$ of defining polynomial
Character	$\chi$	$=$	273.256
Dual form			273.2.l.c.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71549 q^{2} +(-0.500000 - 0.866025i) q^{3} +5.37387 q^{4} +(1.94413 + 3.36734i) q^{5} +(1.35774 + 2.35168i) q^{6} +(1.94064 + 1.79830i) q^{7} -9.16172 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-2.71549 q^{2} +(-0.500000 - 0.866025i) q^{3} +5.37387 q^{4} +(1.94413 + 3.36734i) q^{5} +(1.35774 + 2.35168i) q^{6} +(1.94064 + 1.79830i) q^{7} -9.16172 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-5.27927 - 9.14396i) q^{10} +(0.815825 + 1.41305i) q^{11} +(-2.68694 - 4.65391i) q^{12} +(-3.59984 - 0.202826i) q^{13} +(-5.26980 - 4.88327i) q^{14} +(1.94413 - 3.36734i) q^{15} +14.1308 q^{16} -4.19163 q^{17} +(1.35774 - 2.35168i) q^{18} +(-0.847266 + 1.46751i) q^{19} +(10.4475 + 18.0956i) q^{20} +(0.587055 - 2.57980i) q^{21} +(-2.21536 - 3.83712i) q^{22} +0.791415 q^{23} +(4.58086 + 7.93428i) q^{24} +(-5.05930 + 8.76296i) q^{25} +(9.77533 + 0.550770i) q^{26} +1.00000 q^{27} +(10.4288 + 9.66386i) q^{28} +(-0.242434 + 0.419908i) q^{29} +(-5.27927 + 9.14396i) q^{30} +(-0.915382 + 1.58549i) q^{31} -20.0485 q^{32} +(0.815825 - 1.41305i) q^{33} +11.3823 q^{34} +(-2.28262 + 10.0309i) q^{35} +(-2.68694 + 4.65391i) q^{36} +0.689242 q^{37} +(2.30074 - 3.98500i) q^{38} +(1.62427 + 3.21897i) q^{39} +(-17.8116 - 30.8506i) q^{40} +(2.96941 - 5.14316i) q^{41} +(-1.59414 + 7.00542i) q^{42} +(2.79224 + 4.83630i) q^{43} +(4.38414 + 7.59355i) q^{44} -3.88826 q^{45} -2.14908 q^{46} +(-0.292223 - 0.506146i) q^{47} +(-7.06539 - 12.2376i) q^{48} +(0.532204 + 6.97974i) q^{49} +(13.7385 - 23.7957i) q^{50} +(2.09582 + 3.63006i) q^{51} +(-19.3451 - 1.08996i) q^{52} +(3.04896 - 5.28096i) q^{53} -2.71549 q^{54} +(-3.17214 + 5.49431i) q^{55} +(-17.7796 - 16.4756i) q^{56} +1.69453 q^{57} +(0.658326 - 1.14025i) q^{58} +8.27708 q^{59} +(10.4475 - 18.0956i) q^{60} +(4.54246 - 7.86777i) q^{61} +(2.48571 - 4.30537i) q^{62} +(-2.52770 + 0.781496i) q^{63} +26.1800 q^{64} +(-6.31559 - 12.5162i) q^{65} +(-2.21536 + 3.83712i) q^{66} +(-0.500271 - 0.866495i) q^{67} -22.5253 q^{68} +(-0.395707 - 0.685385i) q^{69} +(6.19844 - 27.2389i) q^{70} +(7.93720 + 13.7476i) q^{71} +(4.58086 - 7.93428i) q^{72} +(-2.92626 + 5.06843i) q^{73} -1.87163 q^{74} +10.1186 q^{75} +(-4.55310 + 7.88620i) q^{76} +(-0.957867 + 4.20933i) q^{77} +(-4.41068 - 8.74107i) q^{78} +(0.643065 + 1.11382i) q^{79} +(27.4721 + 47.5831i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.06339 + 13.9662i) q^{82} -6.18202 q^{83} +(3.15476 - 13.8635i) q^{84} +(-8.14908 - 14.1146i) q^{85} +(-7.58229 - 13.1329i) q^{86} +0.484868 q^{87} +(-7.47435 - 12.9460i) q^{88} -4.40869 q^{89} +10.5585 q^{90} +(-6.62127 - 6.86722i) q^{91} +4.25296 q^{92} +1.83076 q^{93} +(0.793529 + 1.37443i) q^{94} -6.58879 q^{95} +(10.0243 + 17.3625i) q^{96} +(5.08782 + 8.81236i) q^{97} +(-1.44519 - 18.9534i) q^{98} -1.63165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.71549			−1.92014			−0.960070	−	0.279760i	$-0.909745\pi$
$2$	−2.71549			−1.92014			−0.960070	+	0.279760i	$0.909745\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	5.37387			2.68694
$5$	1.94413	+	3.36734i	0.869442	+	1.50592i	0.862568	+	0.505942i	$0.168855\pi$
$5$	1.94413	+	3.36734i	0.869442	+	1.50592i	0.00687463	+	0.999976i	$0.497812\pi$
$6$	1.35774	+	2.35168i	0.554297	+	0.960070i
$7$	1.94064	+	1.79830i	0.733495	+	0.679695i
$7$	1.94064	+	1.79830i	0.733495	+	0.679695i
$8$	−9.16172			−3.23916
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−5.27927	−	9.14396i	−1.66945	−	2.89157i
$11$	0.815825	+	1.41305i	0.245980	+	0.426051i	0.962407	−	0.271612i	$-0.0875568\pi$
$11$	0.815825	+	1.41305i	0.245980	+	0.426051i	−0.716426	+	0.697663i	$0.754223\pi$
$12$	−2.68694	−	4.65391i	−0.775652	−	1.34347i
$13$	−3.59984	−	0.202826i	−0.998417	−	0.0562537i
$13$	−3.59984	−	0.202826i	−0.998417	−	0.0562537i
$14$	−5.26980	−	4.88327i	−1.40841	−	1.30511i
$15$	1.94413	−	3.36734i	0.501973	−	0.869442i
$16$	14.1308			3.53269
$17$	−4.19163			−1.01662			−0.508310	−	0.861174i	$-0.669730\pi$
$17$	−4.19163			−1.01662			−0.508310	+	0.861174i	$0.669730\pi$
$18$	1.35774	−	2.35168i	0.320023	−	0.554297i
$19$	−0.847266	+	1.46751i	−0.194376	+	0.336669i	−0.946696	−	0.322129i	$-0.895602\pi$
$19$	−0.847266	+	1.46751i	−0.194376	+	0.336669i	0.752320	+	0.658798i	$0.228935\pi$
$20$	10.4475	+	18.0956i	2.33614	+	4.04631i
$21$	0.587055	−	2.57980i	0.128106	−	0.562958i
$22$	−2.21536	−	3.83712i	−0.472317	−	0.818077i
$23$	0.791415			0.165021			0.0825107	−	0.996590i	$-0.473706\pi$
$23$	0.791415			0.165021			0.0825107	+	0.996590i	$0.473706\pi$
$24$	4.58086	+	7.93428i	0.935064	+	1.61958i
$25$	−5.05930	+	8.76296i	−1.01186	+	1.75259i
$26$	9.77533	+	0.550770i	1.91710	+	0.108015i
$27$	1.00000			0.192450
$28$	10.4288	+	9.66386i	1.97085	+	1.82630i
$29$	−0.242434	+	0.419908i	−0.0450188	+	0.0779749i	−0.887657	−	0.460506i	$-0.847668\pi$
$29$	−0.242434	+	0.419908i	−0.0450188	+	0.0779749i	0.842638	+	0.538481i	$0.181001\pi$
$30$	−5.27927	+	9.14396i	−0.963858	+	1.66945i
$31$	−0.915382	+	1.58549i	−0.164407	+	0.284762i	−0.936445	−	0.350815i	$-0.885905\pi$
$31$	−0.915382	+	1.58549i	−0.164407	+	0.284762i	0.772037	+	0.635577i	$0.219238\pi$
$32$	−20.0485			−3.54411
$33$	0.815825	−	1.41305i	0.142017	−	0.245980i
$34$	11.3823			1.95205
$35$	−2.28262	+	10.0309i	−0.385834	+	1.69554i
$36$	−2.68694	+	4.65391i	−0.447823	+	0.775652i
$37$	0.689242			0.113311			0.0566553	−	0.998394i	$-0.481956\pi$
$37$	0.689242			0.113311			0.0566553	+	0.998394i	$0.481956\pi$
$38$	2.30074	−	3.98500i	0.373229	−	0.646452i
$39$	1.62427	+	3.21897i	0.260091	+	0.515447i
$40$	−17.8116	−	30.8506i	−2.81626	−	4.87790i
$41$	2.96941	−	5.14316i	0.463743	−	0.803227i	−0.535400	−	0.844598i	$-0.679839\pi$
$41$	2.96941	−	5.14316i	0.463743	−	0.803227i	0.999144	+	0.0413712i	$0.0131726\pi$
$42$	−1.59414	+	7.00542i	−0.245981	+	1.08096i
$43$	2.79224	+	4.83630i	0.425813	+	0.737529i	0.996496	−	0.0836411i	$-0.0266549\pi$
$43$	2.79224	+	4.83630i	0.425813	+	0.737529i	−0.570683	+	0.821170i	$0.693322\pi$
$44$	4.38414	+	7.59355i	0.660934	+	1.14477i
$45$	−3.88826			−0.579628
$46$	−2.14908			−0.316864
$47$	−0.292223	−	0.506146i	−0.0426252	−	0.0738289i	0.843926	−	0.536460i	$-0.180239\pi$
$47$	−0.292223	−	0.506146i	−0.0426252	−	0.0738289i	−0.886551	+	0.462631i	$0.846905\pi$
$48$	−7.06539	−	12.2376i	−1.01980	−	1.76635i
$49$	0.532204	+	6.97974i	0.0760292	+	0.997106i
$50$	13.7385	−	23.7957i	1.94291	−	3.36522i
$51$	2.09582	+	3.63006i	0.293473	+	0.508310i
$52$	−19.3451	−	1.08996i	−2.68268	−	0.151150i
$53$	3.04896	−	5.28096i	0.418807	−	0.725396i	−0.577012	−	0.816735i	$-0.695782\pi$
$53$	3.04896	−	5.28096i	0.418807	−	0.725396i	0.995820	+	0.0913397i	$0.0291149\pi$
$54$	−2.71549			−0.369531
$55$	−3.17214	+	5.49431i	−0.427731	+	0.740853i
$56$	−17.7796	−	16.4756i	−2.37590	−	2.20164i
$57$	1.69453			0.224446
$58$	0.658326	−	1.14025i	0.0864425	−	0.149723i
$59$	8.27708			1.07758			0.538792	−	0.842439i	$-0.318881\pi$
$59$	8.27708			1.07758			0.538792	+	0.842439i	$0.318881\pi$
$60$	10.4475	−	18.0956i	1.34877	−	2.33614i
$61$	4.54246	−	7.86777i	0.581602	−	1.00736i	−0.413688	−	0.910419i	$-0.635759\pi$
$61$	4.54246	−	7.86777i	0.581602	−	1.00736i	0.995290	−	0.0969455i	$-0.0309072\pi$
$62$	2.48571	−	4.30537i	0.315685	−	0.546783i
$63$	−2.52770	+	0.781496i	−0.318460	+	0.0984592i
$64$	26.1800			3.27250
$65$	−6.31559	−	12.5162i	−0.783352	−	1.55244i
$66$	−2.21536	+	3.83712i	−0.272692	+	0.472317i
$67$	−0.500271	−	0.866495i	−0.0611178	−	0.105859i	0.833847	−	0.551995i	$-0.186133\pi$
$67$	−0.500271	−	0.866495i	−0.0611178	−	0.105859i	−0.894965	+	0.446136i	$0.852800\pi$
$68$	−22.5253			−2.73159
$69$	−0.395707	−	0.685385i	−0.0476376	−	0.0825107i
$70$	6.19844	−	27.2389i	0.740855	−	3.25567i
$71$	7.93720	+	13.7476i	0.941972	+	1.63154i	0.761703	+	0.647927i	$0.224364\pi$
$71$	7.93720	+	13.7476i	0.941972	+	1.63154i	0.180270	+	0.983617i	$0.442303\pi$
$72$	4.58086	−	7.93428i	0.539859	−	0.935064i
$73$	−2.92626	+	5.06843i	−0.342492	+	0.593214i	−0.984895	−	0.173153i	$-0.944604\pi$
$73$	−2.92626	+	5.06843i	−0.342492	+	0.593214i	0.642402	+	0.766367i	$0.277938\pi$
$74$	−1.87163			−0.217572
$75$	10.1186			1.16839
$76$	−4.55310	+	7.88620i	−0.522276	+	0.904609i
$77$	−0.957867	+	4.20933i	−0.109159	+	0.479698i
$78$	−4.41068	−	8.74107i	−0.499411	−	0.989731i
$79$	0.643065	+	1.11382i	0.0723505	+	0.125315i	0.899931	−	0.436032i	$-0.143617\pi$
$79$	0.643065	+	1.11382i	0.0723505	+	0.125315i	−0.827581	+	0.561347i	$0.810283\pi$
$80$	27.4721	+	47.5831i	3.07147	+	5.31995i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.06339	+	13.9662i	−0.890452	+	1.54231i
$83$	−6.18202			−0.678565			−0.339283	−	0.940684i	$-0.610184\pi$
$83$	−6.18202			−0.678565			−0.339283	+	0.940684i	$0.610184\pi$
$84$	3.15476	−	13.8635i	0.344212	−	1.51263i
$85$	−8.14908	−	14.1146i	−0.883892	−	1.53095i
$86$	−7.58229	−	13.1329i	−0.817620	−	1.41616i
$87$	0.484868			0.0519833
$88$	−7.47435	−	12.9460i	−0.796769	−	1.38004i
$89$	−4.40869			−0.467320			−0.233660	−	0.972318i	$-0.575070\pi$
$89$	−4.40869			−0.467320			−0.233660	+	0.972318i	$0.575070\pi$
$90$	10.5585			1.11297
$91$	−6.62127	−	6.86722i	−0.694098	−	0.719881i
$92$	4.25296			0.443402
$93$	1.83076			0.189841
$94$	0.793529	+	1.37443i	0.0818463	+	0.141762i
$95$	−6.58879			−0.675995
$96$	10.0243	+	17.3625i	1.02310	+	1.77206i
$97$	5.08782	+	8.81236i	0.516590	+	0.894759i	0.999814	+	0.0192631i	$0.00613202\pi$
$97$	5.08782	+	8.81236i	0.516590	+	0.894759i	−0.483225	+	0.875496i	$0.660535\pi$
$98$	−1.44519	−	18.9534i	−0.145987	−	1.91458i
$99$	−1.63165			−0.163987
$100$	−27.1880	+	47.0911i	−2.71880	+	4.70911i
$101$	−7.08643	−	12.2741i	−0.705126	−	1.22131i	−0.966646	−	0.256116i	$-0.917557\pi$
$101$	−7.08643	−	12.2741i	−0.705126	−	1.22131i	0.261520	−	0.965198i	$-0.415776\pi$
$102$	−5.69116	−	9.85738i	−0.563509	−	0.976026i
$103$	−0.891175	−	1.54356i	−0.0878101	−	0.152092i	0.818775	−	0.574114i	$-0.194654\pi$
$103$	−0.891175	−	1.54356i	−0.0878101	−	0.152092i	−0.906585	+	0.422023i	$0.861320\pi$
$104$	32.9807	+	1.85823i	3.23403	+	0.182214i
$105$	9.82836	−	3.03866i	0.959150	−	0.296543i
$106$	−8.27942	+	14.3404i	−0.804169	+	1.39286i
$107$	19.2154			1.85763			0.928814	−	0.370547i	$-0.120830\pi$
$107$	19.2154			1.85763			0.928814	+	0.370547i	$0.120830\pi$
$108$	5.37387			0.517101
$109$	−5.34907	+	9.26486i	−0.512348	+	0.887413i	0.487550	+	0.873095i	$0.337891\pi$
$109$	−5.34907	+	9.26486i	−0.512348	+	0.887413i	−0.999898	+	0.0143174i	$0.995442\pi$
$110$	8.61391	−	14.9197i	0.821304	−	1.42254i
$111$	−0.344621	−	0.596901i	−0.0327100	−	0.0566553i
$112$	27.4228	+	25.4114i	2.59121	+	2.40116i
$113$	−3.82284	−	6.62135i	−0.359622	−	0.622884i	0.628275	−	0.777991i	$-0.283761\pi$
$113$	−3.82284	−	6.62135i	−0.359622	−	0.622884i	−0.987898	+	0.155107i	$0.950428\pi$
$114$	−4.60148			−0.430968
$115$	1.53861	+	2.66496i	0.143477	+	0.248509i
$116$	−1.30281	+	2.25653i	−0.120963	+	0.209514i
$117$	1.97557	−	3.01614i	0.182642	−	0.278842i
$118$	−22.4763			−2.06911
$119$	−8.13447	−	7.53783i	−0.745685	−	0.690991i
$120$	−17.8116	+	30.8506i	−1.62597	+	2.81626i
$121$	4.16886	−	7.22068i	0.378987	−	0.656425i
$122$	−12.3350	+	21.3648i	−1.11676	+	1.93428i
$123$	−5.93881			−0.535485
$124$	−4.91915	+	8.52021i	−0.441752	+	0.765138i
$125$	−19.9025			−1.78013
$126$	6.86394	−	2.12214i	0.611488	−	0.189055i
$127$	1.88510	−	3.26510i	0.167276	−	0.289730i	−0.770185	−	0.637820i	$-0.779836\pi$
$127$	1.88510	−	3.26510i	0.167276	−	0.289730i	0.937461	+	0.348090i	$0.113170\pi$
$128$	−30.9944			−2.73954
$129$	2.79224	−	4.83630i	0.245843	−	0.425813i
$130$	17.1499	+	33.9876i	1.50415	+	2.98091i
$131$	9.00807	+	15.6024i	0.787039	+	1.36319i	0.927774	+	0.373143i	$0.121720\pi$
$131$	9.00807	+	15.6024i	0.787039	+	1.36319i	−0.140735	+	0.990047i	$0.544947\pi$
$132$	4.38414	−	7.59355i	0.381590	−	0.660934i
$133$	−4.28327	+	1.32427i	−0.371406	+	0.114829i
$134$	1.35848	+	2.35296i	0.117355	+	0.203264i
$135$	1.94413	+	3.36734i	0.167324	+	0.289814i
$136$	38.4025			3.29299
$137$	21.7972			1.86226			0.931128	−	0.364692i	$-0.118826\pi$
$137$	21.7972			1.86226			0.931128	+	0.364692i	$0.118826\pi$
$138$	1.07454	+	1.86116i	0.0914708	+	0.158432i
$139$	0.355981	+	0.616576i	0.0301939	+	0.0522973i	0.880727	−	0.473623i	$-0.157054\pi$
$139$	0.355981	+	0.616576i	0.0301939	+	0.0522973i	−0.850534	+	0.525921i	$0.823721\pi$
$140$	−12.2665	+	53.9050i	−1.03671	+	4.55581i
$141$	−0.292223	+	0.506146i	−0.0246096	+	0.0426252i
$142$	−21.5534	−	37.3315i	−1.80872	−	3.13279i
$143$	−2.65024	−	5.25223i	−0.221624	−	0.439213i
$144$	−7.06539	+	12.2376i	−0.588782	+	1.01980i
$145$	−1.88529			−0.156565
$146$	7.94622	−	13.7632i	0.657633	−	1.13905i
$147$	5.77853	−	3.95077i	0.476605	−	0.325854i
$148$	3.70390			0.304459
$149$	2.79640	−	4.84351i	0.229090	−	0.396796i	−0.728448	−	0.685101i	$-0.759758\pi$
$149$	2.79640	−	4.84351i	0.229090	−	0.396796i	0.957539	+	0.288305i	$0.0930916\pi$
$150$	−27.4769			−2.24348
$151$	4.99718	−	8.65536i	0.406664	−	0.704364i	−0.587849	−	0.808971i	$-0.700025\pi$
$151$	4.99718	−	8.65536i	0.406664	−	0.704364i	0.994514	+	0.104607i	$0.0333585\pi$
$152$	7.76241	−	13.4449i	0.629614	−	1.09052i
$153$	2.09582	−	3.63006i	0.169437	−	0.293473i
$154$	2.60108	−	11.4304i	0.209601	−	0.921086i
$155$	−7.11849			−0.571771
$156$	8.72862	+	17.2983i	0.698849	+	1.38497i
$157$	9.42039	−	16.3166i	0.751829	−	1.30221i	−0.195106	−	0.980782i	$-0.562505\pi$
$157$	9.42039	−	16.3166i	0.751829	−	1.30221i	0.946935	−	0.321424i	$-0.104162\pi$
$158$	−1.74624	−	3.02457i	−0.138923	−	0.240622i
$159$	−6.09793			−0.483597
$160$	−38.9770	−	67.5101i	−3.08140	−	5.33714i
$161$	1.53586	+	1.42320i	0.121042	+	0.112164i
$162$	1.35774	+	2.35168i	0.106674	+	0.184766i
$163$	12.2236	−	21.1718i	0.957423	−	1.65830i	0.228699	−	0.973497i	$-0.426553\pi$
$163$	12.2236	−	21.1718i	0.957423	−	1.65830i	0.728724	−	0.684808i	$-0.240114\pi$
$164$	15.9572	−	27.6387i	1.24605	−	2.15822i
$165$	6.34428			0.493902
$166$	16.7872			1.30294
$167$	−4.28482	+	7.42152i	−0.331569	+	0.574295i	−0.982820	−	0.184568i	$-0.940911\pi$
$167$	−4.28482	+	7.42152i	−0.331569	+	0.574295i	0.651251	+	0.758863i	$0.274245\pi$
$168$	−5.37843	+	23.6354i	−0.414955	+	1.82351i
$169$	12.9177	+	1.46028i	0.993671	+	0.112329i
$170$	22.1287	+	38.3281i	1.69720	+	2.93963i
$171$	−0.847266	−	1.46751i	−0.0647920	−	0.112223i
$172$	15.0051	+	25.9897i	1.14413	+	1.98169i
$173$	−3.84040	+	6.65176i	−0.291980	+	0.505724i	−0.974278	−	0.225350i	$-0.927647\pi$
$173$	−3.84040	+	6.65176i	−0.291980	+	0.505724i	0.682298	+	0.731074i	$0.260981\pi$
$174$	−1.31665			−0.0998152
$175$	−25.5768	+	7.90764i	−1.93342	+	0.597761i
$176$	11.5282	+	19.9675i	0.868974	+	1.50511i
$177$	−4.13854	−	7.16816i	−0.311072	−	0.538792i
$178$	11.9717			0.897319
$179$	−4.87194	−	8.43845i	−0.364146	−	0.630719i	0.624493	−	0.781031i	$-0.285306\pi$
$179$	−4.87194	−	8.43845i	−0.364146	−	0.630719i	−0.988639	+	0.150311i	$0.951972\pi$
$180$	−20.8950			−1.55742
$181$	−6.23699			−0.463592			−0.231796	−	0.972764i	$-0.574460\pi$
$181$	−6.23699			−0.463592			−0.231796	+	0.972764i	$0.574460\pi$
$182$	17.9800	+	18.6479i	1.33277	+	1.38227i
$183$	−9.08491			−0.671576
$184$	−7.25072			−0.534530
$185$	1.33998	+	2.32091i	0.0985171	+	0.170637i
$186$	−4.97142			−0.364522
$187$	−3.41964	−	5.92298i	−0.250069	−	0.433131i
$188$	−1.57037	−	2.71996i	−0.114531	−	0.198374i
$189$	1.94064	+	1.79830i	0.141161	+	0.130807i
$190$	17.8918			1.29801
$191$	−1.52382	+	2.63934i	−0.110260	+	0.190976i	−0.915875	−	0.401464i	$-0.868502\pi$
$191$	−1.52382	+	2.63934i	−0.110260	+	0.190976i	0.805615	+	0.592439i	$0.201835\pi$
$192$	−13.0900	−	22.6725i	−0.944689	−	1.63625i
$193$	−4.49172	−	7.77988i	−0.323321	−	0.560008i	0.657850	−	0.753149i	$-0.271466\pi$
$193$	−4.49172	−	7.77988i	−0.323321	−	0.560008i	−0.981171	+	0.193141i	$0.938133\pi$
$194$	−13.8159	−	23.9299i	−0.991924	−	1.71806i
$195$	−7.68155	+	11.7276i	−0.550087	+	0.839828i
$196$	2.86000	+	37.5082i	0.204286	+	2.67916i
$197$	−8.42977	+	14.6008i	−0.600596	+	1.04026i	0.392135	+	0.919908i	$0.371737\pi$
$197$	−8.42977	+	14.6008i	−0.600596	+	1.04026i	−0.992731	+	0.120355i	$0.961597\pi$
$198$	4.43072			0.314878
$199$	−2.04525			−0.144984			−0.0724919	−	0.997369i	$-0.523095\pi$
$199$	−2.04525			−0.144984			−0.0724919	+	0.997369i	$0.523095\pi$
$200$	46.3519	−	80.2838i	3.27757	−	5.67692i
$201$	−0.500271	+	0.866495i	−0.0352864	+	0.0611178i
$202$	19.2431	+	33.3300i	1.35394	+	2.34509i
$203$	−1.22560	+	0.378922i	−0.0860203	+	0.0265951i
$204$	11.2626	+	19.5075i	0.788543	+	1.36580i
$205$	23.0917			1.61279
$206$	2.41998	+	4.19152i	0.168608	+	0.292037i
$207$	−0.395707	+	0.685385i	−0.0275036	+	0.0476376i
$208$	−50.8686	−	2.86608i	−3.52710	−	0.198727i
$209$	−2.76488			−0.191251
$210$	−26.6888	+	8.25145i	−1.84170	+	0.569404i
$211$	12.3382	−	21.3705i	0.849400	−	1.47120i	−0.0323446	−	0.999477i	$-0.510297\pi$
$211$	12.3382	−	21.3705i	0.849400	−	1.47120i	0.881745	−	0.471727i	$-0.156369\pi$
$212$	16.3847	−	28.3792i	1.12531	−	1.94909i
$213$	7.93720	−	13.7476i	0.543848	−	0.941972i
$214$	−52.1793			−3.56690
$215$	−10.8570	+	18.8048i	−0.740439	+	1.28248i
$216$	−9.16172			−0.623376
$217$	−4.62762	+	1.43073i	−0.314143	+	0.0971245i
$218$	14.5253	−	25.1586i	0.983780	−	1.70396i
$219$	5.85251			0.395476
$220$	−17.0467	+	29.5257i	−1.14929	+	1.99062i
$221$	15.0892	+	0.850170i	1.01501	+	0.0571886i
$222$	0.935814	+	1.62088i	0.0628077	+	0.108786i
$223$	−8.99595	+	15.5814i	−0.602413	+	1.04341i	0.390041	+	0.920797i	$0.372461\pi$
$223$	−8.99595	+	15.5814i	−0.602413	+	1.04341i	−0.992455	+	0.122613i	$0.960873\pi$
$224$	−38.9071	−	36.0534i	−2.59959	−	2.40892i
$225$	−5.05930	−	8.76296i	−0.337287	−	0.584197i
$226$	10.3809	+	17.9802i	0.690525	+	1.19603i
$227$	−8.34572			−0.553925			−0.276963	−	0.960881i	$-0.589328\pi$
$227$	−8.34572			−0.553925			−0.276963	+	0.960881i	$0.589328\pi$
$228$	9.10620			0.603073
$229$	−11.1172	−	19.2556i	−0.734647	−	1.27245i	−0.954878	−	0.296998i	$-0.904015\pi$
$229$	−11.1172	−	19.2556i	−0.734647	−	1.27245i	0.220232	−	0.975448i	$-0.429319\pi$
$230$	−4.17809	−	7.23666i	−0.275495	−	0.477172i
$231$	4.12432	−	1.27513i	0.271360	−	0.0838972i
$232$	2.22111	−	3.84708i	0.145823	−	0.252573i
$233$	2.50918	+	4.34602i	0.164382	+	0.284717i	0.936435	−	0.350840i	$-0.114104\pi$
$233$	2.50918	+	4.34602i	0.164382	+	0.284717i	−0.772054	+	0.635557i	$0.780771\pi$
$234$	−5.36464	+	8.19030i	−0.350698	+	0.535416i
$235$	1.13624	−	1.96803i	0.0741202	−	0.128380i
$236$	44.4800			2.89540
$237$	0.643065	−	1.11382i	0.0417716	−	0.0723505i
$238$	22.0890	+	20.4689i	1.43182	+	1.32680i
$239$	9.28305			0.600470			0.300235	−	0.953865i	$-0.402935\pi$
$239$	9.28305			0.600470			0.300235	+	0.953865i	$0.402935\pi$
$240$	27.4721	−	47.5831i	1.77332	−	3.07147i
$241$	−14.7894			−0.952668			−0.476334	−	0.879264i	$-0.658035\pi$
$241$	−14.7894			−0.952668			−0.476334	+	0.879264i	$0.658035\pi$
$242$	−11.3205	+	19.6077i	−0.727709	+	1.26043i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	24.4106	−	42.2804i	1.56273	−	2.70672i
$245$	−22.4684	+	15.3616i	−1.43546	+	0.981419i
$246$	16.1268			1.02821
$247$	3.34767	−	5.11095i	0.213007	−	0.325202i
$248$	8.38647	−	14.5258i	0.532541	−	0.922388i
$249$	3.09101	+	5.35379i	0.195885	+	0.339283i
$250$	54.0449			3.41810
$251$	4.80626	+	8.32468i	0.303368	+	0.525449i	0.976897	−	0.213712i	$-0.0685555\pi$
$251$	4.80626	+	8.32468i	0.303368	+	0.525449i	−0.673529	+	0.739161i	$0.735222\pi$
$252$	−13.5835	+	4.19966i	−0.855683	+	0.264554i
$253$	0.645656	+	1.11831i	0.0405920	+	0.0703075i
$254$	−5.11898	+	8.86633i	−0.321193	+	0.556323i
$255$	−8.14908	+	14.1146i	−0.510315	+	0.883892i
$256$	31.8049			1.98780
$257$	5.05576			0.315370			0.157685	−	0.987489i	$-0.449597\pi$
$257$	5.05576			0.315370			0.157685	+	0.987489i	$0.449597\pi$
$258$	−7.58229	+	13.1329i	−0.472053	+	0.817620i
$259$	1.33757	+	1.23947i	0.0831128	+	0.0770167i
$260$	−33.9392	−	67.2605i	−2.10482	−	4.17132i
$261$	−0.242434	−	0.419908i	−0.0150063	−	0.0259916i
$262$	−24.4613	−	42.3682i	−1.51122	−	2.61752i
$263$	−11.6769	−	20.2250i	−0.720027	−	1.24712i	−0.960988	−	0.276589i	$-0.910796\pi$
$263$	−11.6769	−	20.2250i	−0.720027	−	1.24712i	0.240961	−	0.970535i	$-0.422537\pi$
$264$	−7.47435	+	12.9460i	−0.460015	+	0.796769i
$265$	23.7104			1.45652
$266$	11.6312	−	3.59604i	0.713152	−	0.220487i
$267$	2.20434	+	3.81803i	0.134904	+	0.233660i
$268$	−2.68839	−	4.65644i	−0.164220	−	0.284437i
$269$	−31.3914			−1.91397			−0.956984	−	0.290141i	$-0.906298\pi$
$269$	−31.3914			−1.91397			−0.956984	+	0.290141i	$0.906298\pi$
$270$	−5.27927	−	9.14396i	−0.321286	−	0.556484i
$271$	−11.3303			−0.688267			−0.344134	−	0.938921i	$-0.611827\pi$
$271$	−11.3303			−0.688267			−0.344134	+	0.938921i	$0.611827\pi$
$272$	−59.2310			−3.59141
$273$	−2.63655	+	9.16780i	−0.159571	+	0.554861i
$274$	−59.1899			−3.57579
$275$	−16.5100			−0.995591
$276$	−2.12648	−	3.68318i	−0.127999	−	0.221701i
$277$	17.9226			1.07686			0.538432	−	0.842669i	$-0.319017\pi$
$277$	17.9226			1.07686			0.538432	+	0.842669i	$0.319017\pi$
$278$	−0.966661	−	1.67431i	−0.0579765	−	0.100418i
$279$	−0.915382	−	1.58549i	−0.0548025	−	0.0949207i
$280$	20.9127	−	91.9006i	1.24978	−	5.49211i
$281$	−11.6172			−0.693021			−0.346511	−	0.938046i	$-0.612634\pi$
$281$	−11.6172			−0.693021			−0.346511	+	0.938046i	$0.612634\pi$
$282$	0.793529	−	1.37443i	0.0472540	−	0.0818463i
$283$	4.04596	+	7.00781i	0.240507	+	0.416571i	0.960859	−	0.277038i	$-0.0893528\pi$
$283$	4.04596	+	7.00781i	0.240507	+	0.416571i	−0.720352	+	0.693609i	$0.756019\pi$
$284$	42.6535	+	73.8781i	2.53102	+	4.38386i
$285$	3.29439	+	5.70606i	0.195143	+	0.337998i
$286$	7.19669	+	14.2624i	0.425549	+	0.843351i
$287$	15.0115	−	4.64116i	0.886103	−	0.273959i
$288$	10.0243	−	17.3625i	0.590685	−	1.02310i
$289$	0.569768			0.0335158
$290$	5.11949			0.300627
$291$	5.08782	−	8.81236i	0.298253	−	0.516590i
$292$	−15.7253	+	27.2371i	−0.920256	+	1.59393i
$293$	−8.90887	−	15.4306i	−0.520461	−	0.901466i	−0.999717	−	0.0237903i	$-0.992427\pi$
$293$	−8.90887	−	15.4306i	−0.520461	−	0.901466i	0.479255	−	0.877675i	$-0.340907\pi$
$294$	−15.6915	+	10.7283i	−0.915148	+	0.625686i
$295$	16.0917	+	27.8717i	0.936897	+	1.62275i
$296$	−6.31464			−0.367031
$297$	0.815825	+	1.41305i	0.0473389	+	0.0819935i
$298$	−7.59360	+	13.1525i	−0.439885	+	0.761904i
$299$	−2.84897	−	0.160519i	−0.164760	−	0.00928306i
$300$	54.3761			3.13940
$301$	−3.27840	+	14.4068i	−0.188964	+	0.830396i
$302$	−13.5698	+	23.5035i	−0.780853	+	1.35248i
$303$	−7.08643	+	12.2741i	−0.407105	+	0.705126i
$304$	−11.9725	+	20.7370i	−0.686671	+	1.18935i
$305$	35.3245			2.02268
$306$	−5.69116	+	9.85738i	−0.325342	+	0.563509i
$307$	16.1633			0.922487			0.461244	−	0.887274i	$-0.347403\pi$
$307$	16.1633			0.922487			0.461244	+	0.887274i	$0.347403\pi$
$308$	−5.14746	+	22.6204i	−0.293304	+	1.28892i
$309$	−0.891175	+	1.54356i	−0.0506972	+	0.0878101i
$310$	19.3302			1.09788
$311$	9.06145	−	15.6949i	0.513827	−	0.889975i	−0.486044	−	0.873934i	$-0.661560\pi$
$311$	9.06145	−	15.6949i	0.513827	−	0.889975i	0.999871	−	0.0160409i	$-0.00510619\pi$
$312$	−14.8811	−	29.4913i	−0.842476	−	1.66961i
$313$	12.8068	+	22.1820i	0.723882	+	1.25380i	0.959432	+	0.281939i	$0.0909774\pi$
$313$	12.8068	+	22.1820i	0.723882	+	1.25380i	−0.235550	+	0.971862i	$0.575689\pi$
$314$	−25.5810	+	44.3075i	−1.44362	+	2.50042i
$315$	−7.54574	−	6.99228i	−0.425154	−	0.393970i
$316$	3.45575	+	5.98554i	0.194401	+	0.336713i
$317$	13.7304	+	23.7817i	0.771174	+	1.33571i	0.936920	+	0.349544i	$0.113663\pi$
$317$	13.7304	+	23.7817i	0.771174	+	1.33571i	−0.165746	+	0.986168i	$0.553003\pi$
$318$	16.5588			0.928574
$319$	−0.791134			−0.0442950
$320$	50.8973	+	88.1568i	2.84525	+	4.92811i
$321$	−9.60772	−	16.6411i	−0.536251	−	0.928814i
$322$	−4.17060	−	3.86470i	−0.232418	−	0.215371i
$323$	3.55143	−	6.15125i	0.197607	−	0.342265i
$324$	−2.68694	−	4.65391i	−0.149274	−	0.258551i
$325$	19.9900	−	30.5191i	1.10885	−	1.69290i
$326$	−33.1929	+	57.4918i	−1.83839	+	3.18418i
$327$	10.6981			0.591609
$328$	−27.2049	+	47.1202i	−1.50214	+	2.60178i
$329$	0.343102	−	1.50776i	0.0189158	−	0.0831252i
$330$	−17.2278			−0.948361
$331$	−3.47563	+	6.01996i	−0.191038	+	0.330887i	−0.945594	−	0.325348i	$-0.894519\pi$
$331$	−3.47563	+	6.01996i	−0.191038	+	0.330887i	0.754557	+	0.656235i	$0.227852\pi$
$332$	−33.2214			−1.82326
$333$	−0.344621	+	0.596901i	−0.0188851	+	0.0327100i
$334$	11.6354	−	20.1531i	0.636659	−	1.10273i
$335$	1.94519	−	3.36916i	0.106277	−	0.184077i
$336$	8.29554	−	36.4546i	0.452559	−	1.98876i
$337$	29.0505			1.58248			0.791242	−	0.611503i	$-0.209435\pi$
$337$	29.0505			1.58248			0.791242	+	0.611503i	$0.209435\pi$
$338$	−35.0779	−	3.96537i	−1.90799	−	0.215688i
$339$	−3.82284	+	6.62135i	−0.207628	+	0.359622i
$340$	−43.7922	−	75.8502i	−2.37496	−	4.11356i
$341$	−2.98716			−0.161764
$342$	2.30074	+	3.98500i	0.124410	+	0.215484i
$343$	−11.5189	+	14.5023i	−0.621961	+	0.783048i
$344$	−25.5817	−	44.3088i	−1.37927	−	2.38897i
$345$	1.53861	−	2.66496i	0.0828362	−	0.143477i
$346$	10.4285	−	18.0628i	0.560642	−	0.971061i
$347$	5.10846			0.274236			0.137118	−	0.990555i	$-0.456216\pi$
$347$	5.10846			0.274236			0.137118	+	0.990555i	$0.456216\pi$
$348$	2.60562			0.139676
$349$	12.2420	−	21.2038i	0.655300	−	1.13501i	−0.326519	−	0.945191i	$-0.605876\pi$
$349$	12.2420	−	21.2038i	0.655300	−	1.13501i	0.981819	−	0.189822i	$-0.0607911\pi$
$350$	69.4534	−	21.4731i	3.71244	−	1.14779i
$351$	−3.59984	−	0.202826i	−0.192145	−	0.0108260i
$352$	−16.3561	−	28.3296i	−0.871782	−	1.50997i
$353$	−2.07090	−	3.58690i	−0.110223	−	0.190912i	0.805637	−	0.592409i	$-0.201823\pi$
$353$	−2.07090	−	3.58690i	−0.110223	−	0.190912i	−0.915860	+	0.401498i	$0.868490\pi$
$354$	11.2381	+	19.4650i	0.597301	+	1.03456i
$355$	−30.8619	+	53.4544i	−1.63798	+	2.83707i
$356$	−23.6917			−1.25566
$357$	−2.46072	+	10.8136i	−0.130235	+	0.572315i
$358$	13.2297	+	22.9145i	0.699211	+	1.21107i
$359$	6.45007	+	11.1718i	0.340421	+	0.589627i	0.984511	−	0.175323i	$-0.0560969\pi$
$359$	6.45007	+	11.1718i	0.340421	+	0.589627i	−0.644090	+	0.764950i	$0.722764\pi$
$360$	35.6232			1.87751
$361$	8.06428	+	13.9677i	0.424436	+	0.735144i
$362$	16.9365			0.890162
$363$	−8.33772			−0.437617
$364$	−35.5819	−	36.9036i	−1.86500	−	1.93427i
$365$	−22.7561			−1.19111
$366$	24.6700			1.28952
$367$	−3.68288	−	6.37894i	−0.192245	−	0.332978i	0.753749	−	0.657162i	$-0.228243\pi$
$367$	−3.68288	−	6.37894i	−0.192245	−	0.332978i	−0.945994	+	0.324185i	$0.894910\pi$
$368$	11.1833			0.582970
$369$	2.96941	+	5.14316i	0.154581	+	0.267742i
$370$	−3.63869	−	6.30240i	−0.189167	−	0.327646i
$371$	15.4137	−	4.76550i	0.800241	−	0.247413i
$372$	9.83829			0.510092
$373$	11.8284	−	20.4874i	0.612451	−	1.06080i	−0.378375	−	0.925652i	$-0.623517\pi$
$373$	11.8284	−	20.4874i	0.612451	−	1.06080i	0.990826	−	0.135144i	$-0.0431496\pi$
$374$	9.28598	+	16.0838i	0.480167	+	0.831673i
$375$	9.95123	+	17.2360i	0.513879	+	0.890065i
$376$	2.67727	+	4.63716i	0.138070	+	0.239143i
$377$	0.957892	−	1.46243i	0.0493339	−	0.0753190i
$378$	−5.26980	−	4.88327i	−0.271049	−	0.251168i
$379$	−5.12668	+	8.87966i	−0.263340	+	0.456118i	−0.967127	−	0.254293i	$-0.918157\pi$
$379$	−5.12668	+	8.87966i	−0.263340	+	0.456118i	0.703788	+	0.710410i	$0.251491\pi$
$380$	−35.4073			−1.81636
$381$	−3.77021			−0.193154
$382$	4.13792	−	7.16708i	0.211714	−	0.366700i
$383$	9.66599	−	16.7420i	0.493909	−	0.855475i	−0.506067	−	0.862494i	$-0.668901\pi$
$383$	9.66599	−	16.7420i	0.493909	−	0.855475i	0.999975	+	0.00701929i	$0.00223433\pi$
$384$	15.4972	+	26.8419i	0.790837	+	1.36977i
$385$	−16.0364	+	4.95803i	−0.817293	+	0.252685i
$386$	12.1972	+	21.1262i	0.620821	+	1.07529i
$387$	−5.58448			−0.283875
$388$	27.3413	+	47.3565i	1.38804	+	2.40416i
$389$	−5.95876	+	10.3209i	−0.302121	+	0.523289i	−0.976616	−	0.214990i	$-0.931028\pi$
$389$	−5.95876	+	10.3209i	−0.302121	+	0.523289i	0.674495	+	0.738279i	$0.264361\pi$
$390$	20.8592	−	31.8460i	1.05624	−	1.61259i
$391$	−3.31732			−0.167764
$392$	−4.87590	−	63.9464i	−0.246270	−	3.22978i
$393$	9.00807	−	15.6024i	0.454397	−	0.787039i
$394$	22.8909	−	39.6483i	1.15323	−	1.99745i
$395$	−2.50041	+	4.33083i	−0.125809	+	0.217908i
$396$	−8.76828			−0.440623
$397$	−0.483606	+	0.837630i	−0.0242715	+	0.0420395i	−0.877906	−	0.478833i	$-0.841060\pi$
$397$	−0.483606	+	0.837630i	−0.0242715	+	0.0420395i	0.853635	+	0.520872i	$0.174393\pi$
$398$	5.55385			0.278389
$399$	3.28848	+	3.04728i	0.164630	+	0.152555i
$400$	−71.4918	+	123.827i	−3.57459	+	6.19137i
$401$	−23.4745			−1.17226			−0.586131	−	0.810217i	$-0.699349\pi$
$401$	−23.4745			−1.17226			−0.586131	+	0.810217i	$0.699349\pi$
$402$	1.35848	−	2.35296i	0.0677548	−	0.117355i
$403$	3.61681	−	5.52184i	0.180166	−	0.275063i
$404$	−38.0816	−	65.9592i	−1.89463	−	3.28159i
$405$	1.94413	−	3.36734i	0.0966047	−	0.167324i
$406$	3.32810	−	1.02896i	0.165171	−	0.0510663i
$407$	0.562300	+	0.973933i	0.0278722	+	0.0482761i
$408$	−19.2013	−	33.2576i	−0.950604	−	1.64649i
$409$	−19.0317			−0.941059			−0.470529	−	0.882384i	$-0.655937\pi$
$409$	−19.0317			−0.941059			−0.470529	+	0.882384i	$0.655937\pi$
$410$	−62.7052			−3.09679
$411$	−10.8986	−	18.8769i	−0.537587	−	0.931128i
$412$	−4.78907	−	8.29490i	−0.235940	−	0.408661i
$413$	16.0629	+	14.8847i	0.790402	+	0.732428i
$414$	1.07454	−	1.86116i	0.0528107	−	0.0914708i
$415$	−12.0187	−	20.8169i	−0.589973	−	1.02186i
$416$	72.1715	+	4.06635i	3.53850	+	0.199369i
$417$	0.355981	−	0.616576i	0.0174324	−	0.0301939i
$418$	7.50800			0.367228
$419$	16.1312	−	27.9400i	0.788060	−	1.36496i	−0.139093	−	0.990279i	$-0.544419\pi$
$419$	16.1312	−	27.9400i	0.788060	−	1.36496i	0.927154	−	0.374681i	$-0.122248\pi$
$420$	52.8164	−	16.3294i	2.57718	−	0.796792i
$421$	−34.4202			−1.67754			−0.838769	−	0.544488i	$-0.816724\pi$
$421$	−34.4202			−1.67754			−0.838769	+	0.544488i	$0.816724\pi$
$422$	−33.5044	+	58.0313i	−1.63097	+	2.82492i
$423$	0.584447			0.0284168
$424$	−27.9337	+	48.3827i	−1.35658	+	2.34967i
$425$	21.2067	−	36.7311i	1.02868	−	1.78172i
$426$	−21.5534	+	37.3315i	−1.04426	+	1.80872i
$427$	22.9639	−	7.09982i	1.11130	−	0.343584i
$428$	103.261			4.99133
$429$	−3.22344	+	4.92129i	−0.155629	+	0.237602i
$430$	29.4820	−	51.0643i	1.42175	−	2.46254i
$431$	−0.996911	−	1.72670i	−0.0480195	−	0.0831722i	0.841017	−	0.541009i	$-0.181958\pi$
$431$	−0.996911	−	1.72670i	−0.0480195	−	0.0831722i	−0.889036	+	0.457837i	$0.848624\pi$
$432$	14.1308			0.679867
$433$	3.70848	+	6.42328i	0.178218	+	0.308683i	0.941270	−	0.337654i	$-0.109633\pi$
$433$	3.70848	+	6.42328i	0.178218	+	0.308683i	−0.763052	+	0.646337i	$0.776300\pi$
$434$	12.5662	−	3.88514i	0.603199	−	0.186493i
$435$	0.942647	+	1.63271i	0.0451965	+	0.0782826i
$436$	−28.7452	+	49.7882i	−1.37665	+	2.38442i
$437$	−0.670539	+	1.16141i	−0.0320762	+	0.0555576i
$438$	−15.8924			−0.759370
$439$	20.7746			0.991520			0.495760	−	0.868460i	$-0.334890\pi$
$439$	20.7746			0.991520			0.495760	+	0.868460i	$0.334890\pi$
$440$	29.0623	−	50.3373i	1.38549	−	2.39974i
$441$	−6.31073	−	3.02897i	−0.300511	−	0.144237i
$442$	−40.9746	−	2.30863i	−1.94896	−	0.109810i
$443$	−2.67178	−	4.62766i	−0.126940	−	0.219867i	0.795550	−	0.605889i	$-0.207182\pi$
$443$	−2.67178	−	4.62766i	−0.126940	−	0.219867i	−0.922490	+	0.386022i	$0.873849\pi$
$444$	−1.85195	−	3.20767i	−0.0878896	−	0.152229i
$445$	−8.57107	−	14.8455i	−0.406308	−	0.703745i
$446$	24.4284	−	42.3112i	1.15672	−	2.00349i
$447$	−5.59281			−0.264531
$448$	50.8060	+	47.0796i	2.40036	+	2.22430i
$449$	−15.0969	−	26.1486i	−0.712468	−	1.23403i	−0.963928	−	0.266163i	$-0.914244\pi$
$449$	−15.0969	−	26.1486i	−0.712468	−	1.23403i	0.251460	−	0.967868i	$-0.419089\pi$
$450$	13.7385	+	23.7957i	0.647637	+	1.12174i
$451$	9.69006			0.456287
$452$	−20.5435	−	35.5823i	−0.966283	−	1.67365i
$453$	−9.99435			−0.469576
$454$	22.6627			1.06361
$455$	10.2516	−	35.6468i	0.480603	−	1.67115i
$456$	−15.5248			−0.727016
$457$	−31.0204			−1.45108			−0.725538	−	0.688182i	$-0.758409\pi$
$457$	−31.0204			−1.45108			−0.725538	+	0.688182i	$0.758409\pi$
$458$	30.1887	+	52.2883i	1.41062	+	2.44327i
$459$	−4.19163			−0.195649
$460$	8.26832	+	14.3212i	0.385513	+	0.667727i
$461$	−2.19226	−	3.79710i	−0.102104	−	0.176848i	0.810448	−	0.585811i	$-0.199224\pi$
$461$	−2.19226	−	3.79710i	−0.102104	−	0.176848i	−0.912551	+	0.408963i	$0.865891\pi$
$462$	−11.1995	+	3.46259i	−0.521050	+	0.161094i
$463$	4.93368			0.229288			0.114644	−	0.993407i	$-0.463427\pi$
$463$	4.93368			0.229288			0.114644	+	0.993407i	$0.463427\pi$
$464$	−3.42578	+	5.93362i	−0.159038	+	0.275462i
$465$	3.55925	+	6.16479i	0.165056	+	0.285885i
$466$	−6.81364	−	11.8016i	−0.315636	−	0.546697i
$467$	3.98764	+	6.90680i	0.184526	+	0.319609i	0.943417	−	0.331610i	$-0.107592\pi$
$467$	3.98764	+	6.90680i	0.184526	+	0.319609i	−0.758891	+	0.651218i	$0.774258\pi$
$468$	10.6165	−	16.2084i	0.490747	−	0.749232i
$469$	0.587373	−	2.58120i	0.0271224	−	0.119189i
$470$	−3.08545	+	5.34416i	−0.142321	+	0.246508i
$471$	−18.8408			−0.868138
$472$	−75.8322			−3.49046
$473$	−4.55596	+	7.89115i	−0.209483	+	0.362835i
$474$	−1.74624	+	3.02457i	−0.0802073	+	0.138923i
$475$	−8.57314	−	14.8491i	−0.393363	−	0.681324i
$476$	−43.7136	−	40.5073i	−2.00361	−	1.85665i
$477$	3.04896	+	5.28096i	0.139602	+	0.241799i
$478$	−25.2080			−1.15299
$479$	16.1727	+	28.0119i	0.738949	+	1.27990i	0.952969	+	0.303068i	$0.0980108\pi$
$479$	16.1727	+	28.0119i	0.738949	+	1.27990i	−0.214020	+	0.976829i	$0.568656\pi$
$480$	−38.9770	+	67.5101i	−1.77905	+	3.08140i
$481$	−2.48116	−	0.139796i	−0.113131	−	0.00637414i
$482$	40.1604			1.82926
$483$	0.464604	−	2.04169i	0.0211402	−	0.0929002i
$484$	22.4029	−	38.8030i	1.01832	−	1.76377i
$485$	−19.7828	+	34.2648i	−0.898290	+	1.55588i
$486$	1.35774	−	2.35168i	0.0615885	−	0.106674i
$487$	33.1101			1.50036			0.750182	−	0.661232i	$-0.229966\pi$
$487$	33.1101			1.50036			0.750182	+	0.661232i	$0.229966\pi$
$488$	−41.6167	+	72.0822i	−1.88390	+	3.26301i
$489$	−24.4471			−1.10554
$490$	61.0128	−	41.7144i	2.75628	−	1.88446i
$491$	5.01799	−	8.69141i	0.226459	−	0.392238i	−0.730297	−	0.683129i	$-0.760618\pi$
$491$	5.01799	−	8.69141i	0.226459	−	0.392238i	0.956756	+	0.290891i	$0.0939518\pi$
$492$	−31.9144			−1.43881
$493$	1.01619	−	1.76010i	0.0457670	−	0.0792708i
$494$	−9.09056	+	13.8787i	−0.409004	+	0.624433i
$495$	−3.17214	−	5.49431i	−0.142577	−	0.246951i
$496$	−12.9351	+	22.4042i	−0.580801	+	1.00598i
$497$	−9.31914	+	40.9528i	−0.418021	+	1.83698i
$498$	−8.39361	−	14.5382i	−0.376126	−	0.651470i
$499$	−10.4771	−	18.1469i	−0.469021	−	0.812369i	0.530352	−	0.847778i	$-0.322060\pi$
$499$	−10.4771	−	18.1469i	−0.469021	−	0.812369i	−0.999373	+	0.0354090i	$0.988727\pi$
$500$	−106.953			−4.78310
$501$	8.56964			0.382863
$502$	−13.0513	−	22.6056i	−0.582509	−	1.00894i
$503$	18.5489	+	32.1277i	0.827056	+	1.43250i	0.900338	+	0.435192i	$0.143319\pi$
$503$	18.5489	+	32.1277i	0.827056	+	1.43250i	−0.0732818	+	0.997311i	$0.523347\pi$
$504$	23.1581	−	7.15984i	1.03154	−	0.318925i
$505$	27.5539	−	47.7248i	1.22613	−	2.12372i
$506$	−1.75327	−	3.03675i	−0.0779424	−	0.135000i
$507$	−5.19422	−	11.9172i	−0.230684	−	0.529262i
$508$	10.1303	−	17.5462i	0.449460	−	0.778488i
$509$	7.42063			0.328913			0.164457	−	0.986384i	$-0.447413\pi$
$509$	7.42063			0.328913			0.164457	+	0.986384i	$0.447413\pi$
$510$	22.1287	−	38.3281i	0.979877	−	1.69720i
$511$	−14.7934	+	4.57371i	−0.654421	+	0.202329i
$512$	−24.3770			−1.07732
$513$	−0.847266	+	1.46751i	−0.0374077	+	0.0647920i
$514$	−13.7289			−0.605554
$515$	3.46513	−	6.00177i	0.152692	−	0.264470i
$516$	15.0051	−	25.9897i	0.660565	−	1.14413i
$517$	0.476806	−	0.825852i	0.0209699	−	0.0363209i
$518$	−3.63216	−	3.36576i	−0.159588	−	0.147883i
$519$	7.68079			0.337149
$520$	57.8616	+	114.670i	2.53740	+	5.02860i
$521$	−4.32959	+	7.49907i	−0.189683	+	0.328540i	−0.945144	−	0.326653i	$-0.894079\pi$
$521$	−4.32959	+	7.49907i	−0.189683	+	0.328540i	0.755462	+	0.655193i	$0.227413\pi$
$522$	0.658326	+	1.14025i	0.0288142	+	0.0499076i
$523$	−22.0580			−0.964530			−0.482265	−	0.876025i	$-0.660186\pi$
$523$	−22.0580			−0.964530			−0.482265	+	0.876025i	$0.660186\pi$
$524$	48.4082	+	83.8455i	2.11472	+	3.66281i
$525$	19.6366	+	18.1963i	0.857012	+	0.794152i
$526$	31.7084	+	54.9206i	1.38255	+	2.39465i
$527$	3.83694	−	6.64578i	0.167140	−	0.289495i
$528$	11.5282	−	19.9675i	0.501702	−	0.868974i
$529$	−22.3737			−0.972768
$530$	−64.3852			−2.79671
$531$	−4.13854	+	7.16816i	−0.179597	+	0.311072i
$532$	−23.0177	+	7.11645i	−0.997945	+	0.308537i
$533$	−11.7326	+	17.9123i	−0.508194	+	0.775868i
$534$	−5.98587	−	10.3678i	−0.259034	−	0.448660i
$535$	37.3574	+	64.7049i	1.61510	+	2.79744i
$536$	4.58334	+	7.93858i	0.197970	+	0.342894i
$537$	−4.87194	+	8.43845i	−0.210240	+	0.364146i
$538$	85.2430			3.67509
$539$	−9.42853	+	6.44627i	−0.406116	+	0.277661i
$540$	10.4475	+	18.0956i	0.449590	+	0.778712i
$541$	1.78963	+	3.09972i	0.0769421	+	0.133268i	0.901929	−	0.431884i	$-0.142151\pi$
$541$	1.78963	+	3.09972i	0.0769421	+	0.133268i	−0.824987	+	0.565152i	$0.808818\pi$
$542$	30.7673			1.32157
$543$	3.11850	+	5.40139i	0.133828	+	0.231796i
$544$	84.0360			3.60302
$545$	−41.5972			−1.78183
$546$	7.15953	−	24.8951i	0.306400	−	1.06541i
$547$	−11.6996			−0.500238			−0.250119	−	0.968215i	$-0.580470\pi$
$547$	−11.6996			−0.500238			−0.250119	+	0.968215i	$0.580470\pi$
$548$	117.135			5.00377
$549$	4.54246	+	7.86777i	0.193867	+	0.335788i
$550$	44.8327			1.91167
$551$	−0.410812	−	0.711547i	−0.0175012	−	0.0303129i
$552$	3.62536	+	6.27931i	0.154306	+	0.267265i
$553$	−0.755029	+	3.31796i	−0.0321071	+	0.141094i
$554$	−48.6686			−2.06773
$555$	1.33998	−	2.32091i	0.0568788	−	0.0985171i
$556$	1.91300	+	3.31340i	0.0811291	+	0.140520i
$557$	−8.08689	−	14.0069i	−0.342653	−	0.593492i	0.642272	−	0.766477i	$-0.277992\pi$
$557$	−8.08689	−	14.0069i	−0.342653	−	0.593492i	−0.984924	+	0.172985i	$0.944659\pi$
$558$	2.48571	+	4.30537i	0.105228	+	0.182261i
$559$	−9.07070	−	17.9763i	−0.383650	−	0.760315i
$560$	−32.2553	+	141.745i	−1.36303	+	5.98982i
$561$	−3.41964	+	5.92298i	−0.144377	+	0.250069i
$562$	31.5462			1.33070
$563$	−24.7715			−1.04400			−0.521998	−	0.852947i	$-0.674813\pi$
$563$	−24.7715			−1.04400			−0.521998	+	0.852947i	$0.674813\pi$
$564$	−1.57037	+	2.71996i	−0.0661246	+	0.114531i
$565$	14.8642	−	25.7456i	0.625342	−	1.08312i
$566$	−10.9868	−	19.0296i	−0.461808	−	0.799875i
$567$	0.587055	−	2.57980i	0.0246540	−	0.108341i
$568$	−72.7184	−	125.952i	−3.05119	−	5.28482i
$569$	33.4519			1.40238			0.701189	−	0.712975i	$-0.252653\pi$
$569$	33.4519			1.40238			0.701189	+	0.712975i	$0.252653\pi$
$570$	−8.94588	−	15.4947i	−0.374702	−	0.649003i
$571$	−6.32788	+	10.9602i	−0.264814	+	0.458671i	−0.967515	−	0.252815i	$-0.918644\pi$
$571$	−6.32788	+	10.9602i	−0.264814	+	0.458671i	0.702701	+	0.711485i	$0.251977\pi$
$572$	−14.2420	−	28.2248i	−0.595490	−	1.18014i
$573$	3.04764			0.127317
$574$	−40.7636	+	12.6030i	−1.70144	+	0.526039i
$575$	−4.00400	+	6.93514i	−0.166979	+	0.289215i
$576$	−13.0900	+	22.6725i	−0.545416	+	0.944689i
$577$	10.9471	−	18.9609i	0.455733	−	0.789352i	−0.542997	−	0.839734i	$-0.682711\pi$
$577$	10.9471	−	18.9609i	0.455733	−	0.789352i	0.998730	+	0.0503824i	$0.0160440\pi$
$578$	−1.54720			−0.0643550
$579$	−4.49172	+	7.77988i	−0.186669	+	0.323321i
$580$	−10.1313			−0.420681
$581$	−11.9971	−	11.1172i	−0.497724	−	0.461217i
$582$	−13.8159	+	23.9299i	−0.572688	+	0.991924i
$583$	9.94968			0.412074
$584$	26.8095	−	46.4355i	1.10939	−	1.92151i
$585$	13.9971	+	0.788639i	0.578710	+	0.0326062i
$586$	24.1919	+	41.9016i	0.999359	+	1.73094i
$587$	20.0260	−	34.6860i	0.826561	−	1.43164i	−0.0741601	−	0.997246i	$-0.523628\pi$
$587$	20.0260	−	34.6860i	0.826561	−	1.43164i	0.900721	−	0.434399i	$-0.143039\pi$
$588$	31.0531	−	21.2310i	1.28061	−	0.875550i
$589$	−1.55114	−	2.68666i	−0.0639137	−	0.110702i
$590$	−43.6969	−	75.6852i	−1.79897	−	3.11591i
$591$	16.8595			0.693509
$592$	9.73952			0.400292
$593$	5.18181	+	8.97516i	0.212791	+	0.368566i	0.952587	−	0.304266i	$-0.0984112\pi$
$593$	5.18181	+	8.97516i	0.212791	+	0.368566i	−0.739796	+	0.672832i	$0.765078\pi$
$594$	−2.21536	−	3.83712i	−0.0908974	−	0.157439i
$595$	9.56792	−	42.0460i	0.392246	−	1.72372i
$596$	15.0275	−	26.0284i	0.615551	−	1.06617i
$597$	1.02262	+	1.77124i	0.0418532	+	0.0724919i
$598$	7.73634	+	0.435888i	0.316362	+	0.0178248i
$599$	6.86263	−	11.8864i	0.280400	−	0.485666i	−0.691084	−	0.722775i	$-0.742866\pi$
$599$	6.86263	−	11.8864i	0.280400	−	0.485666i	0.971483	+	0.237108i	$0.0761997\pi$
$600$	−92.7037			−3.78461
$601$	−0.234944	+	0.406935i	−0.00958356	+	0.0165992i	−0.870777	−	0.491677i	$-0.836384\pi$
$601$	−0.234944	+	0.406935i	−0.00958356	+	0.0165992i	0.861194	+	0.508277i	$0.169717\pi$
$602$	8.90244	−	39.1216i	0.362836	−	1.59448i
$603$	1.00054			0.0407452
$604$	26.8542	−	46.5128i	1.09268	−	1.89258i
$605$	32.4193			1.31803
$606$	19.2431	−	33.3300i	0.781698	−	1.35394i
$607$	−11.5258	+	19.9633i	−0.467819	+	0.810287i	−0.999324	−	0.0367685i	$-0.988294\pi$
$607$	−11.5258	+	19.9633i	−0.467819	+	0.810287i	0.531504	+	0.847056i	$0.321627\pi$
$608$	16.9864	−	29.4214i	0.688891	−	1.19319i
$609$	0.940956	+	0.871940i	0.0381295	+	0.0353328i
$610$	−95.9234			−3.88382
$611$	0.949298	+	1.88131i	0.0384045	+	0.0761098i
$612$	11.2626	−	19.5075i	0.455266	−	0.788543i
$613$	−17.4005	−	30.1386i	−0.702801	−	1.21729i	−0.967479	−	0.252951i	$-0.918599\pi$
$613$	−17.4005	−	30.1386i	−0.702801	−	1.21729i	0.264678	−	0.964337i	$-0.414734\pi$
$614$	−43.8912			−1.77130
$615$	−11.5458	−	19.9980i	−0.465573	−	0.806396i
$616$	8.77571	−	38.5647i	0.353583	−	1.55381i
$617$	15.9481	+	27.6229i	0.642045	+	1.11205i	0.984976	+	0.172694i	$0.0552470\pi$
$617$	15.9481	+	27.6229i	0.642045	+	1.11205i	−0.342931	+	0.939361i	$0.611420\pi$
$618$	2.41998	−	4.19152i	0.0973457	−	0.168608i
$619$	−11.1376	+	19.2910i	−0.447660	+	0.775369i	−0.998233	−	0.0594173i	$-0.981076\pi$
$619$	−11.1376	+	19.2910i	−0.447660	+	0.775369i	0.550574	+	0.834787i	$0.314409\pi$
$620$	−38.2539			−1.53631
$621$	0.791415			0.0317584
$622$	−24.6062	+	42.6193i	−0.986621	+	1.70888i
$623$	−8.55569	−	7.92816i	−0.342777	−	0.317635i
$624$	22.9522	+	45.4865i	0.918823	+	1.82092i
$625$	−13.3965	−	23.2034i	−0.535860	−	0.928137i
$626$	−34.7767	−	60.2349i	−1.38996	−	2.40747i
$627$	1.38244	+	2.39446i	0.0552094	+	0.0956254i
$628$	50.6240	−	87.6834i	2.02012	−	3.49895i
$629$	−2.88905			−0.115194
$630$	20.4904	+	18.9875i	0.816356	+	0.756478i
$631$	23.9160	+	41.4237i	0.952081	+	1.64905i	0.740910	+	0.671604i	$0.234394\pi$
$631$	23.9160	+	41.4237i	0.952081	+	1.64905i	0.211171	+	0.977449i	$0.432272\pi$
$632$	−5.89158	−	10.2045i	−0.234355	−	0.405914i
$633$	−24.6765			−0.980803
$634$	−37.2846	−	64.5789i	−1.48076	−	2.56475i
$635$	14.6596			0.581747
$636$	−32.7695			−1.29940
$637$	−0.500181	−	25.2339i	−0.0198179	−	0.999804i
$638$	2.14832			0.0850526
$639$	−15.8744			−0.627982
$640$	−60.2571	−	104.368i	−2.38187	−	4.12552i
$641$	−14.6228			−0.577565			−0.288783	−	0.957395i	$-0.593250\pi$
$641$	−14.6228			−0.577565			−0.288783	+	0.957395i	$0.593250\pi$
$642$	26.0897	+	45.1886i	1.02968	+	1.78345i
$643$	−17.9675	−	31.1207i	−0.708570	−	1.22728i	−0.965388	−	0.260819i	$-0.916007\pi$
$643$	−17.9675	−	31.1207i	−0.708570	−	1.22728i	0.256818	−	0.966460i	$-0.417326\pi$
$644$	8.25349	+	7.64812i	0.325233	+	0.301378i
$645$	21.7139			0.854985
$646$	−9.64385	+	16.7036i	−0.379432	+	0.657196i
$647$	15.2232	+	26.3674i	0.598487	+	1.03661i	0.993045	+	0.117738i	$0.0375643\pi$
$647$	15.2232	+	26.3674i	0.598487	+	1.03661i	−0.394558	+	0.918871i	$0.629102\pi$
$648$	4.58086	+	7.93428i	0.179953	+	0.311688i
$649$	6.75264	+	11.6959i	0.265064	+	0.459105i
$650$	−54.2827	+	82.8743i	−2.12914	+	3.25060i
$651$	3.55286	+	3.29227i	0.139248	+	0.129034i
$652$	65.6879	−	113.775i	2.57253	−	4.45576i
$653$	30.3431			1.18742			0.593709	−	0.804680i	$-0.297663\pi$
$653$	30.3431			1.18742			0.593709	+	0.804680i	$0.297663\pi$
$654$	−29.0507			−1.13597
$655$	−35.0257	+	60.6664i	−1.36857	+	2.37043i
$656$	41.9600	−	72.6769i	1.63826	−	2.83756i
$657$	−2.92626	−	5.06843i	−0.114164	−	0.197738i
$658$	−0.931690	+	4.09429i	−0.0363210	+	0.159612i
$659$	−18.9462	−	32.8157i	−0.738038	−	1.27832i	−0.953377	−	0.301781i	$-0.902419\pi$
$659$	−18.9462	−	32.8157i	−0.738038	−	1.27832i	0.215339	−	0.976539i	$-0.430914\pi$
$660$	34.0934			1.32708
$661$	−5.47928	−	9.49040i	−0.213119	−	0.369134i	0.739570	−	0.673080i	$-0.235029\pi$
$661$	−5.47928	−	9.49040i	−0.213119	−	0.369134i	−0.952689	+	0.303946i	$0.901696\pi$
$662$	9.43802	−	16.3471i	0.366819	−	0.635349i
$663$	−6.80834	−	13.4927i	−0.264414	−	0.524014i
$664$	56.6379			2.19798
$665$	−12.7865	−	11.8486i	−0.495839	−	0.459471i
$666$	0.935814	−	1.62088i	0.0362620	−	0.0628077i
$667$	−0.191866	+	0.332321i	−0.00742907	+	0.0128675i
$668$	−23.0261	+	39.8823i	−0.890906	+	1.54309i
$669$	17.9919			0.695607
$670$	−5.28213	+	9.14892i	−0.204066	+	0.353453i
$671$	14.8234			0.572251
$672$	−11.7696	+	51.7212i	−0.454022	+	1.99519i
$673$	−11.7007	+	20.2661i	−0.451027	+	0.781202i	−0.998450	−	0.0556538i	$-0.982276\pi$
$673$	−11.7007	+	20.2661i	−0.451027	+	0.781202i	0.547423	+	0.836856i	$0.315609\pi$
$674$	−78.8864			−3.03859
$675$	−5.05930	+	8.76296i	−0.194732	+	0.337287i
$676$	69.4182	+	7.84736i	2.66993	+	0.301822i
$677$	−4.05218	−	7.01858i	−0.155738	−	0.269746i	0.777590	−	0.628772i	$-0.216442\pi$
$677$	−4.05218	−	7.01858i	−0.155738	−	0.269746i	−0.933327	+	0.359026i	$0.883109\pi$
$678$	10.3809	−	17.9802i	0.398675	−	0.690525i
$679$	−5.97365	+	26.2511i	−0.229248	+	1.00742i
$680$	74.6596	+	129.314i	2.86306	+	4.95897i
$681$	4.17286	+	7.22761i	0.159904	+	0.276963i
$682$	8.11161			0.310609
$683$	0.681766			0.0260870			0.0130435	−	0.999915i	$-0.495848\pi$
$683$	0.681766			0.0260870			0.0130435	+	0.999915i	$0.495848\pi$
$684$	−4.55310	−	7.88620i	−0.174092	−	0.301536i
$685$	42.3765	+	73.3983i	1.61912	+	2.80441i
$686$	31.2794	−	39.3807i	1.19425	−	1.50356i
$687$	−11.1172	+	19.2556i	−0.424148	+	0.734647i
$688$	39.4565	+	68.3407i	1.50427	+	2.60547i
$689$	−12.0469	+	18.3922i	−0.458950	+	0.700688i
$690$	−4.17809	+	7.23666i	−0.159057	+	0.275495i
$691$	41.9339			1.59524			0.797620	−	0.603161i	$-0.206092\pi$
$691$	41.9339			1.59524			0.797620	+	0.603161i	$0.206092\pi$
$692$	−20.6378	+	35.7457i	−0.784532	+	1.35885i
$693$	−3.16645	−	2.93420i	−0.120284	−	0.111461i
$694$	−13.8720			−0.526572
$695$	−1.38415	+	2.39741i	−0.0525037	+	0.0909390i
$696$	−4.44222			−0.168382
$697$	−12.4467	+	21.5582i	−0.471451	+	0.816577i
$698$	−33.2430	+	57.5786i	−1.25827	+	2.17938i
$699$	2.50918	−	4.34602i	0.0949057	−	0.164382i
$700$	−137.446	+	42.4947i	−5.19498	+	1.60615i
$701$	5.85701			0.221216			0.110608	−	0.993864i	$-0.464720\pi$
$701$	5.85701			0.221216			0.110608	+	0.993864i	$0.464720\pi$
$702$	9.77533	+	0.550770i	0.368946	+	0.0207875i
$703$	−0.583971	+	1.01147i	−0.0220249	+	0.0381482i
$704$	21.3583	+	36.9936i	0.804970	+	1.39425i
$705$	−2.27248			−0.0855867
$706$	5.62350	+	9.74019i	0.211643	+	0.366577i
$707$	8.32024	−	36.5631i	0.312915	−	1.37510i
$708$	−22.2400	−	38.5208i	−0.835830	−	1.44770i
$709$	7.31760	−	12.6745i	0.274818	−	0.475999i	−0.695271	−	0.718748i	$-0.744716\pi$
$709$	7.31760	−	12.6745i	0.274818	−	0.475999i	0.970089	+	0.242748i	$0.0780489\pi$
$710$	83.8052	−	145.155i	3.14515	−	5.44756i
$711$	−1.28613			−0.0482337
$712$	40.3911			1.51372
$713$	−0.724447	+	1.25478i	−0.0271307	+	0.0469918i
$714$	6.68205	−	29.3641i	0.250069	−	1.09892i
$715$	12.5336	−	19.1353i	0.468730	−	0.715618i
$716$	−26.1812	−	45.3472i	−0.978438	−	1.69470i
$717$	−4.64152	−	8.03935i	−0.173341	−	0.300235i
$718$	−17.5151	−	30.3370i	−0.653657	−	1.13217i
$719$	−4.80565	+	8.32363i	−0.179220	+	0.310419i	−0.941614	−	0.336695i	$-0.890691\pi$
$719$	−4.80565	+	8.32363i	−0.179220	+	0.310419i	0.762393	+	0.647114i	$0.224024\pi$
$720$	−54.9442			−2.04765
$721$	1.04634	−	4.59811i	0.0389676	−	0.171243i
$722$	−21.8985	−	37.9292i	−0.814976	−	1.41158i
$723$	7.39469	+	12.8080i	0.275012	+	0.476334i
$724$	−33.5168			−1.24564
$725$	−2.45309	−	4.24888i	−0.0911055	−	0.157799i
$726$	22.6410			0.840286
$727$	−42.7269			−1.58465			−0.792327	−	0.610097i	$-0.791131\pi$
$727$	−42.7269			−1.58465			−0.792327	+	0.610097i	$0.791131\pi$
$728$	60.6622	+	62.9155i	2.24829	+	2.33181i
$729$	1.00000			0.0370370
$730$	61.7940			2.28710
$731$	−11.7040	−	20.2720i	−0.432890	−	0.749787i
$732$	−48.8212			−1.80448
$733$	4.17505	+	7.23139i	0.154209	+	0.267098i	0.932771	−	0.360470i	$-0.117384\pi$
$733$	4.17505	+	7.23139i	0.154209	+	0.267098i	−0.778562	+	0.627568i	$0.784050\pi$
$734$	10.0008	+	17.3219i	0.369137	+	0.639364i
$735$	24.5378	+	11.7774i	0.905090	+	0.434417i
$736$	−15.8667			−0.584854
$737$	0.816267	−	1.41382i	0.0300676	−	0.0520786i
$738$	−8.06339	−	13.9662i	−0.296817	−	0.514103i
$739$	−14.5181	−	25.1461i	−0.534056	−	0.925013i	−0.999208	−	0.0397818i	$-0.987334\pi$
$739$	−14.5181	−	25.1461i	−0.534056	−	0.925013i	0.465152	−	0.885231i	$-0.346000\pi$
$740$	7.20087	+	12.4723i	0.264709	+	0.458490i
$741$	−6.10005	−	0.343694i	−0.224091	−	0.0126259i
$742$	−41.8558	+	12.9407i	−1.53657	+	0.475067i
$743$	−12.5402	+	21.7202i	−0.460055	+	0.796838i	−0.998963	−	0.0455263i	$-0.985504\pi$
$743$	−12.5402	+	21.7202i	−0.460055	+	0.796838i	0.538909	+	0.842364i	$0.318837\pi$
$744$	−16.7729			−0.614926
$745$	21.7463			0.796723
$746$	−32.1199	+	55.6332i	−1.17599	+	2.03688i
$747$	3.09101	−	5.35379i	0.113094	−	0.195885i
$748$	−18.3767	−	31.8294i	−0.671918	−	1.16380i
$749$	37.2904	+	34.5552i	1.36256	+	1.26262i
$750$	−27.0224	−	46.8042i	−0.986720	−	1.70905i
$751$	0.357389			0.0130413			0.00652065	−	0.999979i	$-0.497924\pi$
$751$	0.357389			0.0130413			0.00652065	+	0.999979i	$0.497924\pi$
$752$	−4.12934	−	7.15223i	−0.150582	−	0.260815i
$753$	4.80626	−	8.32468i	0.175150	−	0.303368i
$754$	−2.60114	+	3.97121i	−0.0947281	+	0.144623i
$755$	38.8607			1.41429
$756$	10.4288	+	9.66386i	0.379291	+	0.351471i
$757$	−25.0343	+	43.3607i	−0.909888	+	1.57597i	−0.0956688	+	0.995413i	$0.530499\pi$
$757$	−25.0343	+	43.3607i	−0.909888	+	1.57597i	−0.814219	+	0.580558i	$0.802834\pi$
$758$	13.9214	−	24.1126i	0.505649	−	0.875810i
$759$	0.645656	−	1.11831i	0.0234358	−	0.0405920i
$760$	60.3646			2.18965
$761$	4.41889	−	7.65375i	0.160185	−	0.277448i	−0.774750	−	0.632268i	$-0.782124\pi$
$761$	4.41889	−	7.65375i	0.160185	−	0.277448i	0.934935	+	0.354819i	$0.115458\pi$
$762$	10.2380			0.370882
$763$	−27.0417	+	8.36055i	−0.978975	+	0.302672i
$764$	−8.18882	+	14.1835i	−0.296261	+	0.513139i
$765$	16.2982			0.589261
$766$	−26.2479	+	45.4626i	−0.948374	+	1.64263i
$767$	−29.7962	−	1.67880i	−1.07588	−	0.0606180i
$768$	−15.9024	−	27.5438i	−0.573829	−	0.993902i
$769$	−13.9753	+	24.2059i	−0.503962	+	0.872887i	0.496028	+	0.868307i	$0.334791\pi$
$769$	−13.9753	+	24.2059i	−0.503962	+	0.872887i	−0.999990	+	0.00458075i	$0.998542\pi$
$770$	43.5468	−	13.4635i	1.56932	−	0.485190i
$771$	−2.52788	−	4.37842i	−0.0910394	−	0.157685i
$772$	−24.1379	−	41.8081i	−0.868743	−	1.50471i
$773$	−30.7833			−1.10720			−0.553600	−	0.832783i	$-0.686746\pi$
$773$	−30.7833			−1.10720			−0.553600	+	0.832783i	$0.686746\pi$
$774$	15.1646			0.545080
$775$	−9.26238	−	16.0429i	−0.332714	−	0.576278i
$776$	−46.6131	−	80.7363i	−1.67331	−	2.89827i
$777$	0.404623	−	1.77811i	0.0145158	−	0.0637892i
$778$	16.1809	−	28.0262i	0.580115	−	1.00479i
$779$	5.03175	+	8.71525i	0.180281	+	0.312256i
$780$	−41.2797	+	63.0224i	−1.47805	+	2.25656i
$781$	−12.9507	+	22.4313i	−0.463413	+	0.802656i
$782$	9.00814			0.322130
$783$	−0.242434	+	0.419908i	−0.00866388	+	0.0150063i
$784$	7.52046	+	98.6292i	0.268588	+	3.52247i
$785$	73.2579			2.61469
$786$	−24.4613	+	42.3682i	−0.872506	+	1.51122i
$787$	44.3310			1.58023			0.790114	−	0.612959i	$-0.210021\pi$
$787$	44.3310			1.58023			0.790114	+	0.612959i	$0.210021\pi$
$788$	−45.3005	+	78.4628i	−1.61376	+	2.79512i
$789$	−11.6769	+	20.2250i	−0.415708	+	0.720027i
$790$	6.78983	−	11.7603i	0.241571	−	0.418414i
$791$	4.48843	−	19.7243i	0.159590	−	0.701316i
$792$	14.9487			0.531179
$793$	−17.9479	+	27.4014i	−0.637349	+	0.973052i
$794$	1.31323	−	2.27458i	0.0466047	−	0.0807217i
$795$	−11.8552	−	20.5338i	−0.420460	−	0.728258i
$796$	−10.9909			−0.389562
$797$	2.40661	+	4.16837i	0.0852464	+	0.147651i	0.905496	−	0.424354i	$-0.139499\pi$
$797$	2.40661	+	4.16837i	0.0852464	+	0.147651i	−0.820250	+	0.572005i	$0.806166\pi$
$798$	−8.92984	−	8.27486i	−0.316113	−	0.292927i
$799$	1.22489	+	2.12158i	0.0433336	+	0.0750560i
$800$	101.431	−	175.684i	3.58614	−	6.21138i
$801$	2.20434	−	3.81803i	0.0778866	−	0.134904i
$802$	63.7448			2.25091
$803$	−9.54925			−0.336986
$804$	−2.68839	+	4.65644i	−0.0948124	+	0.164220i
$805$	−1.80650	+	7.93864i	−0.0636708	+	0.279800i
$806$	−9.82139	+	14.9945i	−0.345944	+	0.528159i
$807$	15.6957	+	27.1858i	0.552515	+	0.956984i
$808$	64.9238	+	112.451i	2.28401	+	3.95603i
$809$	−3.98543	−	6.90297i	−0.140120	−	0.242696i	0.787421	−	0.616415i	$-0.211416\pi$
$809$	−3.98543	−	6.90297i	−0.140120	−	0.242696i	−0.927542	+	0.373719i	$0.878082\pi$
$810$	−5.27927	+	9.14396i	−0.185495	+	0.321286i
$811$	−41.5780			−1.46000			−0.730000	−	0.683447i	$-0.760480\pi$
$811$	−41.5780			−1.46000			−0.730000	+	0.683447i	$0.760480\pi$
$812$	−6.58622	+	2.03628i	−0.231131	+	0.0714594i
$813$	5.66515	+	9.81233i	0.198686	+	0.344134i
$814$	−1.52692	−	2.64470i	−0.0535185	−	0.0926968i
$815$	95.0568			3.32970
$816$	29.6155	+	51.2956i	1.03675	+	1.79570i
$817$	−9.46308			−0.331071
$818$	51.6804			1.80696
$819$	9.25783	−	2.30058i	0.323495	−	0.0803887i
$820$	124.092			4.33347
$821$	−10.5631			−0.368656			−0.184328	−	0.982865i	$-0.559011\pi$
$821$	−10.5631			−0.368656			−0.184328	+	0.982865i	$0.559011\pi$
$822$	29.5950	+	51.2600i	1.03224	+	1.78790i
$823$	39.0405			1.36087			0.680433	−	0.732810i	$-0.261792\pi$
$823$	39.0405			1.36087			0.680433	+	0.732810i	$0.261792\pi$
$824$	8.16470	+	14.1417i	0.284431	+	0.492648i
$825$	8.25500	+	14.2981i	0.287402	+	0.497795i
$826$	−43.6185	−	40.4192i	−1.51768	−	1.40636i
$827$	35.0709			1.21954			0.609768	−	0.792580i	$-0.291263\pi$
$827$	35.0709			1.21954			0.609768	+	0.792580i	$0.291263\pi$
$828$	−2.12648	+	3.68318i	−0.0739004	+	0.127999i
$829$	−4.55649	−	7.89208i	−0.158254	−	0.274103i	0.775985	−	0.630751i	$-0.217253\pi$
$829$	−4.55649	−	7.89208i	−0.158254	−	0.274103i	−0.934239	+	0.356648i	$0.883920\pi$
$830$	32.6366	+	56.5282i	1.13283	+	1.96212i
$831$	−8.96129	−	15.5214i	−0.310864	−	0.538432i
$832$	−94.2438	−	5.30997i	−3.26732	−	0.184090i
$833$	−2.23080	−	29.2565i	−0.0772928	−	1.01368i
$834$	−0.966661	+	1.67431i	−0.0334727	+	0.0579765i
$835$	−33.3210			−1.15312
$836$	−14.8581			−0.513879
$837$	−0.915382	+	1.58549i	−0.0316402	+	0.0548025i
$838$	−43.8041	+	75.8709i	−1.51319	+	2.62092i
$839$	−7.08223	−	12.2668i	−0.244506	−	0.423496i	0.717487	−	0.696572i	$-0.245292\pi$
$839$	−7.08223	−	12.2668i	−0.244506	−	0.423496i	−0.961993	+	0.273076i	$0.911959\pi$
$840$	−90.0447	+	27.8393i	−3.10684	+	0.960549i
$841$	14.3825	+	24.9111i	0.495947	+	0.859005i
$842$	93.4676			3.22111
$843$	5.80858	+	10.0607i	0.200058	+	0.346511i
$844$	66.3042	−	114.842i	2.28228	−	3.95303i
$845$	20.1965	+	46.3373i	0.694781	+	1.59405i
$846$	−1.58706			−0.0545642
$847$	21.0753	−	6.51589i	0.724154	−	0.223889i
$848$	43.0842	−	74.6241i	1.47952	−	2.56260i
$849$	4.04596	−	7.00781i	0.138857	−	0.240507i
$850$	−57.5866	+	99.7429i	−1.97520	+	3.42115i
$851$	0.545476			0.0186987
$852$	42.6535	−	73.8781i	1.46129	−	2.53102i
$853$	0.914536			0.0313131			0.0156566	−	0.999877i	$-0.495016\pi$
$853$	0.914536			0.0313131			0.0156566	+	0.999877i	$0.495016\pi$
$854$	−62.3583	+	19.2795i	−2.13386	+	0.659730i
$855$	3.29439	−	5.70606i	0.112666	−	0.195143i
$856$	−176.046			−6.01714
$857$	−9.58886	+	16.6084i	−0.327549	+	0.567332i	−0.982025	−	0.188751i	$-0.939556\pi$
$857$	−9.58886	+	16.6084i	−0.327549	+	0.567332i	0.654476	+	0.756083i	$0.272889\pi$
$858$	8.75322	−	13.3637i	0.298830	−	0.456229i
$859$	−2.83001	−	4.90173i	−0.0965588	−	0.167245i	0.813699	−	0.581286i	$-0.197450\pi$
$859$	−2.83001	−	4.90173i	−0.0965588	−	0.167245i	−0.910258	+	0.414041i	$0.864117\pi$
$860$	−58.3440	+	101.055i	−1.98951	+	3.44594i
$861$	−11.5251	−	10.6798i	−0.392775	−	0.363966i
$862$	2.70710	+	4.68883i	0.0922042	+	0.159702i
$863$	−14.6246	−	25.3305i	−0.497826	−	0.862259i	0.502171	−	0.864768i	$-0.332535\pi$
$863$	−14.6246	−	25.3305i	−0.497826	−	0.862259i	−0.999997	+	0.00250891i	$0.999201\pi$
$864$	−20.0485			−0.682065
$865$	−29.8649			−1.01544
$866$	−10.0703	−	17.4423i	−0.342204	−	0.592714i
$867$	−0.284884	−	0.493434i	−0.00967518	−	0.0167579i
$868$	−24.8682	+	7.68858i	−0.844083	+	0.260967i
$869$	−1.04926	+	1.81737i	−0.0355936	+	0.0616499i
$870$	−2.55975	−	4.43361i	−0.0867835	−	0.150313i
$871$	1.62515	+	3.22071i	0.0550661	+	0.109130i
$872$	49.0067	−	84.8820i	1.65957	−	2.87447i
$873$	−10.1756			−0.344393
$874$	1.82084	−	3.15379i	0.0615908	−	0.106678i
$875$	−38.6236	−	35.7907i	−1.30572	−	1.20995i
$876$	31.4507			1.06262
$877$	4.54681	−	7.87530i	0.153535	−	0.265930i	−0.778990	−	0.627037i	$-0.784268\pi$
$877$	4.54681	−	7.87530i	0.153535	−	0.265930i	0.932525	+	0.361107i	$0.117601\pi$
$878$	−56.4133			−1.90386
$879$	−8.90887	+	15.4306i	−0.300489	+	0.520461i
$880$	−44.8248	+	77.6389i	−1.51104	+	2.61721i
$881$	−4.38792	+	7.60010i	−0.147833	+	0.256054i	−0.930426	−	0.366479i	$-0.880563\pi$
$881$	−4.38792	+	7.60010i	−0.147833	+	0.256054i	0.782593	+	0.622533i	$0.213896\pi$
$882$	17.1367	+	8.22512i	0.577023	+	0.276954i
$883$	−53.6724			−1.80622			−0.903111	−	0.429408i	$-0.858722\pi$
$883$	−53.6724			−1.80622			−0.903111	+	0.429408i	$0.858722\pi$
$884$	81.0875	+	4.56871i	2.72727	+	0.153662i
$885$	16.0917	−	27.8717i	0.540917	−	0.936897i
$886$	7.25519	+	12.5664i	0.243743	+	0.422175i
$887$	−29.8272			−1.00150			−0.500749	−	0.865593i	$-0.666942\pi$
$887$	−29.8272			−1.00150			−0.500749	+	0.865593i	$0.666942\pi$
$888$	3.15732	+	5.46864i	0.105953	+	0.183515i
$889$	9.52995	−	2.94640i	0.319624	−	0.0988191i
$890$	23.2746	+	40.3128i	0.780167	+	1.35129i
$891$	0.815825	−	1.41305i	0.0273312	−	0.0473389i
$892$	−48.3431	+	83.7327i	−1.61865	+	2.80358i
$893$	0.990363			0.0331412
$894$	15.1872			0.507936
$895$	18.9434	−	32.8109i	0.633208	−	1.09675i
$896$	−60.1490	−	55.7373i	−2.00944	−	1.86205i
$897$	1.28547	+	2.54754i	0.0429206	+	0.0850598i
$898$	40.9955	+	71.0063i	1.36804	+	2.36951i
$899$	−0.443839	−	0.768752i	−0.0148029	−	0.0256393i
$900$	−27.1880	−	47.0911i	−0.906268	−	1.56970i
$901$	−12.7801	+	22.1358i	−0.425768	+	0.737452i
$902$	−26.3132			−0.876135
$903$	14.1159	−	4.36425i	0.469747	−	0.145233i
$904$	35.0238	+	60.6629i	1.16487	+	2.01762i
$905$	−12.1255	−	21.0020i	−0.403067	−	0.698132i
$906$	27.1395			0.901651
$907$	−8.20448	−	14.2106i	−0.272425	−	0.471855i	0.697057	−	0.717016i	$-0.254492\pi$
$907$	−8.20448	−	14.2106i	−0.272425	−	0.471855i	−0.969482	+	0.245161i	$0.921159\pi$
$908$	−44.8489			−1.48836
$909$	14.1729			0.470084
$910$	−27.8381	+	96.7985i	−0.922825	+	3.20884i
$911$	−30.3790			−1.00650			−0.503251	−	0.864140i	$-0.667863\pi$
$911$	−30.3790			−1.00650			−0.503251	+	0.864140i	$0.667863\pi$
$912$	23.9451			0.792900
$913$	−5.04345	−	8.73551i	−0.166914	−	0.289103i
$914$	84.2357			2.78627
$915$	−17.6623	−	30.5920i	−0.583897	−	1.01134i
$916$	−59.7426	−	103.477i	−1.97395	−	3.41898i
$917$	−10.5765	+	46.4780i	−0.349265	+	1.53484i
$918$	11.3823			0.375673
$919$	−0.579644	+	1.00397i	−0.0191207	+	0.0331180i	−0.875427	−	0.483350i	$-0.839420\pi$
$919$	−0.579644	+	1.00397i	−0.0191207	+	0.0331180i	0.856307	+	0.516468i	$0.172753\pi$
$920$	−14.0964	−	24.4156i	−0.464743	−	0.804958i
$921$	−8.08164	−	13.9978i	−0.266299	−	0.461244i
$922$	5.95304	+	10.3110i	0.196053	+	0.339574i
$923$	−25.7843	−	51.0992i	−0.848700	−	1.68195i
$924$	22.1636	−	6.85237i	0.729128	−	0.225426i
$925$	−3.48708	+	6.03980i	−0.114654	+	0.198587i
$926$	−13.3973			−0.440264
$927$	1.78235			0.0585401
$928$	4.86044	−	8.41853i	0.159552	−	0.276352i
$929$	−11.5792	+	20.0557i	−0.379901	+	0.658008i	−0.991048	−	0.133510i	$-0.957375\pi$
$929$	−11.5792	+	20.0557i	−0.379901	+	0.658008i	0.611147	+	0.791517i	$0.290709\pi$
$930$	−9.66509	−	16.7404i	−0.316931	−	0.548940i
$931$	−10.6937	−	5.13268i	−0.350473	−	0.168217i
$932$	13.4840	+	23.3550i	0.441683	+	0.765017i
$933$	−18.1229			−0.593317
$934$	−10.8284	−	18.7553i	−0.354316	−	0.613693i
$935$	13.2964	−	23.0301i	0.434840	−	0.753165i
$936$	−18.0996	+	27.6330i	−0.591605	+	0.903214i
$937$	40.2025			1.31336			0.656679	−	0.754170i	$-0.271961\pi$
$937$	40.2025			1.31336			0.656679	+	0.754170i	$0.271961\pi$
$938$	−1.59500	+	7.00921i	−0.0520787	+	0.228859i
$939$	12.8068	−	22.1820i	0.417934	−	0.723882i
$940$	6.10602	−	10.5759i	0.199156	−	0.344949i
$941$	−0.479740	+	0.830934i	−0.0156391	+	0.0270877i	−0.873739	−	0.486395i	$-0.838312\pi$
$941$	−0.479740	+	0.830934i	−0.0156391	+	0.0270877i	0.858100	+	0.513483i	$0.171645\pi$
$942$	51.1619			1.66695
$943$	2.35003	−	4.07038i	0.0765276	−	0.132550i
$944$	116.962			3.80677
$945$	−2.28262	+	10.0309i	−0.0742538	+	0.326307i
$946$	12.3716	−	21.4283i	0.402237	−	0.696695i
$947$	−34.0561			−1.10668			−0.553338	−	0.832957i	$-0.686646\pi$
$947$	−34.0561			−1.10668			−0.553338	+	0.832957i	$0.686646\pi$
$948$	3.45575	−	5.98554i	0.112238	−	0.194401i
$949$	11.5621	−	17.6520i	0.375321	−	0.573009i
$950$	23.2803	+	40.3226i	0.755311	+	1.30824i
$951$	13.7304	−	23.7817i	0.445237	−	0.771174i
$952$	74.5257	+	69.0594i	2.41539	+	2.23823i
$953$	−19.1908	−	33.2394i	−0.621651	−	1.07673i	−0.989178	−	0.146718i	$-0.953129\pi$
$953$	−19.1908	−	33.2394i	−0.621651	−	1.07673i	0.367528	−	0.930013i	$-0.380204\pi$
$954$	−8.27942	−	14.3404i	−0.268056	−	0.464287i
$955$	−11.8500			−0.383458
$956$	49.8859			1.61343
$957$	0.395567	+	0.685142i	0.0127869	+	0.0221475i
$958$	−43.9167	−	76.0660i	−1.41888	−	2.45758i
$959$	42.3005	+	39.1979i	1.36596	+	1.26577i
$960$	50.8973	−	88.1568i	1.64270	−	2.84525i
$961$	13.8242	+	23.9441i	0.445940	+	0.772391i
$962$	6.73756	+	0.379614i	0.217228	+	0.0122392i
$963$	−9.60772	+	16.6411i	−0.309605	+	0.536251i
$964$	−79.4763			−2.55976
$965$	17.4650	−	30.2502i	0.562217	−	0.973789i
$966$	−1.26163	+	5.54419i	−0.0405922	+	0.178381i
$967$	−10.7031			−0.344188			−0.172094	−	0.985080i	$-0.555053\pi$
$967$	−10.7031			−0.344188			−0.172094	+	0.985080i	$0.555053\pi$
$968$	−38.1939	+	66.1538i	−1.22760	+	2.12626i
$969$	−7.10285			−0.228176
$970$	53.7199	−	93.0456i	1.72484	−	2.98751i
$971$	9.99173	−	17.3062i	0.320650	−	0.555382i	−0.659972	−	0.751290i	$-0.729432\pi$
$971$	9.99173	−	17.3062i	0.320650	−	0.555382i	0.980622	+	0.195908i	$0.0627654\pi$
$972$	−2.68694	+	4.65391i	−0.0861836	+	0.149274i
$973$	−0.417960	+	1.83672i	−0.0133992	+	0.0588825i
$974$	−89.9102			−2.88091
$975$	−36.4253	−	2.05231i	−1.16654	−	0.0657265i
$976$	64.1885	−	111.178i	2.05462	−	3.55871i
$977$	1.51427	+	2.62279i	0.0484457	+	0.0839105i	0.889231	−	0.457458i	$-0.151240\pi$
$977$	1.51427	+	2.62279i	0.0484457	+	0.0839105i	−0.840786	+	0.541368i	$0.817907\pi$
$978$	66.3858			2.12278
$979$	−3.59671	−	6.22969i	−0.114952	−	0.199102i
$980$	−120.743	+	82.5516i	−3.85698	+	2.63701i
$981$	−5.34907	−	9.26486i	−0.170783	−	0.295804i
$982$	−13.6263	+	23.6014i	−0.434832	+	0.753152i
$983$	−17.7590	+	30.7595i	−0.566425	+	0.981076i	0.430491	+	0.902595i	$0.358340\pi$
$983$	−17.7590	+	30.7595i	−0.566425	+	0.981076i	−0.996916	+	0.0784815i	$0.974993\pi$
$984$	54.4097			1.73452
$985$	−65.5543			−2.08873
$986$	−2.75946	+	4.77953i	−0.0878791	+	0.152211i
$987$	−1.47731	+	0.456742i	−0.0470232	+	0.0145383i
$988$	17.9900	−	27.4656i	0.572337	−	0.873797i
$989$	2.20982	+	3.82752i	0.0702682	+	0.121708i
$990$	8.61391	+	14.9197i	0.273768	+	0.474180i
$991$	17.6510	+	30.5724i	0.560701	+	0.971163i	0.997435	+	0.0715726i	$0.0228017\pi$
$991$	17.6510	+	30.5724i	0.560701	+	0.971163i	−0.436734	+	0.899591i	$0.643865\pi$
$992$	18.3521	−	31.7867i	0.582678	−	1.00923i
$993$	6.95125			0.220591
$994$	25.3060	−	111.207i	0.802658	−	3.52726i
$995$	−3.97623	−	6.88704i	−0.126055	−	0.218334i
$996$	16.6107	+	28.7706i	0.526331	+	0.911631i
$997$	−15.4531			−0.489406			−0.244703	−	0.969598i	$-0.578690\pi$
$997$	−15.4531			−0.489406			−0.244703	+	0.969598i	$0.578690\pi$
$998$	28.4506	+	49.2778i	0.900587	+	1.55986i
$999$	0.689242			0.0218066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.c.256.1	yes	20
3.2	odd	2		819.2.s.f.802.10		20
7.2	even	3		273.2.j.c.100.10	✓	20
13.3	even	3		273.2.j.c.172.10	yes	20
21.2	odd	6		819.2.n.f.100.1		20
39.29	odd	6		819.2.n.f.172.1		20
91.16	even	3	inner	273.2.l.c.16.1	yes	20
273.107	odd	6		819.2.s.f.289.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.10	✓	20	7.2	even	3
273.2.j.c.172.10	yes	20	13.3	even	3
273.2.l.c.16.1	yes	20	91.16	even	3	inner
273.2.l.c.256.1	yes	20	1.1	even	1	trivial
819.2.n.f.100.1		20	21.2	odd	6
819.2.n.f.172.1		20	39.29	odd	6
819.2.s.f.289.10		20	273.107	odd	6
819.2.s.f.802.10		20	3.2	odd	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.71549 q^{2} +(-0.500000 - 0.866025i) q^{3} +5.37387 q^{4} +(1.94413 + 3.36734i) q^{5} +(1.35774 + 2.35168i) q^{6} +(1.94064 + 1.79830i) q^{7} -9.16172 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-2.71549 q^{2} +(-0.500000 - 0.866025i) q^{3} +5.37387 q^{4} +(1.94413 + 3.36734i) q^{5} +(1.35774 + 2.35168i) q^{6} +(1.94064 + 1.79830i) q^{7} -9.16172 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-5.27927 - 9.14396i) q^{10} +(0.815825 + 1.41305i) q^{11} +(-2.68694 - 4.65391i) q^{12} +(-3.59984 - 0.202826i) q^{13} +(-5.26980 - 4.88327i) q^{14} +(1.94413 - 3.36734i) q^{15} +14.1308 q^{16} -4.19163 q^{17} +(1.35774 - 2.35168i) q^{18} +(-0.847266 + 1.46751i) q^{19} +(10.4475 + 18.0956i) q^{20} +(0.587055 - 2.57980i) q^{21} +(-2.21536 - 3.83712i) q^{22} +0.791415 q^{23} +(4.58086 + 7.93428i) q^{24} +(-5.05930 + 8.76296i) q^{25} +(9.77533 + 0.550770i) q^{26} +1.00000 q^{27} +(10.4288 + 9.66386i) q^{28} +(-0.242434 + 0.419908i) q^{29} +(-5.27927 + 9.14396i) q^{30} +(-0.915382 + 1.58549i) q^{31} -20.0485 q^{32} +(0.815825 - 1.41305i) q^{33} +11.3823 q^{34} +(-2.28262 + 10.0309i) q^{35} +(-2.68694 + 4.65391i) q^{36} +0.689242 q^{37} +(2.30074 - 3.98500i) q^{38} +(1.62427 + 3.21897i) q^{39} +(-17.8116 - 30.8506i) q^{40} +(2.96941 - 5.14316i) q^{41} +(-1.59414 + 7.00542i) q^{42} +(2.79224 + 4.83630i) q^{43} +(4.38414 + 7.59355i) q^{44} -3.88826 q^{45} -2.14908 q^{46} +(-0.292223 - 0.506146i) q^{47} +(-7.06539 - 12.2376i) q^{48} +(0.532204 + 6.97974i) q^{49} +(13.7385 - 23.7957i) q^{50} +(2.09582 + 3.63006i) q^{51} +(-19.3451 - 1.08996i) q^{52} +(3.04896 - 5.28096i) q^{53} -2.71549 q^{54} +(-3.17214 + 5.49431i) q^{55} +(-17.7796 - 16.4756i) q^{56} +1.69453 q^{57} +(0.658326 - 1.14025i) q^{58} +8.27708 q^{59} +(10.4475 - 18.0956i) q^{60} +(4.54246 - 7.86777i) q^{61} +(2.48571 - 4.30537i) q^{62} +(-2.52770 + 0.781496i) q^{63} +26.1800 q^{64} +(-6.31559 - 12.5162i) q^{65} +(-2.21536 + 3.83712i) q^{66} +(-0.500271 - 0.866495i) q^{67} -22.5253 q^{68} +(-0.395707 - 0.685385i) q^{69} +(6.19844 - 27.2389i) q^{70} +(7.93720 + 13.7476i) q^{71} +(4.58086 - 7.93428i) q^{72} +(-2.92626 + 5.06843i) q^{73} -1.87163 q^{74} +10.1186 q^{75} +(-4.55310 + 7.88620i) q^{76} +(-0.957867 + 4.20933i) q^{77} +(-4.41068 - 8.74107i) q^{78} +(0.643065 + 1.11382i) q^{79} +(27.4721 + 47.5831i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.06339 + 13.9662i) q^{82} -6.18202 q^{83} +(3.15476 - 13.8635i) q^{84} +(-8.14908 - 14.1146i) q^{85} +(-7.58229 - 13.1329i) q^{86} +0.484868 q^{87} +(-7.47435 - 12.9460i) q^{88} -4.40869 q^{89} +10.5585 q^{90} +(-6.62127 - 6.86722i) q^{91} +4.25296 q^{92} +1.83076 q^{93} +(0.793529 + 1.37443i) q^{94} -6.58879 q^{95} +(10.0243 + 17.3625i) q^{96} +(5.08782 + 8.81236i) q^{97} +(-1.44519 - 18.9534i) q^{98} -1.63165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more