LMFDB - Embedded newform 78.3.l.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,3,Mod(7,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("78.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	78.l (of order $12$, degree $4$, 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:	$2.12534606201$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	78.7
Dual form			78.3.l.a.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 0.366025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-4.73205 - 4.73205i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(-2.50000 - 0.669873i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.36603 + 0.366025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-4.73205 - 4.73205i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(-2.50000 - 0.669873i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(8.19615 + 4.73205i) q^{10} +(-3.92820 - 14.6603i) q^{11} -3.46410i q^{12} +(11.2583 - 6.50000i) q^{13} +3.66025 q^{14} +(-11.1962 + 3.00000i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-4.39230 + 2.53590i) q^{17} +(3.00000 + 3.00000i) q^{18} +(-0.954483 + 3.56218i) q^{19} +(-12.9282 - 3.46410i) q^{20} +(-3.16987 + 3.16987i) q^{21} +(10.7321 + 18.5885i) q^{22} +(27.5885 + 15.9282i) q^{23} +(1.26795 + 4.73205i) q^{24} +19.7846i q^{25} +(-13.0000 + 13.0000i) q^{26} -5.19615 q^{27} +(-5.00000 + 1.33975i) q^{28} +(-8.66025 + 15.0000i) q^{29} +(14.1962 - 8.19615i) q^{30} +(30.8301 + 30.8301i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-25.3923 - 6.80385i) q^{33} +(5.07180 - 5.07180i) q^{34} +(8.66025 + 15.0000i) q^{35} +(-5.19615 - 3.00000i) q^{36} +(-13.2417 - 49.4186i) q^{37} -5.21539i q^{38} -22.5167i q^{39} +18.9282 q^{40} +(-41.3205 + 11.0718i) q^{41} +(3.16987 - 5.49038i) q^{42} +(28.2846 - 16.3301i) q^{43} +(-21.4641 - 21.4641i) q^{44} +(-5.19615 + 19.3923i) q^{45} +(-43.5167 - 11.6603i) q^{46} +(58.9808 - 58.9808i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-36.6340 - 21.1506i) q^{49} +(-7.24167 - 27.0263i) q^{50} +8.78461i q^{51} +(13.0000 - 22.5167i) q^{52} +97.6743 q^{53} +(7.09808 - 1.90192i) q^{54} +(-50.7846 + 87.9615i) q^{55} +(6.33975 - 3.66025i) q^{56} +(4.51666 + 4.51666i) q^{57} +(6.33975 - 23.6603i) q^{58} +(59.1051 + 15.8372i) q^{59} +(-16.3923 + 16.3923i) q^{60} +(-39.6506 - 68.6769i) q^{61} +(-53.3993 - 30.8301i) q^{62} +(2.00962 + 7.50000i) q^{63} -8.00000i q^{64} +(-84.0333 - 22.5167i) q^{65} +37.1769 q^{66} +(-63.8468 + 17.1077i) q^{67} +(-5.07180 + 8.78461i) q^{68} +(47.7846 - 27.5885i) q^{69} +(-17.3205 - 17.3205i) q^{70} +(-13.8897 + 51.8372i) q^{71} +(8.19615 + 2.19615i) q^{72} +(-27.5814 + 27.5814i) q^{73} +(36.1769 + 62.6603i) q^{74} +(29.6769 + 17.1340i) q^{75} +(1.90897 + 7.12436i) q^{76} +39.2820i q^{77} +(8.24167 + 30.7583i) q^{78} +36.1244 q^{79} +(-25.8564 + 6.92820i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(52.3923 - 30.2487i) q^{82} +(20.9667 + 20.9667i) q^{83} +(-2.32051 + 8.66025i) q^{84} +(32.7846 + 8.78461i) q^{85} +(-32.6603 + 32.6603i) q^{86} +(15.0000 + 25.9808i) q^{87} +(37.1769 + 21.4641i) q^{88} +(-18.0666 - 67.4256i) q^{89} -28.3923i q^{90} +(-32.5000 + 8.70835i) q^{91} +63.7128 q^{92} +(72.9449 - 19.5455i) q^{93} +(-58.9808 + 102.158i) q^{94} +(21.3731 - 12.3397i) q^{95} +(6.92820 + 6.92820i) q^{96} +(4.75387 - 17.7417i) q^{97} +(57.7846 + 15.4833i) q^{98} +(-32.1962 + 32.1962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 12 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 12 * q^5 - 6 * q^6 - 10 * q^7 - 8 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} - 12 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9} + 12 q^{10} + 12 q^{11} - 20 q^{14} - 24 q^{15} + 8 q^{16} + 24 q^{17} + 12 q^{18} + 62 q^{19} - 24 q^{20} - 30 q^{21} + 36 q^{22} + 48 q^{23} + 12 q^{24} - 52 q^{26} - 20 q^{28} + 36 q^{30} + 106 q^{31} + 8 q^{32} - 60 q^{33} + 48 q^{34} - 98 q^{37} + 48 q^{40} - 96 q^{41} + 30 q^{42} + 30 q^{43} - 72 q^{44} - 84 q^{46} + 132 q^{47} - 150 q^{49} - 74 q^{50} + 52 q^{52} + 72 q^{53} + 18 q^{54} - 120 q^{55} + 60 q^{56} - 72 q^{57} + 60 q^{58} + 84 q^{59} - 24 q^{60} - 72 q^{61} - 30 q^{62} + 60 q^{63} - 156 q^{65} + 24 q^{66} - 148 q^{67} - 48 q^{68} + 108 q^{69} + 180 q^{71} + 12 q^{72} - 190 q^{73} + 20 q^{74} - 6 q^{75} - 124 q^{76} + 78 q^{78} + 96 q^{79} - 48 q^{80} - 18 q^{81} + 168 q^{82} + 264 q^{83} + 60 q^{84} + 48 q^{85} - 96 q^{86} + 60 q^{87} + 24 q^{88} + 288 q^{89} - 130 q^{91} + 144 q^{92} + 174 q^{93} - 132 q^{94} - 60 q^{95} + 310 q^{97} + 148 q^{98} - 108 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 12 * q^5 - 6 * q^6 - 10 * q^7 - 8 * q^8 - 6 * q^9 + 12 * q^10 + 12 * q^11 - 20 * q^14 - 24 * q^15 + 8 * q^16 + 24 * q^17 + 12 * q^18 + 62 * q^19 - 24 * q^20 - 30 * q^21 + 36 * q^22 + 48 * q^23 + 12 * q^24 - 52 * q^26 - 20 * q^28 + 36 * q^30 + 106 * q^31 + 8 * q^32 - 60 * q^33 + 48 * q^34 - 98 * q^37 + 48 * q^40 - 96 * q^41 + 30 * q^42 + 30 * q^43 - 72 * q^44 - 84 * q^46 + 132 * q^47 - 150 * q^49 - 74 * q^50 + 52 * q^52 + 72 * q^53 + 18 * q^54 - 120 * q^55 + 60 * q^56 - 72 * q^57 + 60 * q^58 + 84 * q^59 - 24 * q^60 - 72 * q^61 - 30 * q^62 + 60 * q^63 - 156 * q^65 + 24 * q^66 - 148 * q^67 - 48 * q^68 + 108 * q^69 + 180 * q^71 + 12 * q^72 - 190 * q^73 + 20 * q^74 - 6 * q^75 - 124 * q^76 + 78 * q^78 + 96 * q^79 - 48 * q^80 - 18 * q^81 + 168 * q^82 + 264 * q^83 + 60 * q^84 + 48 * q^85 - 96 * q^86 + 60 * q^87 + 24 * q^88 + 288 * q^89 - 130 * q^91 + 144 * q^92 + 174 * q^93 - 132 * q^94 - 60 * q^95 + 310 * q^97 + 148 * q^98 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−1.36603	+	0.366025i	−0.683013	+	0.183013i
$2$	−1.36603	+	0.366025i	−0.683013	+	0.183013i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	−4.73205	−	4.73205i	−0.946410	−	0.946410i	0.0522252	−	0.998635i	$-0.483369\pi$
$5$	−4.73205	−	4.73205i	−0.946410	−	0.946410i	−0.998635	+	0.0522252i	$0.983369\pi$
$6$	−0.633975	+	2.36603i	−0.105662	+	0.394338i
$7$	−2.50000	−	0.669873i	−0.357143	−	0.0956961i	0.0757863	−	0.997124i	$-0.475853\pi$
$7$	−2.50000	−	0.669873i	−0.357143	−	0.0956961i	−0.432929	+	0.901428i	$0.642520\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$	8.19615	+	4.73205i	0.819615	+	0.473205i
$11$	−3.92820	−	14.6603i	−0.357109	−	1.33275i	−0.877809	−	0.479011i	$-0.840996\pi$
$11$	−3.92820	−	14.6603i	−0.357109	−	1.33275i	0.520700	−	0.853740i	$-0.325671\pi$
$12$		−	3.46410i		−	0.288675i
$13$	11.2583	−	6.50000i	0.866025	−	0.500000i
$13$	11.2583	−	6.50000i	0.866025	−	0.500000i
$14$	3.66025			0.261447
$15$	−11.1962	+	3.00000i	−0.746410	+	0.200000i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−4.39230	+	2.53590i	−0.258371	+	0.149170i	−0.623591	−	0.781751i	$-0.714327\pi$
$17$	−4.39230	+	2.53590i	−0.258371	+	0.149170i	0.365220	+	0.930921i	$0.380994\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$	−0.954483	+	3.56218i	−0.0502359	+	0.187483i	−0.986484	−	0.163856i	$-0.947607\pi$
$19$	−0.954483	+	3.56218i	−0.0502359	+	0.187483i	0.936248	+	0.351339i	$0.114273\pi$
$20$	−12.9282	−	3.46410i	−0.646410	−	0.173205i
$21$	−3.16987	+	3.16987i	−0.150946	+	0.150946i
$22$	10.7321	+	18.5885i	0.487820	+	0.844930i
$23$	27.5885	+	15.9282i	1.19950	+	0.692531i	0.960443	−	0.278476i	$-0.0898291\pi$
$23$	27.5885	+	15.9282i	1.19950	+	0.692531i	0.239055	+	0.971006i	$0.423162\pi$
$24$	1.26795	+	4.73205i	0.0528312	+	0.197169i
$25$			19.7846i			0.791384i
$26$	−13.0000	+	13.0000i	−0.500000	+	0.500000i
$27$	−5.19615			−0.192450
$28$	−5.00000	+	1.33975i	−0.178571	+	0.0478481i
$29$	−8.66025	+	15.0000i	−0.298629	+	0.517241i	−0.975823	−	0.218564i	$-0.929863\pi$
$29$	−8.66025	+	15.0000i	−0.298629	+	0.517241i	0.677193	+	0.735805i	$0.263196\pi$
$30$	14.1962	−	8.19615i	0.473205	−	0.273205i
$31$	30.8301	+	30.8301i	0.994520	+	0.994520i	0.999985	−	0.00546484i	$-0.00173952\pi$
$31$	30.8301	+	30.8301i	0.994520	+	0.994520i	−0.00546484	+	0.999985i	$0.501740\pi$
$32$	−1.46410	+	5.46410i	−0.0457532	+	0.170753i
$33$	−25.3923	−	6.80385i	−0.769464	−	0.206177i
$34$	5.07180	−	5.07180i	0.149170	−	0.149170i
$35$	8.66025	+	15.0000i	0.247436	+	0.428571i
$36$	−5.19615	−	3.00000i	−0.144338	−	0.0833333i
$37$	−13.2417	−	49.4186i	−0.357883	−	1.33564i	−0.876817	−	0.480823i	$-0.840338\pi$
$37$	−13.2417	−	49.4186i	−0.357883	−	1.33564i	0.518934	−	0.854814i	$-0.326329\pi$
$38$		−	5.21539i		−	0.137247i
$39$		−	22.5167i		−	0.577350i
$40$	18.9282			0.473205
$41$	−41.3205	+	11.0718i	−1.00782	+	0.270044i	−0.724717	−	0.689047i	$-0.758030\pi$
$41$	−41.3205	+	11.0718i	−1.00782	+	0.270044i	−0.283100	+	0.959090i	$0.591363\pi$
$42$	3.16987	−	5.49038i	0.0754732	−	0.130723i
$43$	28.2846	−	16.3301i	0.657782	−	0.379770i	−0.133650	−	0.991029i	$-0.542670\pi$
$43$	28.2846	−	16.3301i	0.657782	−	0.379770i	0.791431	+	0.611258i	$0.209336\pi$
$44$	−21.4641	−	21.4641i	−0.487820	−	0.487820i
$45$	−5.19615	+	19.3923i	−0.115470	+	0.430940i
$46$	−43.5167	−	11.6603i	−0.946014	−	0.253484i
$47$	58.9808	−	58.9808i	1.25491	−	1.25491i	0.301418	−	0.953492i	$-0.402540\pi$
$47$	58.9808	−	58.9808i	1.25491	−	1.25491i	0.953492	−	0.301418i	$-0.0974598\pi$
$48$	−3.46410	−	6.00000i	−0.0721688	−	0.125000i
$49$	−36.6340	−	21.1506i	−0.747632	−	0.431646i
$50$	−7.24167	−	27.0263i	−0.144833	−	0.540526i
$51$			8.78461i			0.172247i
$52$	13.0000	−	22.5167i	0.250000	−	0.433013i
$53$	97.6743			1.84291			0.921456	−	0.388483i	$-0.127001\pi$
$53$	97.6743			1.84291			0.921456	+	0.388483i	$0.127001\pi$
$54$	7.09808	−	1.90192i	0.131446	−	0.0352208i
$55$	−50.7846	+	87.9615i	−0.923357	+	1.59930i
$56$	6.33975	−	3.66025i	0.113210	−	0.0653617i
$57$	4.51666	+	4.51666i	0.0792397	+	0.0792397i
$58$	6.33975	−	23.6603i	0.109306	−	0.407935i
$59$	59.1051	+	15.8372i	1.00178	+	0.268427i	0.722192	−	0.691693i	$-0.243135\pi$
$59$	59.1051	+	15.8372i	1.00178	+	0.268427i	0.279590	+	0.960120i	$0.409801\pi$
$60$	−16.3923	+	16.3923i	−0.273205	+	0.273205i
$61$	−39.6506	−	68.6769i	−0.650010	−	1.12585i	−0.983120	−	0.182963i	$-0.941431\pi$
$61$	−39.6506	−	68.6769i	−0.650010	−	1.12585i	0.333109	−	0.942888i	$-0.391902\pi$
$62$	−53.3993	−	30.8301i	−0.861280	−	0.497260i
$63$	2.00962	+	7.50000i	0.0318987	+	0.119048i
$64$		−	8.00000i		−	0.125000i
$65$	−84.0333	−	22.5167i	−1.29282	−	0.346410i
$66$	37.1769			0.563287
$67$	−63.8468	+	17.1077i	−0.952937	+	0.255339i	−0.701608	−	0.712563i	$-0.747534\pi$
$67$	−63.8468	+	17.1077i	−0.952937	+	0.255339i	−0.251329	+	0.967902i	$0.580868\pi$
$68$	−5.07180	+	8.78461i	−0.0745852	+	0.129185i
$69$	47.7846	−	27.5885i	0.692531	−	0.399833i
$70$	−17.3205	−	17.3205i	−0.247436	−	0.247436i
$71$	−13.8897	+	51.8372i	−0.195630	+	0.730101i	0.796473	+	0.604674i	$0.206697\pi$
$71$	−13.8897	+	51.8372i	−0.195630	+	0.730101i	−0.992103	+	0.125427i	$0.959970\pi$
$72$	8.19615	+	2.19615i	0.113835	+	0.0305021i
$73$	−27.5814	+	27.5814i	−0.377828	+	0.377828i	−0.870318	−	0.492490i	$-0.836087\pi$
$73$	−27.5814	+	27.5814i	−0.377828	+	0.377828i	0.492490	+	0.870318i	$0.336087\pi$
$74$	36.1769	+	62.6603i	0.488877	+	0.846760i
$75$	29.6769	+	17.1340i	0.395692	+	0.228453i
$76$	1.90897	+	7.12436i	0.0251180	+	0.0937415i
$77$			39.2820i			0.510156i
$78$	8.24167	+	30.7583i	0.105662	+	0.394338i
$79$	36.1244			0.457270			0.228635	−	0.973512i	$-0.426574\pi$
$79$	36.1244			0.457270			0.228635	+	0.973512i	$0.426574\pi$
$80$	−25.8564	+	6.92820i	−0.323205	+	0.0866025i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	52.3923	−	30.2487i	0.638931	−	0.368887i
$83$	20.9667	+	20.9667i	0.252611	+	0.252611i	0.822040	−	0.569430i	$-0.192836\pi$
$83$	20.9667	+	20.9667i	0.252611	+	0.252611i	−0.569430	+	0.822040i	$0.692836\pi$
$84$	−2.32051	+	8.66025i	−0.0276251	+	0.103098i
$85$	32.7846	+	8.78461i	0.385701	+	0.103348i
$86$	−32.6603	+	32.6603i	−0.379770	+	0.379770i
$87$	15.0000	+	25.9808i	0.172414	+	0.298629i
$88$	37.1769	+	21.4641i	0.422465	+	0.243910i
$89$	−18.0666	−	67.4256i	−0.202996	−	0.757591i	−0.990051	−	0.140709i	$-0.955062\pi$
$89$	−18.0666	−	67.4256i	−0.202996	−	0.757591i	0.787055	−	0.616883i	$-0.211605\pi$
$90$		−	28.3923i		−	0.315470i
$91$	−32.5000	+	8.70835i	−0.357143	+	0.0956961i
$92$	63.7128			0.692531
$93$	72.9449	−	19.5455i	0.784353	−	0.210167i
$94$	−58.9808	+	102.158i	−0.627455	+	1.08678i
$95$	21.3731	−	12.3397i	0.224980	−	0.129892i
$96$	6.92820	+	6.92820i	0.0721688	+	0.0721688i
$97$	4.75387	−	17.7417i	0.0490089	−	0.182904i	−0.937082	−	0.349108i	$-0.886485\pi$
$97$	4.75387	−	17.7417i	0.0490089	−	0.182904i	0.986091	+	0.166205i	$0.0531512\pi$
$98$	57.7846	+	15.4833i	0.589639	+	0.157993i
$99$	−32.1962	+	32.1962i	−0.325214	+	0.325214i
$100$	19.7846	+	34.2679i	0.197846	+	0.342679i
$101$	−120.215	−	69.4064i	−1.19025	−	0.687192i	−0.231888	−	0.972743i	$-0.574490\pi$
$101$	−120.215	−	69.4064i	−1.19025	−	0.687192i	−0.958364	+	0.285551i	$0.907824\pi$
$102$	−3.21539	−	12.0000i	−0.0315234	−	0.117647i
$103$		−	107.263i		−	1.04139i	−0.853744	−	0.520693i	$-0.825674\pi$
$103$		−	107.263i		−	1.04139i	0.853744	−	0.520693i	$-0.174326\pi$
$104$	−9.51666	+	35.5167i	−0.0915064	+	0.341506i
$105$	30.0000			0.285714
$106$	−133.426	+	35.7513i	−1.25873	+	0.337276i
$107$	−2.75129	+	4.76537i	−0.0257130	+	0.0445362i	−0.878596	−	0.477567i	$-0.841519\pi$
$107$	−2.75129	+	4.76537i	−0.0257130	+	0.0445362i	0.852883	+	0.522103i	$0.174852\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	108.811	+	108.811i	0.998265	+	0.998265i	0.999998	−	0.00173346i	$-0.000551778\pi$
$109$	108.811	+	108.811i	0.998265	+	0.998265i	−0.00173346	+	0.999998i	$0.500552\pi$
$110$	37.1769	−	138.746i	0.337972	−	1.26133i
$111$	−85.5955	−	22.9352i	−0.771131	−	0.206624i
$112$	−7.32051	+	7.32051i	−0.0653617	+	0.0653617i
$113$	43.3923	+	75.1577i	0.384003	+	0.665112i	0.991630	−	0.129110i	$-0.0412120\pi$
$113$	43.3923	+	75.1577i	0.384003	+	0.665112i	−0.607628	+	0.794222i	$0.707879\pi$
$114$	−7.82309	−	4.51666i	−0.0686236	−	0.0396198i
$115$	−55.1769	−	205.923i	−0.479799	−	1.79064i
$116$			34.6410i			0.298629i
$117$	−33.7750	−	19.5000i	−0.288675	−	0.166667i
$118$	−86.5359			−0.733355
$119$	12.6795	−	3.39746i	0.106550	−	0.0285501i
$120$	16.3923	−	28.3923i	0.136603	−	0.236603i
$121$	−94.7032	+	54.6769i	−0.782671	+	0.451875i
$122$	79.3013	+	79.3013i	0.650010	+	0.650010i
$123$	−19.1769	+	71.5692i	−0.155910	+	0.581864i
$124$	84.2295	+	22.5692i	0.679270	+	0.182010i
$125$	−24.6795	+	24.6795i	−0.197436	+	0.197436i
$126$	−5.49038	−	9.50962i	−0.0435745	−	0.0754732i
$127$	154.885	+	89.4230i	1.21957	+	0.704118i	0.964826	−	0.262890i	$-0.0846757\pi$
$127$	154.885	+	89.4230i	1.21957	+	0.704118i	0.254743	+	0.967009i	$0.418009\pi$
$128$	2.92820	+	10.9282i	0.0228766	+	0.0853766i
$129$		−	56.5692i		−	0.438521i
$130$	123.033			0.946410
$131$	53.6359			0.409434			0.204717	−	0.978821i	$-0.434373\pi$
$131$	53.6359			0.409434			0.204717	+	0.978821i	$0.434373\pi$
$132$	−50.7846	+	13.6077i	−0.384732	+	0.103089i
$133$	4.77241	−	8.26606i	0.0358828	−	0.0621508i
$134$	80.9545	−	46.7391i	0.604138	−	0.348799i
$135$	24.5885	+	24.5885i	0.182137	+	0.182137i
$136$	3.71281	−	13.8564i	0.0273001	−	0.101885i
$137$	−119.478	−	32.0141i	−0.872104	−	0.233679i	−0.205106	−	0.978740i	$-0.565754\pi$
$137$	−119.478	−	32.0141i	−0.872104	−	0.233679i	−0.666997	+	0.745060i	$0.732421\pi$
$138$	−55.1769	+	55.1769i	−0.399833	+	0.399833i
$139$	−76.8538	−	133.115i	−0.552905	−	0.957660i	−0.998063	−	0.0622079i	$-0.980186\pi$
$139$	−76.8538	−	133.115i	−0.552905	−	0.957660i	0.445158	−	0.895452i	$-0.353148\pi$
$140$	30.0000	+	17.3205i	0.214286	+	0.123718i
$141$	−37.3923	−	139.550i	−0.265194	−	0.989716i
$142$		−	75.8949i		−	0.534471i
$143$	−139.517	−	139.517i	−0.975641	−	0.975641i
$144$	−12.0000			−0.0833333
$145$	111.962	−	30.0000i	0.772148	−	0.206897i
$146$	27.5814	−	47.7724i	0.188914	−	0.327208i
$147$	−63.4519	+	36.6340i	−0.431646	+	0.249211i
$148$	−72.3538	−	72.3538i	−0.488877	−	0.488877i
$149$	−41.0718	+	153.282i	−0.275650	+	1.02874i	0.679755	+	0.733439i	$0.262086\pi$
$149$	−41.0718	+	153.282i	−0.275650	+	1.02874i	−0.955405	+	0.295299i	$0.904581\pi$
$150$	−46.8109	−	12.5429i	−0.312073	−	0.0836196i
$151$	−158.962	+	158.962i	−1.05273	+	1.05273i	−0.0541950	+	0.998530i	$0.517259\pi$
$151$	−158.962	+	158.962i	−1.05273	+	1.05273i	−0.998530	+	0.0541950i	$0.982741\pi$
$152$	−5.21539	−	9.03332i	−0.0343118	−	0.0594297i
$153$	13.1769	+	7.60770i	0.0861236	+	0.0497235i
$154$	−14.3782	−	53.6603i	−0.0933651	−	0.348443i
$155$		−	291.779i		−	1.88245i
$156$	−22.5167	−	39.0000i	−0.144338	−	0.250000i
$157$	138.569			0.882606			0.441303	−	0.897358i	$-0.354516\pi$
$157$	138.569			0.882606			0.441303	+	0.897358i	$0.354516\pi$
$158$	−49.3468	+	13.2224i	−0.312321	+	0.0836863i
$159$	84.5885	−	146.512i	0.532003	−	0.921456i
$160$	32.7846	−	18.9282i	0.204904	−	0.118301i
$161$	−58.3013	−	58.3013i	−0.362120	−	0.362120i
$162$	3.29423	−	12.2942i	0.0203347	−	0.0758903i
$163$	270.947	+	72.6000i	1.66225	+	0.445399i	0.963005	−	0.269484i	$-0.0868530\pi$
$163$	270.947	+	72.6000i	1.66225	+	0.445399i	0.699245	+	0.714882i	$0.253520\pi$
$164$	−60.4974	+	60.4974i	−0.368887	+	0.368887i
$165$	87.9615	+	152.354i	0.533100	+	0.923357i
$166$	−36.3154	−	20.9667i	−0.218767	−	0.126305i
$167$	72.3154	+	269.885i	0.433026	+	1.61608i	0.745746	+	0.666230i	$0.232093\pi$
$167$	72.3154	+	269.885i	0.433026	+	1.61608i	−0.312720	+	0.949845i	$0.601240\pi$
$168$		−	12.6795i		−	0.0754732i
$169$	84.5000	−	146.358i	0.500000	−	0.866025i
$170$	−48.0000			−0.282353
$171$	10.6865	−	2.86345i	0.0624943	−	0.0167453i
$172$	32.6603	−	56.5692i	0.189885	−	0.328891i
$173$	−58.4923	+	33.7705i	−0.338106	+	0.195205i	−0.659434	−	0.751762i	$-0.729204\pi$
$173$	−58.4923	+	33.7705i	−0.338106	+	0.195205i	0.321328	+	0.946968i	$0.395871\pi$
$174$	−30.0000	−	30.0000i	−0.172414	−	0.172414i
$175$	13.2532	−	49.4615i	0.0757324	−	0.282637i
$176$	−58.6410	−	15.7128i	−0.333188	−	0.0892773i
$177$	74.9423	−	74.9423i	0.423403	−	0.423403i
$178$	49.3590	+	85.4923i	0.277298	+	0.480294i
$179$	43.4923	+	25.1103i	0.242974	+	0.140281i	0.616543	−	0.787322i	$-0.288533\pi$
$179$	43.4923	+	25.1103i	0.242974	+	0.140281i	−0.373569	+	0.927602i	$0.621866\pi$
$180$	10.3923	+	38.7846i	0.0577350	+	0.215470i
$181$			302.354i			1.67046i	0.549898	+	0.835232i	$0.314666\pi$
$181$			302.354i			1.67046i	−0.549898	+	0.835232i	$0.685334\pi$
$182$	41.2083	−	23.7917i	0.226419	−	0.130723i
$183$	−137.354			−0.750567
$184$	−87.0333	+	23.3205i	−0.473007	+	0.126742i
$185$	−171.191	+	296.512i	−0.925357	+	1.60276i
$186$	−92.4904	+	53.3993i	−0.497260	+	0.287093i
$187$	54.4308	+	54.4308i	0.291074	+	0.291074i
$188$	43.1769	−	161.138i	0.229664	−	0.857119i
$189$	12.9904	+	3.48076i	0.0687322	+	0.0184167i
$190$	−24.6795	+	24.6795i	−0.129892	+	0.129892i
$191$	−81.3397	−	140.885i	−0.425863	−	0.737616i	0.570638	−	0.821202i	$-0.306696\pi$
$191$	−81.3397	−	140.885i	−0.425863	−	0.737616i	−0.996501	+	0.0835862i	$0.973363\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	21.2846	+	79.4352i	0.110283	+	0.411582i	0.998891	−	0.0470861i	$-0.0149935\pi$
$193$	21.2846	+	79.4352i	0.110283	+	0.411582i	−0.888608	+	0.458668i	$0.848327\pi$
$194$			25.9756i			0.133895i
$195$	−106.550	+	106.550i	−0.546410	+	0.546410i
$196$	−84.6025			−0.431646
$197$	260.851	−	69.8949i	1.32412	−	0.354796i	0.473599	−	0.880741i	$-0.342955\pi$
$197$	260.851	−	69.8949i	1.32412	−	0.354796i	0.850519	+	0.525944i	$0.176288\pi$
$198$	32.1962	−	55.7654i	0.162607	−	0.281643i
$199$	−55.2391	+	31.8923i	−0.277583	+	0.160263i	−0.632329	−	0.774700i	$-0.717901\pi$
$199$	−55.2391	+	31.8923i	−0.277583	+	0.160263i	0.354745	+	0.934963i	$0.384568\pi$
$200$	−39.5692	−	39.5692i	−0.197846	−	0.197846i
$201$	−29.6314	+	110.586i	−0.147420	+	0.550179i
$202$	189.622	+	50.8090i	0.938722	+	0.251530i
$203$	31.6987	−	31.6987i	0.156151	−	0.156151i
$204$	8.78461	+	15.2154i	0.0430618	+	0.0745852i
$205$	247.923	+	143.138i	1.20938	+	0.698236i
$206$	39.2609	+	146.524i	0.190587	+	0.711280i
$207$		−	95.5692i		−	0.461687i
$208$		−	52.0000i		−	0.250000i
$209$	55.9718			0.267808
$210$	−40.9808	+	10.9808i	−0.195146	+	0.0522893i
$211$	−123.899	+	214.600i	−0.587201	+	1.01706i	0.407396	+	0.913251i	$0.366437\pi$
$211$	−123.899	+	214.600i	−0.587201	+	1.01706i	−0.994597	+	0.103810i	$0.966897\pi$
$212$	169.177	−	97.6743i	0.798004	−	0.460728i
$213$	65.7269	+	65.7269i	0.308577	+	0.308577i
$214$	2.01408	−	7.51666i	0.00941160	−	0.0351246i
$215$	−211.119	−	56.5692i	−0.981950	−	0.263113i
$216$	10.3923	−	10.3923i	0.0481125	−	0.0481125i
$217$	−56.4230	−	97.7276i	−0.260014	−	0.450358i
$218$	−188.466	−	108.811i	−0.864523	−	0.499133i
$219$	17.4859	+	65.2583i	0.0798444	+	0.297983i
$220$			203.138i			0.923357i
$221$	−32.9667	+	57.1000i	−0.149170	+	0.258371i
$222$	125.321			0.564507
$223$	−44.4378	+	11.9071i	−0.199273	+	0.0533950i	−0.357075	−	0.934076i	$-0.616226\pi$
$223$	−44.4378	+	11.9071i	−0.199273	+	0.0533950i	0.157802	+	0.987471i	$0.449559\pi$
$224$	7.32051	−	12.6795i	0.0326808	−	0.0566049i
$225$	51.4019	−	29.6769i	0.228453	−	0.131897i
$226$	−86.7846	−	86.7846i	−0.384003	−	0.384003i
$227$	3.55514	−	13.2679i	0.0156614	−	0.0584491i	−0.957653	−	0.287925i	$-0.907035\pi$
$227$	3.55514	−	13.2679i	0.0156614	−	0.0584491i	0.973314	+	0.229476i	$0.0737012\pi$
$228$	12.3397	+	3.30642i	0.0541217	+	0.0145019i
$229$	287.315	−	287.315i	1.25465	−	1.25465i	0.301041	−	0.953611i	$-0.402666\pi$
$229$	287.315	−	287.315i	1.25465	−	1.25465i	0.953611	−	0.301041i	$-0.0973341\pi$
$230$	150.746	+	261.100i	0.655418	+	1.13522i
$231$	58.9230	+	34.0192i	0.255078	+	0.147269i
$232$	−12.6795	−	47.3205i	−0.0546530	−	0.203968i
$233$			27.3308i			0.117300i	0.998279	+	0.0586498i	$0.0186795\pi$
$233$			27.3308i			0.117300i	−0.998279	+	0.0586498i	$0.981320\pi$
$234$	53.2750	+	14.2750i	0.227671	+	0.0610042i
$235$	−558.200			−2.37532
$236$	118.210	−	31.6743i	0.500891	−	0.134213i
$237$	31.2846	−	54.1865i	0.132003	−	0.228635i
$238$	−16.0770	+	9.28203i	−0.0675502	+	0.0390001i
$239$	−0.861561	−	0.861561i	−0.00360486	−	0.00360486i	0.705302	−	0.708907i	$-0.250811\pi$
$239$	−0.861561	−	0.861561i	−0.00360486	−	0.00360486i	−0.708907	+	0.705302i	$0.750811\pi$
$240$	−12.0000	+	44.7846i	−0.0500000	+	0.186603i
$241$	82.2032	+	22.0263i	0.341092	+	0.0913954i	0.425299	−	0.905053i	$-0.360169\pi$
$241$	82.2032	+	22.0263i	0.341092	+	0.0913954i	−0.0842068	+	0.996448i	$0.526836\pi$
$242$	109.354	−	109.354i	0.451875	−	0.451875i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$	−137.354	−	79.3013i	−0.562926	−	0.325005i
$245$	73.2679	+	273.440i	0.299053	+	1.11608i
$246$		−	104.785i		−	0.425954i
$247$	12.4083	+	46.3083i	0.0502359	+	0.187483i
$248$	−123.321			−0.497260
$249$	49.6077	−	13.2923i	0.199228	−	0.0533829i
$250$	24.6795	−	42.7461i	0.0987180	−	0.170985i
$251$	−35.2539	+	20.3538i	−0.140454	+	0.0810910i	−0.568580	−	0.822628i	$-0.692507\pi$
$251$	−35.2539	+	20.3538i	−0.140454	+	0.0810910i	0.428127	+	0.903719i	$0.359174\pi$
$252$	10.9808	+	10.9808i	0.0435745	+	0.0435745i
$253$	125.138	−	467.023i	0.494618	−	1.84594i
$254$	−244.308	−	65.4622i	−0.961844	−	0.257725i
$255$	41.5692	−	41.5692i	0.163017	−	0.163017i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−268.277	−	154.890i	−1.04388	−	0.602684i	−0.122949	−	0.992413i	$-0.539235\pi$
$257$	−268.277	−	154.890i	−1.04388	−	0.602684i	−0.920930	+	0.389729i	$0.872569\pi$
$258$	20.7058	+	77.2750i	0.0802549	+	0.299515i
$259$			132.417i			0.511261i
$260$	−168.067	+	45.0333i	−0.646410	+	0.173205i
$261$	51.9615			0.199086
$262$	−73.2679	+	19.6321i	−0.279649	+	0.0749316i
$263$	143.818	−	249.100i	0.546836	−	0.947148i	−0.451653	−	0.892194i	$-0.649165\pi$
$263$	143.818	−	249.100i	0.546836	−	0.947148i	0.998489	−	0.0549543i	$-0.0175013\pi$
$264$	64.3923	−	37.1769i	0.243910	−	0.140822i
$265$	−462.200	−	462.200i	−1.74415	−	1.74415i
$266$	−3.49365	+	13.0385i	−0.0131340	+	0.0490168i
$267$	−116.785	−	31.2923i	−0.437396	−	0.117200i
$268$	−93.4782	+	93.4782i	−0.348799	+	0.348799i
$269$	−81.8705	−	141.804i	−0.304351	−	0.527152i	0.672765	−	0.739856i	$-0.265106\pi$
$269$	−81.8705	−	141.804i	−0.304351	−	0.527152i	−0.977117	+	0.212704i	$0.931773\pi$
$270$	−42.5885	−	24.5885i	−0.157735	−	0.0910684i
$271$	−84.1692	−	314.124i	−0.310587	−	1.15913i	−0.928028	−	0.372510i	$-0.878497\pi$
$271$	−84.1692	−	314.124i	−0.310587	−	1.15913i	0.617441	−	0.786617i	$-0.288170\pi$
$272$			20.2872i			0.0745852i
$273$	−15.0833	+	56.2917i	−0.0552502	+	0.206197i
$274$	174.928			0.638424
$275$	290.047	−	77.7180i	1.05472	−	0.282611i
$276$	55.1769	−	95.5692i	0.199916	−	0.346265i
$277$	−116.900	+	67.4923i	−0.422022	+	0.243654i	−0.695942	−	0.718098i	$-0.745013\pi$
$277$	−116.900	+	67.4923i	−0.422022	+	0.243654i	0.273920	+	0.961752i	$0.411680\pi$
$278$	153.708	+	153.708i	0.552905	+	0.552905i
$279$	33.8538	−	126.344i	0.121340	−	0.452847i
$280$	−47.3205	−	12.6795i	−0.169002	−	0.0452839i
$281$	323.545	−	323.545i	1.15141	−	1.15141i	0.165134	−	0.986271i	$-0.447194\pi$
$281$	323.545	−	323.545i	1.15141	−	1.15141i	0.986271	−	0.165134i	$-0.0528056\pi$
$282$	102.158	+	176.942i	0.362261	+	0.627455i
$283$	−122.416	−	70.6769i	−0.432565	−	0.249742i	0.267874	−	0.963454i	$-0.413679\pi$
$283$	−122.416	−	70.6769i	−0.432565	−	0.249742i	−0.700439	+	0.713712i	$0.747012\pi$
$284$	27.7795	+	103.674i	0.0978150	+	0.365050i
$285$		−	42.7461i		−	0.149986i
$286$	241.650	+	139.517i	0.844930	+	0.487820i
$287$	110.718			0.385777
$288$	16.3923	−	4.39230i	0.0569177	−	0.0152511i
$289$	−131.638	+	228.004i	−0.455496	+	0.788943i
$290$	−141.962	+	81.9615i	−0.489522	+	0.282626i
$291$	−22.4955	−	22.4955i	−0.0773042	−	0.0773042i
$292$	−20.1910	+	75.3538i	−0.0691473	+	0.258061i
$293$	287.512	+	77.0385i	0.981268	+	0.262930i	0.713578	−	0.700575i	$-0.247073\pi$
$293$	287.512	+	77.0385i	0.981268	+	0.262930i	0.267689	+	0.963505i	$0.413740\pi$
$294$	73.2679	−	73.2679i	0.249211	−	0.249211i
$295$	−204.746	−	354.631i	−0.694055	−	1.20214i
$296$	125.321	+	72.3538i	0.423380	+	0.244439i
$297$	20.4115	+	76.1769i	0.0687257	+	0.256488i
$298$		−	224.420i		−	0.753089i
$299$	414.133			1.38506
$300$	68.5359			0.228453
$301$	−81.6506	+	21.8782i	−0.271265	+	0.0726851i
$302$	158.962	−	275.329i	0.526363	−	0.911687i
$303$	−208.219	+	120.215i	−0.687192	+	0.396750i
$304$	10.4308	+	10.4308i	0.0343118	+	0.0343118i
$305$	−137.354	+	512.611i	−0.450340	+	1.68069i
$306$	−20.7846	−	5.56922i	−0.0679236	−	0.0182001i
$307$	−70.0685	+	70.0685i	−0.228236	+	0.228236i	−0.811956	−	0.583719i	$-0.801597\pi$
$307$	−70.0685	+	70.0685i	−0.228236	+	0.228236i	0.583719	+	0.811956i	$0.301597\pi$
$308$	39.2820	+	68.0385i	0.127539	+	0.220904i
$309$	−160.894	−	92.8923i	−0.520693	−	0.300622i
$310$	106.799	+	398.578i	0.344512	+	1.28574i
$311$			140.238i			0.450927i	0.974252	+	0.225464i	$0.0723897\pi$
$311$			140.238i			0.450927i	−0.974252	+	0.225464i	$0.927610\pi$
$312$	45.0333	+	45.0333i	0.144338	+	0.144338i
$313$	−550.286			−1.75810			−0.879051	−	0.476728i	$-0.841823\pi$
$313$	−550.286			−1.75810			−0.879051	+	0.476728i	$0.841823\pi$
$314$	−189.289	+	50.7199i	−0.602831	+	0.161528i
$315$	25.9808	−	45.0000i	0.0824786	−	0.142857i
$316$	62.5692	−	36.1244i	0.198004	−	0.114318i
$317$	−31.2923	−	31.2923i	−0.0987140	−	0.0987140i	0.656025	−	0.754739i	$-0.272237\pi$
$317$	−31.2923	−	31.2923i	−0.0987140	−	0.0987140i	−0.754739	+	0.656025i	$0.772237\pi$
$318$	−61.9230	+	231.100i	−0.194727	+	0.726729i
$319$	253.923	+	68.0385i	0.795997	+	0.213287i
$320$	−37.8564	+	37.8564i	−0.118301	+	0.118301i
$321$	4.76537	+	8.25387i	0.0148454	+	0.0257130i
$322$	100.981	+	58.3013i	0.313605	+	0.181060i
$323$	−4.84094	−	18.0666i	−0.0149874	−	0.0559339i
$324$			18.0000i			0.0555556i
$325$	128.600	+	222.742i	0.395692	+	0.685359i
$326$	−396.694			−1.21685
$327$	257.449	−	68.9833i	0.787307	−	0.210958i
$328$	60.4974	−	104.785i	0.184443	−	0.319465i
$329$	−186.962	+	107.942i	−0.568272	+	0.328092i
$330$	−175.923	−	175.923i	−0.533100	−	0.533100i
$331$	−104.546	+	390.169i	−0.315847	+	1.17876i	0.607350	+	0.794434i	$0.292232\pi$
$331$	−104.546	+	390.169i	−0.315847	+	1.17876i	−0.923198	+	0.384325i	$0.874434\pi$
$332$	57.2820	+	15.3487i	0.172536	+	0.0462309i
$333$	−108.531	+	108.531i	−0.325918	+	0.325918i
$334$	−197.569	−	342.200i	−0.591525	−	1.02455i
$335$	383.081	+	221.172i	1.14352	+	0.660214i
$336$	4.64102	+	17.3205i	0.0138125	+	0.0515491i
$337$			638.492i			1.89464i	0.320295	+	0.947318i	$0.396218\pi$
$337$			638.492i			1.89464i	−0.320295	+	0.947318i	$0.603782\pi$
$338$	−61.8583	+	230.858i	−0.183013	+	0.683013i
$339$	150.315			0.443408
$340$	65.5692	−	17.5692i	0.192851	−	0.0516742i
$341$	330.870	−	573.084i	0.970295	−	1.68060i
$342$	−13.5500	+	7.82309i	−0.0396198	+	0.0228745i
$343$	167.093	+	167.093i	0.487151	+	0.487151i
$344$	−23.9090	+	89.2295i	−0.0695028	+	0.259388i
$345$	−356.669	−	95.5692i	−1.03382	−	0.277012i
$346$	67.5411	−	67.5411i	0.195205	−	0.195205i
$347$	2.85125	+	4.93851i	0.00821686	+	0.0142320i	0.870105	−	0.492867i	$-0.164051\pi$
$347$	2.85125	+	4.93851i	0.00821686	+	0.0142320i	−0.861888	+	0.507099i	$0.830718\pi$
$348$	51.9615	+	30.0000i	0.149315	+	0.0862069i
$349$	46.8890	+	174.992i	0.134353	+	0.501411i	1.00000		0.000755966i	$0.000240632\pi$
$349$	46.8890	+	174.992i	0.134353	+	0.501411i	−0.865647	+	0.500655i	$0.833093\pi$
$350$			72.4167i			0.206905i
$351$	−58.5000	+	33.7750i	−0.166667	+	0.0962250i
$352$	85.8564			0.243910
$353$	−280.086	+	75.0488i	−0.793444	+	0.212603i	−0.632704	−	0.774394i	$-0.718055\pi$
$353$	−280.086	+	75.0488i	−0.793444	+	0.212603i	−0.160741	+	0.986997i	$0.551388\pi$
$354$	−74.9423	+	129.804i	−0.211701	+	0.366678i
$355$	311.023	−	179.569i	0.876121	−	0.505829i
$356$	−98.7180	−	98.7180i	−0.277298	−	0.277298i
$357$	5.88457	−	21.9615i	0.0164834	−	0.0615169i
$358$	−68.6025	−	18.3820i	−0.191627	−	0.0513464i
$359$	−268.277	+	268.277i	−0.747289	+	0.747289i	−0.973969	−	0.226680i	$-0.927213\pi$
$359$	−268.277	+	268.277i	−0.747289	+	0.747289i	0.226680	+	0.973969i	$0.427213\pi$
$360$	−28.3923	−	49.1769i	−0.0788675	−	0.136603i
$361$	300.857	+	173.700i	0.833399	+	0.481163i
$362$	−110.669	−	413.023i	−0.305716	−	1.14095i
$363$			189.406i			0.521781i
$364$	−47.5833	+	47.5833i	−0.130723	+	0.130723i
$365$	261.033			0.715160
$366$	187.629	−	50.2750i	0.512647	−	0.137363i
$367$	88.1077	−	152.607i	0.240075	−	0.415823i	−0.720660	−	0.693289i	$-0.756161\pi$
$367$	88.1077	−	152.607i	0.240075	−	0.415823i	0.960736	+	0.277466i	$0.0894945\pi$
$368$	110.354	−	63.7128i	0.299875	−	0.173133i
$369$	90.7461	+	90.7461i	0.245924	+	0.245924i
$370$	125.321	−	467.703i	0.338704	−	1.26406i
$371$	−244.186	−	65.4294i	−0.658183	−	0.176360i
$372$	106.799	−	106.799i	0.287093	−	0.287093i
$373$	−241.803	−	418.815i	−0.648266	−	1.12283i	−0.983537	−	0.180708i	$-0.942161\pi$
$373$	−241.803	−	418.815i	−0.648266	−	1.12283i	0.335271	−	0.942122i	$-0.391172\pi$
$374$	−94.2769	−	54.4308i	−0.252077	−	0.145537i
$375$	15.6462	+	58.3923i	0.0417231	+	0.155713i
$376$			235.923i			0.627455i
$377$			225.167i			0.597259i
$378$	−19.0192			−0.0503154
$379$	278.815	−	74.7083i	0.735661	−	0.197120i	0.128512	−	0.991708i	$-0.458980\pi$
$379$	278.815	−	74.7083i	0.735661	−	0.197120i	0.607149	+	0.794588i	$0.292313\pi$
$380$	24.6795	−	42.7461i	0.0649460	−	0.112490i
$381$	268.269	−	154.885i	0.704118	−	0.406523i
$382$	162.679	+	162.679i	0.425863	+	0.425863i
$383$	−68.1718	+	254.420i	−0.177994	+	0.664283i	0.818028	+	0.575178i	$0.195067\pi$
$383$	−68.1718	+	254.420i	−0.177994	+	0.664283i	−0.996022	+	0.0891049i	$0.971599\pi$
$384$	18.9282	+	5.07180i	0.0492922	+	0.0132078i
$385$	185.885	−	185.885i	0.482817	−	0.482817i
$386$	−58.1506	−	100.720i	−0.150649	−	0.260932i
$387$	−84.8538	−	48.9904i	−0.219261	−	0.126590i
$388$	−9.50773	−	35.4833i	−0.0245045	−	0.0914519i
$389$		−	66.2487i		−	0.170305i	−0.996368	−	0.0851526i	$-0.972862\pi$
$389$		−	66.2487i		−	0.170305i	0.996368	−	0.0851526i	$-0.0271378\pi$
$390$	106.550	−	184.550i	0.273205	−	0.473205i
$391$	−161.569			−0.413221
$392$	115.569	−	30.9667i	0.294819	−	0.0789966i
$393$	46.4500	−	80.4538i	0.118193	−	0.204717i
$394$	−330.746	+	190.956i	−0.839457	+	0.484661i
$395$	−170.942	−	170.942i	−0.432765	−	0.432765i
$396$	−23.5692	+	87.9615i	−0.0595182	+	0.222125i
$397$	−130.651	−	35.0077i	−0.329095	−	0.0881807i	0.0904886	−	0.995897i	$-0.471157\pi$
$397$	−130.651	−	35.0077i	−0.329095	−	0.0881807i	−0.419583	+	0.907717i	$0.637824\pi$
$398$	63.7846	−	63.7846i	0.160263	−	0.160263i
$399$	−8.26606	−	14.3172i	−0.0207169	−	0.0358828i
$400$	68.5359	+	39.5692i	0.171340	+	0.0989230i
$401$	−49.5654	−	184.981i	−0.123605	−	0.461299i	0.876181	−	0.481981i	$-0.160083\pi$
$401$	−49.5654	−	184.981i	−0.123605	−	0.461299i	−0.999786	+	0.0206827i	$0.993416\pi$
$402$		−	161.909i		−	0.402759i
$403$	547.492	+	146.700i	1.35854	+	0.364020i
$404$	−277.626			−0.687192
$405$	58.1769	−	15.5885i	0.143647	−	0.0384900i
$406$	−31.6987	+	54.9038i	−0.0780757	+	0.135231i
$407$	−672.473	+	388.252i	−1.65227	+	0.953937i
$408$	−17.5692	−	17.5692i	−0.0430618	−	0.0430618i
$409$	143.838	−	536.812i	0.351683	−	1.31250i	−0.532925	−	0.846163i	$-0.678907\pi$
$409$	143.838	−	536.812i	0.351683	−	1.31250i	0.884608	−	0.466336i	$-0.154426\pi$
$410$	−391.061	−	104.785i	−0.953809	−	0.255572i
$411$	−151.492	+	151.492i	−0.368594	+	0.368594i
$412$	−107.263	−	185.785i	−0.260347	−	0.450934i
$413$	−137.154	−	79.1858i	−0.332092	−	0.191733i
$414$	34.9808	+	130.550i	0.0844946	+	0.315338i
$415$		−	198.431i		−	0.478146i
$416$	19.0333	+	71.0333i	0.0457532	+	0.170753i
$417$	−266.229			−0.638440
$418$	−76.4589	+	20.4871i	−0.182916	+	0.0490122i
$419$	328.823	−	569.538i	0.784781	−	1.35928i	−0.144349	−	0.989527i	$-0.546109\pi$
$419$	328.823	−	569.538i	0.784781	−	1.35928i	0.929130	−	0.369753i	$-0.120558\pi$
$420$	51.9615	−	30.0000i	0.123718	−	0.0714286i
$421$	328.035	+	328.035i	0.779181	+	0.779181i	0.979692	−	0.200511i	$-0.0642601\pi$
$421$	328.035	+	328.035i	0.779181	+	0.779181i	−0.200511	+	0.979692i	$0.564260\pi$
$422$	90.7006	−	338.499i	0.214930	−	0.802131i
$423$	−241.708	−	64.7654i	−0.571413	−	0.153110i
$424$	−195.349	+	195.349i	−0.460728	+	0.460728i
$425$	−50.1718	−	86.9000i	−0.118051	−	0.204471i
$426$	−113.842	−	65.7269i	−0.267236	−	0.154288i
$427$	53.1218	+	198.253i	0.124407	+	0.464293i
$428$			11.0052i			0.0257130i
$429$	−330.100	+	88.4500i	−0.769464	+	0.206177i
$430$	309.100			0.718837
$431$	−30.9948	+	8.30504i	−0.0719138	+	0.0192692i	−0.294597	−	0.955622i	$-0.595185\pi$
$431$	−30.9948	+	8.30504i	−0.0719138	+	0.0192692i	0.222683	+	0.974891i	$0.428519\pi$
$432$	−10.3923	+	18.0000i	−0.0240563	+	0.0416667i
$433$	169.928	−	98.1077i	0.392442	−	0.226577i	−0.290776	−	0.956791i	$-0.593913\pi$
$433$	169.928	−	98.1077i	0.392442	−	0.226577i	0.683218	+	0.730215i	$0.260580\pi$
$434$	112.846	+	112.846i	0.260014	+	0.260014i
$435$	51.9615	−	193.923i	0.119452	−	0.445800i
$436$	297.277	+	79.6551i	0.681828	+	0.182695i
$437$	−83.0718	+	83.0718i	−0.190096	+	0.190096i
$438$	−47.7724	−	82.7442i	−0.109069	−	0.188914i
$439$	35.9078	+	20.7314i	0.0817945	+	0.0472241i	0.540339	−	0.841447i	$-0.318296\pi$
$439$	35.9078	+	20.7314i	0.0817945	+	0.0472241i	−0.458545	+	0.888671i	$0.651629\pi$
$440$	−74.3538	−	277.492i	−0.168986	−	0.630664i
$441$			126.904i			0.287764i
$442$	24.1333	−	90.0666i	0.0546002	−	0.203771i
$443$	−19.9718			−0.0450831			−0.0225416	−	0.999746i	$-0.507176\pi$
$443$	−19.9718			−0.0450831			−0.0225416	+	0.999746i	$0.507176\pi$
$444$	−171.191	+	45.8705i	−0.385565	+	0.103312i
$445$	−233.569	+	404.554i	−0.524875	+	0.909110i
$446$	56.3449	−	32.5307i	0.126334	−	0.0729389i
$447$	194.354	+	194.354i	0.434796	+	0.434796i
$448$	−5.35898	+	20.0000i	−0.0119620	+	0.0446429i
$449$	127.459	+	34.1525i	0.283873	+	0.0760635i	0.397946	−	0.917409i	$-0.369723\pi$
$449$	127.459	+	34.1525i	0.283873	+	0.0760635i	−0.114073	+	0.993472i	$0.536390\pi$
$450$	−59.3538	+	59.3538i	−0.131897	+	0.131897i
$451$	324.631	+	562.277i	0.719802	+	1.24673i
$452$	150.315	+	86.7846i	0.332556	+	0.192001i
$453$	100.778	+	376.107i	0.222467	+	0.830258i
$454$			19.4256i			0.0427877i
$455$	195.000	+	112.583i	0.428571	+	0.247436i
$456$	−18.0666			−0.0396198
$457$	−284.842	+	76.3231i	−0.623286	+	0.167009i	−0.556621	−	0.830766i	$-0.687902\pi$
$457$	−284.842	+	76.3231i	−0.623286	+	0.167009i	−0.0666648	+	0.997775i	$0.521236\pi$
$458$	−287.315	+	497.645i	−0.627326	+	1.08656i
$459$	22.8231	−	13.1769i	0.0497235	−	0.0287079i
$460$	−301.492	−	301.492i	−0.655418	−	0.655418i
$461$	121.565	−	453.688i	0.263699	−	0.984140i	−0.699342	−	0.714787i	$-0.746524\pi$
$461$	121.565	−	453.688i	0.263699	−	0.984140i	0.963042	−	0.269353i	$-0.0868097\pi$
$462$	−92.9423	−	24.9038i	−0.201174	−	0.0539044i
$463$	462.599	−	462.599i	0.999134	−	0.999134i	−0.000865128	−	1.00000i	$-0.500275\pi$
$463$	462.599	−	462.599i	0.999134	−	0.999134i	1.00000		0.000865128i	$0.000275379\pi$
$464$	34.6410	+	60.0000i	0.0746574	+	0.129310i
$465$	−437.669	−	252.688i	−0.941224	−	0.543416i
$466$	−10.0038	−	37.3346i	−0.0214673	−	0.0801171i
$467$		−	396.649i		−	0.849355i	−0.905345	−	0.424677i	$-0.860388\pi$
$467$		−	396.649i		−	0.849355i	0.905345	−	0.424677i	$-0.139612\pi$
$468$	−78.0000			−0.166667
$469$	171.077			0.364770
$470$	762.515	−	204.315i	1.62237	−	0.434714i
$471$	120.004	−	207.854i	0.254787	−	0.441303i
$472$	−149.885	+	86.5359i	−0.317552	+	0.183339i
$473$	−350.512	−	350.512i	−0.741039	−	0.741039i
$474$	−22.9019	+	85.4711i	−0.0483163	+	0.180319i
$475$	−70.4763	−	18.8841i	−0.148371	−	0.0397559i
$476$	18.5641	−	18.5641i	0.0390001	−	0.0390001i
$477$	−146.512	−	253.765i	−0.307152	−	0.532003i
$478$	1.49227	+	0.861561i	0.00312190	+	0.00180243i
$479$	93.1666	+	347.703i	0.194502	+	0.725892i	0.992395	+	0.123093i	$0.0392814\pi$
$479$	93.1666	+	347.703i	0.194502	+	0.725892i	−0.797893	+	0.602799i	$0.794052\pi$
$480$		−	65.5692i		−	0.136603i
$481$	−470.300	−	470.300i	−0.977754	−	0.977754i
$482$	−120.354			−0.249697
$483$	−137.942	+	36.9615i	−0.285595	+	0.0765249i
$484$	−109.354	+	189.406i	−0.225938	+	0.391336i
$485$	−106.450	+	61.4589i	−0.219485	+	0.126719i
$486$	−15.5885	−	15.5885i	−0.0320750	−	0.0320750i
$487$	−50.1455	+	187.145i	−0.102968	+	0.384282i	−0.998107	−	0.0615056i	$-0.980410\pi$
$487$	−50.1455	+	187.145i	−0.102968	+	0.384282i	0.895139	+	0.445788i	$0.147076\pi$
$488$	216.655	+	58.0526i	0.443965	+	0.118960i
$489$	343.547	−	343.547i	0.702550	−	0.702550i
$490$	−200.172	−	346.708i	−0.408514	−	0.707567i
$491$	19.9808	+	11.5359i	0.0406940	+	0.0234947i	0.520209	−	0.854039i	$-0.325854\pi$
$491$	19.9808	+	11.5359i	0.0406940	+	0.0234947i	−0.479515	+	0.877534i	$0.659187\pi$
$492$	38.3538	+	143.138i	0.0779549	+	0.290932i
$493$		−	87.8461i		−	0.178187i
$494$	−33.9000	−	58.7166i	−0.0686236	−	0.118859i
$495$	304.708			0.615571
$496$	168.459	−	45.1384i	0.339635	−	0.0910049i
$497$	69.4486	−	120.289i	0.139736	−	0.242029i
$498$	−62.9000	+	36.3154i	−0.126305	+	0.0729224i
$499$	−160.769	−	160.769i	−0.322183	−	0.322183i	0.527421	−	0.849604i	$-0.323159\pi$
$499$	−160.769	−	160.769i	−0.322183	−	0.322183i	−0.849604	+	0.527421i	$0.823159\pi$
$500$	−18.0666	+	67.4256i	−0.0361333	+	0.134851i
$501$	467.454	+	125.254i	0.933042	+	0.250008i
$502$	40.7077	−	40.7077i	0.0810910	−	0.0810910i
$503$	300.622	+	520.692i	0.597658	+	1.03517i	0.993166	+	0.116711i	$0.0372351\pi$
$503$	300.622	+	520.692i	0.597658	+	1.03517i	−0.395508	+	0.918462i	$0.629432\pi$
$504$	−19.0192	−	10.9808i	−0.0377366	−	0.0217872i
$505$	240.431	+	897.300i	0.476101	+	1.77683i
$506$			683.769i			1.35132i
$507$	−146.358	−	253.500i	−0.288675	−	0.500000i
$508$	357.692			0.704118
$509$	−475.028	+	127.283i	−0.933258	+	0.250066i	−0.693243	−	0.720704i	$-0.743819\pi$
$509$	−475.028	+	127.283i	−0.933258	+	0.250066i	−0.240014	+	0.970769i	$0.577152\pi$
$510$	−41.5692	+	72.0000i	−0.0815083	+	0.141176i
$511$	87.4296	−	50.4775i	0.171095	−	0.0987818i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	4.95964	−	18.5096i	0.00966791	−	0.0360811i
$514$	423.167	+	113.387i	0.823281	+	0.220598i
$515$	−507.573	+	507.573i	−0.985579	+	0.985579i
$516$	−56.5692	−	97.9808i	−0.109630	−	0.189885i
$517$	−1096.36	−	632.985i	−2.12062	−	1.22434i
$518$	−48.4679	−	180.885i	−0.0935673	−	0.349198i
$519$			116.985i			0.225404i
$520$	213.100	−	123.033i	0.409808	−	0.236603i
$521$	647.951			1.24367			0.621834	−	0.783149i	$-0.286388\pi$
$521$	647.951			1.24367			0.621834	+	0.783149i	$0.286388\pi$
$522$	−70.9808	+	19.0192i	−0.135978	+	0.0364353i
$523$	82.9615	−	143.694i	0.158626	−	0.274749i	−0.775747	−	0.631044i	$-0.782627\pi$
$523$	82.9615	−	143.694i	0.158626	−	0.274749i	0.934374	+	0.356295i	$0.115960\pi$
$524$	92.9000	−	53.6359i	0.177290	−	0.102359i
$525$	−62.7147	−	62.7147i	−0.119457	−	0.119457i
$526$	−105.282	+	392.918i	−0.200156	+	0.746992i
$527$	−213.597	−	57.2332i	−0.405308	−	0.108602i
$528$	−74.3538	+	74.3538i	−0.140822	+	0.140822i
$529$	242.915	+	420.742i	0.459197	+	0.795353i
$530$	800.554	+	462.200i	1.51048	+	0.872075i
$531$	−47.5115	−	177.315i	−0.0894755	−	0.333927i
$532$		−	19.0897i		−	0.0358828i
$533$	−393.233	+	393.233i	−0.737773	+	0.737773i
$534$	170.985			0.320196
$535$	35.5692	−	9.53074i	0.0664845	−	0.0178145i
$536$	93.4782	−	161.909i	0.174400	−	0.302069i
$537$	75.3308	−	43.4923i	0.140281	−	0.0809912i
$538$	163.741	+	163.741i	0.304351	+	0.304351i
$539$	−166.168	+	620.147i	−0.308289	+	1.15055i
$540$	67.1769	+	18.0000i	0.124402	+	0.0333333i
$541$	−210.557	+	210.557i	−0.389200	+	0.389200i	−0.874402	−	0.485202i	$-0.838746\pi$
$541$	−210.557	+	210.557i	−0.389200	+	0.389200i	0.485202	+	0.874402i	$0.338746\pi$
$542$	229.954	+	398.293i	0.424270	+	0.734858i
$543$	453.531	+	261.846i	0.835232	+	0.482221i
$544$	−7.42563	−	27.7128i	−0.0136500	−	0.0509427i
$545$		−	1029.80i		−	1.88954i
$546$		−	82.4167i		−	0.150946i
$547$	−392.492			−0.717536			−0.358768	−	0.933427i	$-0.616803\pi$
$547$	−392.492			−0.717536			−0.358768	+	0.933427i	$0.616803\pi$
$548$	−238.956	+	64.0282i	−0.436052	+	0.116840i
$549$	−118.952	+	206.031i	−0.216670	+	0.375284i
$550$	−367.765	+	212.329i	−0.668664	+	0.386054i
$551$	−45.1666	−	45.1666i	−0.0819721	−	0.0819721i
$552$	−40.3923	+	150.746i	−0.0731745	+	0.273091i
$553$	−90.3109	−	24.1987i	−0.163311	−	0.0437590i
$554$	134.985	−	134.985i	0.243654	−	0.243654i
$555$	296.512	+	513.573i	0.534255	+	0.925357i
$556$	−266.229	−	153.708i	−0.478830	−	0.276453i
$557$	18.3576	+	68.5115i	0.0329580	+	0.123001i	0.980445	−	0.196793i	$-0.0630528\pi$
$557$	18.3576	+	68.5115i	0.0329580	+	0.123001i	−0.947487	+	0.319794i	$0.896386\pi$
$558$			184.981i			0.331507i
$559$	212.292	−	367.700i	0.379770	−	0.657782i
$560$	69.2820			0.123718
$561$	128.785	−	34.5077i	0.229563	−	0.0615111i
$562$	−323.545	+	560.396i	−0.575703	+	0.997146i
$563$	721.161	−	416.363i	1.28093	−	0.739543i	0.303908	−	0.952701i	$-0.401708\pi$
$563$	721.161	−	416.363i	1.28093	−	0.739543i	0.977018	+	0.213158i	$0.0683750\pi$
$564$	−204.315	−	204.315i	−0.362261	−	0.362261i
$565$	150.315	−	560.985i	0.266045	−	0.992893i
$566$	193.093	+	51.7391i	0.341154	+	0.0914118i
$567$	16.4711	−	16.4711i	0.0290496	−	0.0290496i
$568$	−75.8949	−	131.454i	−0.133618	−	0.231433i
$569$	301.750	+	174.215i	0.530316	+	0.306178i	0.741145	−	0.671345i	$-0.234283\pi$
$569$	301.750	+	174.215i	0.530316	+	0.306178i	−0.210829	+	0.977523i	$0.567616\pi$
$570$	15.6462	+	58.3923i	0.0274494	+	0.102443i
$571$			411.892i			0.721352i	0.932691	+	0.360676i	$0.117454\pi$
$571$			411.892i			0.721352i	−0.932691	+	0.360676i	$0.882546\pi$
$572$	−381.167	−	102.133i	−0.666375	−	0.178555i
$573$	−281.769			−0.491744
$574$	−151.244	+	40.5256i	−0.263491	+	0.0706021i
$575$	−315.133	+	545.827i	−0.548058	+	0.949264i
$576$	−20.7846	+	12.0000i	−0.0360844	+	0.0208333i
$577$	39.6692	+	39.6692i	0.0687507	+	0.0687507i	0.740646	−	0.671895i	$-0.234520\pi$
$577$	39.6692	+	39.6692i	0.0687507	+	0.0687507i	−0.671895	+	0.740646i	$0.734520\pi$
$578$	96.3660	−	359.643i	0.166723	−	0.622220i
$579$	137.586	+	36.8660i	0.237627	+	0.0636719i
$580$	163.923	−	163.923i	0.282626	−	0.282626i
$581$	−38.3717	−	66.4617i	−0.0660442	−	0.114392i
$582$	38.9634	+	22.4955i	0.0669474	+	0.0386521i
$583$	−383.685	−	1431.93i	−0.658121	−	2.45614i
$584$		−	110.326i		−	0.188914i
$585$	67.5500	+	252.100i	0.115470	+	0.430940i
$586$	−420.946			−0.718338
$587$	−505.435	+	135.431i	−0.861047	+	0.230717i	−0.662212	−	0.749316i	$-0.730382\pi$
$587$	−505.435	+	135.431i	−0.861047	+	0.230717i	−0.198835	+	0.980033i	$0.563716\pi$
$588$	−73.2679	+	126.904i	−0.124605	+	0.215823i
$589$	−139.249	+	80.3956i	−0.236416	+	0.136495i
$590$	409.492	+	409.492i	0.694055	+	0.694055i
$591$	121.061	−	451.808i	0.204842	−	0.764480i
$592$	−197.674	−	52.9667i	−0.333909	−	0.0894707i
$593$	234.771	−	234.771i	0.395903	−	0.395903i	−0.480882	−	0.876785i	$-0.659684\pi$
$593$	234.771	−	234.771i	0.395903	−	0.395903i	0.876785	+	0.480882i	$0.159684\pi$
$594$	−55.7654	−	96.5885i	−0.0938811	−	0.162607i
$595$	−76.0770	−	43.9230i	−0.127860	−	0.0738202i
$596$	82.1436	+	306.564i	0.137825	+	0.514369i
$597$			110.478i			0.185056i
$598$	−565.717	+	151.583i	−0.946014	+	0.253484i
$599$	−652.908			−1.09000			−0.544998	−	0.838437i	$-0.683470\pi$
$599$	−652.908			−1.09000			−0.544998	+	0.838437i	$0.683470\pi$
$600$	−93.6218	+	25.0859i	−0.156036	+	0.0418098i
$601$	−32.7846	+	56.7846i	−0.0545501	+	0.0944835i	−0.892011	−	0.452014i	$-0.850706\pi$
$601$	−32.7846	+	56.7846i	−0.0545501	+	0.0944835i	0.837461	+	0.546497i	$0.184039\pi$
$602$	103.529	−	59.7724i	0.171975	−	0.0992897i
$603$	140.217	+	140.217i	0.232533	+	0.232533i
$604$	−116.368	+	434.291i	−0.192662	+	0.719025i
$605$	706.874	+	189.406i	1.16839	+	0.313068i
$606$	240.431	−	240.431i	0.396750	−	0.396750i
$607$	388.300	+	672.555i	0.639703	+	1.10800i	0.985498	+	0.169688i	$0.0542761\pi$
$607$	388.300	+	672.555i	0.639703	+	1.10800i	−0.345795	+	0.938310i	$0.612391\pi$
$608$	−18.0666	−	10.4308i	−0.0297149	−	0.0171559i
$609$	−20.0962	−	75.0000i	−0.0329987	−	0.123153i
$610$		−	750.515i		−	1.23035i
$611$	280.650	−	1047.40i	0.459329	−	1.71424i
$612$	30.4308			0.0497235
$613$	−410.842	+	110.085i	−0.670215	+	0.179583i	−0.577852	−	0.816142i	$-0.696109\pi$
$613$	−410.842	+	110.085i	−0.670215	+	0.179583i	−0.0923632	+	0.995725i	$0.529442\pi$
$614$	70.0685	−	121.362i	0.114118	−	0.197658i
$615$	429.415	−	247.923i	0.698236	−	0.403127i
$616$	−78.5641	−	78.5641i	−0.127539	−	0.127539i
$617$	−35.0141	+	130.674i	−0.0567489	+	0.211790i	−0.988478	−	0.151364i	$-0.951633\pi$
$617$	−35.0141	+	130.674i	−0.0567489	+	0.211790i	0.931729	+	0.363154i	$0.118300\pi$
$618$	253.786	+	68.0019i	0.410658	+	0.110035i
$619$	−661.030	+	661.030i	−1.06790	+	1.06790i	−0.0703796	+	0.997520i	$0.522421\pi$
$619$	−661.030	+	661.030i	−1.06790	+	1.06790i	−0.997520	+	0.0703796i	$0.977579\pi$
$620$	−291.779	−	505.377i	−0.470612	−	0.815124i
$621$	−143.354	−	82.7654i	−0.230844	−	0.133278i
$622$	−51.3308	−	191.569i	−0.0825254	−	0.307989i
$623$			180.666i			0.289994i
$624$	−78.0000	−	45.0333i	−0.125000	−	0.0721688i
$625$	728.184			1.16510
$626$	751.704	−	201.419i	1.20081	−	0.321755i
$627$	48.4730	−	83.9578i	0.0773095	−	0.133904i
$628$	240.009	−	138.569i	0.382180	−	0.220652i
$629$	183.482	+	183.482i	0.291704	+	0.291704i
$630$	−19.0192	+	70.9808i	−0.0301893	+	0.112668i
$631$	374.899	+	100.454i	0.594135	+	0.159198i	0.543342	−	0.839511i	$-0.317159\pi$
$631$	374.899	+	100.454i	0.594135	+	0.159198i	0.0507928	+	0.998709i	$0.483825\pi$
$632$	−72.2487	+	72.2487i	−0.114318	+	0.114318i
$633$	214.600	+	371.698i	0.339020	+	0.587201i
$634$	54.1999	+	31.2923i	0.0854888	+	0.0493570i
$635$	−309.771	−	1156.08i	−0.487828	−	1.82060i
$636$		−	338.354i		−	0.532003i
$637$	−549.917			−0.863291
$638$	−371.769			−0.582710
$639$	155.512	−	41.6692i	0.243367	−	0.0652100i
$640$	37.8564	−	65.5692i	0.0591506	−	0.102452i
$641$	539.869	−	311.694i	0.842229	−	0.486261i	−0.0157919	−	0.999875i	$-0.505027\pi$
$641$	539.869	−	311.694i	0.842229	−	0.486261i	0.858021	+	0.513614i	$0.171694\pi$
$642$	−9.53074	−	9.53074i	−0.0148454	−	0.0148454i
$643$	211.661	−	789.931i	0.329178	−	1.22851i	−0.580867	−	0.813999i	$-0.697286\pi$
$643$	211.661	−	789.931i	0.329178	−	1.22851i	0.910045	−	0.414510i	$-0.136047\pi$
$644$	−159.282	−	42.6795i	−0.247332	−	0.0662725i
$645$	−267.688	+	267.688i	−0.415021	+	0.415021i
$646$	13.2257	+	22.9076i	0.0204732	+	0.0354607i
$647$	−248.412	−	143.420i	−0.383944	−	0.221670i	0.295589	−	0.955315i	$-0.404484\pi$
$647$	−248.412	−	143.420i	−0.383944	−	0.221670i	−0.679533	+	0.733645i	$0.737817\pi$
$648$	−6.58846	−	24.5885i	−0.0101674	−	0.0379452i
$649$		−	928.708i		−	1.43098i
$650$	−257.200	−	257.200i	−0.395692	−	0.395692i
$651$	−195.455			−0.300238
$652$	541.894	−	145.200i	0.831125	−	0.222699i
$653$	−324.424	+	561.919i	−0.496821	+	0.860520i	−0.999993	−	0.00366668i	$-0.998833\pi$
$653$	−324.424	+	561.919i	−0.496821	+	0.860520i	0.503172	+	0.864186i	$0.332166\pi$
$654$	−326.433	+	188.466i	−0.499133	+	0.288174i
$655$	−253.808	−	253.808i	−0.387493	−	0.387493i
$656$	−44.2872	+	165.282i	−0.0675110	+	0.251954i
$657$	113.031	+	30.2865i	0.172041	+	0.0460982i
$658$	215.885	−	215.885i	0.328092	−	0.328092i
$659$	−228.158	−	395.181i	−0.346218	−	0.599667i	0.639356	−	0.768911i	$-0.279201\pi$
$659$	−228.158	−	395.181i	−0.346218	−	0.599667i	−0.985574	+	0.169243i	$0.945868\pi$
$660$	304.708	+	175.923i	0.461678	+	0.266550i
$661$	−84.1814	−	314.169i	−0.127355	−	0.475294i	0.872558	−	0.488510i	$-0.162460\pi$
$661$	−84.1814	−	314.169i	−0.127355	−	0.475294i	−0.999913	+	0.0132166i	$0.995793\pi$
$662$		−	571.247i		−	0.862911i
$663$	57.1000	+	98.9000i	0.0861236	+	0.149170i
$664$	−83.8667			−0.126305
$665$	−61.6987	+	16.5321i	−0.0927800	+	0.0248603i
$666$	108.531	−	187.981i	0.162959	−	0.282253i
$667$	−477.846	+	275.885i	−0.716411	+	0.413620i
$668$	395.138	+	395.138i	0.591525	+	0.591525i
$669$	−20.6237	+	76.9686i	−0.0308276	+	0.115050i
$670$	−604.252	−	161.909i	−0.901869	−	0.241655i
$671$	−851.065	+	851.065i	−1.26835	+	1.26835i
$672$	−12.6795	−	21.9615i	−0.0188683	−	0.0326808i
$673$	904.138	+	522.004i	1.34344	+	0.775638i	0.987311	−	0.158797i	$-0.0507615\pi$
$673$	904.138	+	522.004i	1.34344	+	0.775638i	0.356133	+	0.934435i	$0.384095\pi$
$674$	−233.704	−	872.197i	−0.346742	−	1.29406i
$675$		−	102.804i		−	0.152302i
$676$		−	338.000i		−	0.500000i
$677$	−193.408			−0.285684			−0.142842	−	0.989746i	$-0.545624\pi$
$677$	−193.408			−0.285684			−0.142842	+	0.989746i	$0.545624\pi$
$678$	−205.335	+	55.0192i	−0.302853	+	0.0811493i
$679$	−23.7693	+	41.1697i	−0.0350064	+	0.0606328i
$680$	−83.1384	+	48.0000i	−0.122262	+	0.0705882i
$681$	−16.8231	−	16.8231i	−0.0247035	−	0.0247035i
$682$	−242.214	+	903.955i	−0.355153	+	1.32545i
$683$	−802.783	−	215.105i	−1.17538	−	0.314942i	−0.382286	−	0.924044i	$-0.624863\pi$
$683$	−802.783	−	215.105i	−1.17538	−	0.314942i	−0.793092	+	0.609102i	$0.791530\pi$
$684$	15.6462	−	15.6462i	0.0228745	−	0.0228745i
$685$	413.885	+	716.869i	0.604211	+	1.04652i
$686$	−289.413	−	167.093i	−0.421885	−	0.243576i
$687$	−182.151	−	679.795i	−0.265139	−	0.989513i
$688$		−	130.641i		−	0.189885i
$689$	1099.65	−	634.883i	1.59601	−	0.921456i
$690$	522.200			0.756811
$691$	224.069	−	60.0392i	0.324268	−	0.0868874i	−0.0930129	−	0.995665i	$-0.529650\pi$
$691$	224.069	−	60.0392i	0.324268	−	0.0868874i	0.417281	+	0.908778i	$0.362983\pi$
$692$	−67.5411	+	116.985i	−0.0976027	+	0.169053i
$693$	102.058	−	58.9230i	0.147269	−	0.0850260i
$694$	−5.70250	−	5.70250i	−0.00821686	−	0.00821686i
$695$	−266.229	+	993.582i	−0.383064	+	1.42961i
$696$	−81.9615	−	21.9615i	−0.117761	−	0.0315539i
$697$	153.415	−	153.415i	0.220108	−	0.220108i
$698$	−128.103	−	221.881i	−0.183529	−	0.317882i
$699$	40.9962	+	23.6692i	0.0586498	+	0.0338615i
$700$	−26.5064	−	98.9230i	−0.0378662	−	0.141319i
$701$		−	55.6565i		−	0.0793958i	−0.999212	−	0.0396979i	$-0.987360\pi$
$701$		−	55.6565i		−	0.0793958i	0.999212	−	0.0396979i	$-0.0126396\pi$
$702$	67.5500	−	67.5500i	0.0962250	−	0.0962250i
$703$	188.677			0.268388
$704$	−117.282	+	31.4256i	−0.166594	+	0.0446387i
$705$	−483.415	+	837.300i	−0.685695	+	1.18766i
$706$	355.135	−	205.037i	0.503024	−	0.290421i
$707$	254.045	+	254.045i	0.359328	+	0.359328i
$708$	54.8616	−	204.746i	0.0774881	−	0.289189i
$709$	−299.954	−	80.3724i	−0.423066	−	0.113360i	0.0410035	−	0.999159i	$-0.486945\pi$
$709$	−299.954	−	80.3724i	−0.423066	−	0.113360i	−0.464069	+	0.885799i	$0.653611\pi$
$710$	−359.138	+	359.138i	−0.505829	+	0.505829i
$711$	−54.1865	−	93.8538i	−0.0762117	−	0.132003i
$712$	170.985	+	98.7180i	0.240147	+	0.138649i
$713$	359.487	+	1341.62i	0.504189	+	1.88166i
$714$			32.1539i			0.0450335i
$715$			1320.40i			1.84671i
$716$	100.441			0.140281
$717$	−2.03848	+	0.546208i	−0.00284306	+	0.000761796i
$718$	268.277	−	464.669i	0.373645	−	0.647172i
$719$	269.785	−	155.760i	0.375222	−	0.216635i	−0.300515	−	0.953777i	$-0.597159\pi$
$719$	269.785	−	155.760i	0.375222	−	0.216635i	0.675737	+	0.737142i	$0.263825\pi$
$720$	56.7846	+	56.7846i	0.0788675	+	0.0788675i
$721$	−71.8524	+	268.157i	−0.0996567	+	0.371924i
$722$	−474.557	−	127.157i	−0.657281	−	0.176118i
$723$	104.229	−	104.229i	0.144162	−	0.144162i
$724$	302.354	+	523.692i	0.417616	+	0.723332i
$725$	−296.769	−	171.340i	−0.409337	−	0.236331i
$726$	−69.3275	−	258.734i	−0.0954925	−	0.356383i
$727$		−	379.585i		−	0.522125i	−0.965322	−	0.261062i	$-0.915927\pi$
$727$		−	379.585i		−	0.522125i	0.965322	−	0.261062i	$-0.0840728\pi$
$728$	47.5833	−	82.4167i	0.0653617	−	0.113210i
$729$	27.0000			0.0370370
$730$	−356.578	+	95.5448i	−0.488463	+	0.130883i
$731$	−82.8231	+	143.454i	−0.113301	+	0.196243i
$732$	−237.904	+	137.354i	−0.325005	+	0.187642i
$733$	769.627	+	769.627i	1.04997	+	1.04997i	0.998684	+	0.0512852i	$0.0163317\pi$
$733$	769.627	+	769.627i	1.04997	+	1.04997i	0.0512852	+	0.998684i	$0.483668\pi$
$734$	−64.4993	+	240.715i	−0.0878737	+	0.327949i
$735$	473.611	+	126.904i	0.644369	+	0.172658i
$736$	−127.426	+	127.426i	−0.173133	+	0.173133i
$737$	501.606	+	868.808i	0.680606	+	1.17884i
$738$	−157.177	−	90.7461i	−0.212977	−	0.122962i
$739$	69.2379	+	258.399i	0.0936913	+	0.349661i	0.996818	−	0.0797139i	$-0.0254007\pi$
$739$	69.2379	+	258.399i	0.0936913	+	0.349661i	−0.903126	+	0.429375i	$0.858734\pi$
$740$			684.764i			0.925357i
$741$	80.2083	+	21.4918i	0.108243	+	0.0290037i
$742$	357.513			0.481823
$743$	−1070.47	+	286.832i	−1.44074	+	0.386046i	−0.892794	−	0.450466i	$-0.851258\pi$
$743$	−1070.47	+	286.832i	−1.44074	+	0.386046i	−0.547949	+	0.836512i	$0.684591\pi$
$744$	−106.799	+	184.981i	−0.143547	+	0.248630i
$745$	919.692	−	530.985i	1.23449	−	0.712731i
$746$	483.606	+	483.606i	0.648266	+	0.648266i
$747$	23.0230	−	85.9230i	0.0308206	−	0.115024i
$748$	148.708	+	39.8461i	0.198807	+	0.0532702i
$749$	10.0704	−	10.0704i	0.0134451	−	0.0134451i
$750$	−42.7461	−	74.0385i	−0.0569948	−	0.0987180i
$751$	318.631	+	183.962i	0.424275	+	0.244955i	0.696905	−	0.717164i	$-0.254560\pi$
$751$	318.631	+	183.962i	0.424275	+	0.244955i	−0.272630	+	0.962119i	$0.587893\pi$
$752$	−86.3538	−	322.277i	−0.114832	−	0.428560i
$753$			70.5077i			0.0936358i
$754$	−82.4167	−	307.583i	−0.109306	−	0.407935i
$755$	1504.43			1.99262
$756$	25.9808	−	6.96152i	0.0343661	−	0.00920837i
$757$	−97.6922	+	169.208i	−0.129052	+	0.223524i	−0.923309	−	0.384057i	$-0.874527\pi$
$757$	−97.6922	+	169.208i	−0.129052	+	0.223524i	0.794258	+	0.607581i	$0.207860\pi$
$758$	−353.524	+	204.107i	−0.466390	+	0.269270i
$759$	−592.161	−	592.161i	−0.780186	−	0.780186i
$760$	−18.0666	+	67.4256i	−0.0237719	+	0.0887179i
$761$	1176.65	+	315.282i	1.54619	+	0.414300i	0.928259	−	0.371935i	$-0.121305\pi$
$761$	1176.65	+	315.282i	1.54619	+	0.414300i	0.617928	+	0.786234i	$0.287972\pi$
$762$	−309.771	+	309.771i	−0.406523	+	0.406523i
$763$	−199.138	−	344.917i	−0.260993	−	0.452053i
$764$	−281.769	−	162.679i	−0.368808	−	0.212931i
$765$	−26.3538	−	98.3538i	−0.0344494	−	0.128567i
$766$		−	372.497i		−	0.486289i
$767$	768.367	−	205.883i	1.00178	−	0.268427i
$768$	−27.7128			−0.0360844
$769$	−1000.87	+	268.181i	−1.30152	+	0.348740i	−0.842023	−	0.539441i	$-0.818635\pi$
$769$	−1000.87	+	268.181i	−1.30152	+	0.348740i	−0.459493	+	0.888181i	$0.651969\pi$
$770$	−185.885	+	321.962i	−0.241409	+	0.418132i
$771$	−464.669	+	268.277i	−0.602684	+	0.347960i
$772$	116.301	+	116.301i	0.150649	+	0.150649i
$773$	242.394	−	904.626i	0.313575	−	1.17028i	−0.611733	−	0.791064i	$-0.709527\pi$
$773$	242.394	−	904.626i	0.313575	−	1.17028i	0.925309	−	0.379215i	$-0.123806\pi$
$774$	133.844	+	35.8634i	0.172925	+	0.0463352i
$775$	−609.962	+	609.962i	−0.787048	+	0.787048i
$776$	25.9756	+	44.9911i	0.0334737	+	0.0579782i
$777$	198.625	+	114.676i	0.255631	+	0.147588i
$778$	24.2487	+	90.4974i	0.0311680	+	0.116321i
$779$		−	157.759i		−	0.202515i
$780$	−78.0000	+	291.100i	−0.100000	+	0.373205i
$781$	814.508			1.04290
$782$	220.708	−	59.1384i	0.282235	−	0.0756246i
$783$	45.0000	−	77.9423i	0.0574713	−	0.0995431i
$784$	−146.536	+	84.6025i	−0.186908	+	0.107911i
$785$	−655.717	−	655.717i	−0.835308	−	0.835308i
$786$	−34.0038	+	126.904i	−0.0432618	+	0.161455i
$787$	−925.546	−	247.999i	−1.17604	−	0.315120i	−0.382687	−	0.923878i	$-0.625001\pi$
$787$	−925.546	−	247.999i	−1.17604	−	0.315120i	−0.793356	+	0.608758i	$0.791668\pi$
$788$	381.913	−	381.913i	0.484661	−	0.484661i
$789$	−249.100	−	431.454i	−0.315716	−	0.546836i
$790$	296.081	+	170.942i	0.374786	+	0.216383i
$791$	−58.1347	−	216.962i	−0.0734952	−	0.274288i
$792$		−	128.785i		−	0.162607i
$793$	−892.800	−	515.458i	−1.12585	−	0.650010i
$794$	191.286			0.240914
$795$	−1093.58	+	293.023i	−1.37557	+	0.368582i
$796$	−63.7846	+	110.478i	−0.0801314	+	0.138792i
$797$	324.862	−	187.559i	0.407605	−	0.235331i	−0.282155	−	0.959369i	$-0.591049\pi$
$797$	324.862	−	187.559i	0.407605	−	0.235331i	0.689760	+	0.724038i	$0.257716\pi$
$798$	16.5321	+	16.5321i	0.0207169	+	0.0207169i
$799$	−109.492	+	408.631i	−0.137037	+	0.511428i
$800$	−108.105	−	28.9667i	−0.135131	−	0.0362083i
$801$	−148.077	+	148.077i	−0.184865	+	0.184865i
$802$	135.415	+	234.546i	0.168847	+	0.292452i
$803$	512.696	+	296.005i	0.638476	+	0.368624i
$804$	59.2628	+	221.172i	0.0737099	+	0.275089i
$805$			551.769i			0.685428i
$806$	−801.583			−0.994520
$807$	−283.608			−0.351435
$808$	379.244	−	101.618i	0.469361	−	0.125765i
$809$	−376.277	+	651.731i	−0.465114	+	0.805600i	−0.999207	−	0.0398253i	$-0.987320\pi$
$809$	−376.277	+	651.731i	−0.465114	+	0.805600i	0.534093	+	0.845426i	$0.320653\pi$
$810$	−73.7654	+	42.5885i	−0.0910684	+	0.0525783i
$811$	−49.8071	−	49.8071i	−0.0614144	−	0.0614144i	0.675732	−	0.737147i	$-0.263827\pi$
$811$	−49.8071	−	49.8071i	−0.0614144	−	0.0614144i	−0.737147	+	0.675732i	$0.763827\pi$
$812$	23.2051	−	86.6025i	0.0285777	−	0.106653i
$813$	−544.078	−	145.785i	−0.669223	−	0.179318i
$814$	776.505	−	776.505i	0.953937	−	0.953937i
$815$	−938.587	−	1625.68i	−1.15164	−	1.99470i
$816$	30.4308	+	17.5692i	0.0372926	+	0.0215309i
$817$	31.1736	+	116.342i	0.0381562	+	0.142401i
$818$			785.947i			0.960816i
$819$	71.3750	+	71.3750i	0.0871489	+	0.0871489i
$820$	572.554			0.698236
$821$	367.119	−	98.3693i	0.447161	−	0.119816i	−0.0282097	−	0.999602i	$-0.508981\pi$
$821$	367.119	−	98.3693i	0.447161	−	0.119816i	0.475371	+	0.879786i	$0.342314\pi$
$822$	151.492	−	262.392i	0.184297	−	0.319212i
$823$	1149.07	−	663.415i	1.39620	−	0.806094i	0.402204	−	0.915550i	$-0.368244\pi$
$823$	1149.07	−	663.415i	1.39620	−	0.806094i	0.993992	+	0.109456i	$0.0349109\pi$
$824$	214.526	+	214.526i	0.260347	+	0.260347i
$825$	134.611	−	502.377i	0.163165	−	0.608942i
$826$	216.340	+	57.9681i	0.261913	+	0.0701792i
$827$	−178.410	+	178.410i	−0.215732	+	0.215732i	−0.806697	−	0.590965i	$-0.798747\pi$
$827$	−178.410	+	178.410i	−0.215732	+	0.215732i	0.590965	+	0.806697i	$0.298747\pi$
$828$	−95.5692	−	165.531i	−0.115422	−	0.199916i
$829$	−839.258	−	484.546i	−1.01237	−	0.584495i	−0.100488	−	0.994938i	$-0.532041\pi$
$829$	−839.258	−	484.546i	−1.01237	−	0.584495i	−0.911886	+	0.410444i	$0.865374\pi$
$830$	72.6307	+	271.061i	0.0875069	+	0.326580i
$831$			233.800i			0.281348i
$832$	−52.0000	−	90.0666i	−0.0625000	−	0.108253i
$833$	214.543			0.257555
$834$	363.676	−	97.4468i	0.436063	−	0.116843i
$835$	934.908	−	1619.31i	1.11965	−	1.93929i
$836$	96.9461	−	55.9718i	0.115964	−	0.0669520i
$837$	−160.198	−	160.198i	−0.191396	−	0.191396i
$838$	−240.715	+	898.361i	−0.287250	+	1.07203i
$839$	−210.464	−	56.3937i	−0.250851	−	0.0672154i	0.131202	−	0.991356i	$-0.458116\pi$
$839$	−210.464	−	56.3937i	−0.250851	−	0.0672154i	−0.382053	+	0.924140i	$0.624783\pi$
$840$	−60.0000	+	60.0000i	−0.0714286	+	0.0714286i
$841$	270.500	+	468.520i	0.321641	+	0.557098i
$842$	−568.174	−	328.035i	−0.674791	−	0.389591i
$843$	−205.119	−	765.515i	−0.243321	−	0.908085i
$844$			495.597i			0.587201i
$845$	−1092.43	+	292.717i	−1.29282	+	0.346410i
$846$	353.885			0.418303
$847$	273.385	−	73.2532i	0.322768	−	0.0864854i
$848$	195.349	−	338.354i	0.230364	−	0.399002i
$849$	−212.031	+	122.416i	−0.249742	+	0.144188i
$850$	100.344	+	100.344i	0.118051	+	0.118051i
$851$	421.832	−	1574.30i	0.495690	−	1.84994i
$852$	179.569	+	48.1154i	0.210762	+	0.0564735i
$853$	−173.527	+	173.527i	−0.203432	+	0.203432i	−0.801469	−	0.598037i	$-0.795948\pi$
$853$	−173.527	+	173.527i	−0.203432	+	0.203432i	0.598037	+	0.801469i	$0.295948\pi$
$854$	−145.131	−	251.375i	−0.169943	−	0.294350i
$855$	−64.1192	−	37.0192i	−0.0749932	−	0.0432974i
$856$	−4.02817	−	15.0333i	−0.00470580	−	0.0175623i
$857$			616.543i			0.719421i	0.933064	+	0.359710i	$0.117124\pi$
$857$			616.543i			0.719421i	−0.933064	+	0.359710i	$0.882876\pi$
$858$	418.550	−	241.650i	0.487820	−	0.281643i
$859$	566.398			0.659370			0.329685	−	0.944091i	$-0.393058\pi$
$859$	566.398			0.659370			0.329685	+	0.944091i	$0.393058\pi$
$860$	−422.238	+	113.138i	−0.490975	+	0.131556i
$861$	95.8846	−	166.077i	0.111364	−	0.192888i
$862$	39.2999	−	22.6898i	0.0455915	−	0.0263223i
$863$	656.627	+	656.627i	0.760866	+	0.760866i	0.976479	−	0.215613i	$-0.0691751\pi$
$863$	656.627	+	656.627i	0.760866	+	0.760866i	−0.215613	+	0.976479i	$0.569175\pi$
$864$	7.60770	−	28.3923i	0.00880520	−	0.0328615i
$865$	436.592	+	116.985i	0.504731	+	0.135242i
$866$	−196.215	+	196.215i	−0.226577	+	0.226577i
$867$	228.004	+	394.915i	0.262981	+	0.455496i
$868$	−195.455	−	112.846i	−0.225179	−	0.130007i
$869$	−141.904	−	529.592i	−0.163296	−	0.609427i
$870$			283.923i			0.326348i
$871$	−607.608	+	607.608i	−0.697598	+	0.697598i
$872$	−435.244			−0.499133
$873$	−53.2250	+	14.2616i	−0.0609679	+	0.0163363i
$874$	83.0718	−	143.885i	0.0950478	−	0.164628i
$875$	78.2309	−	45.1666i	0.0894067	−	0.0516190i
$876$	95.5448	+	95.5448i	0.109069	+	0.109069i
$877$	172.789	−	644.858i	0.197023	−	0.735300i	−0.794711	−	0.606988i	$-0.792377\pi$
$877$	172.789	−	644.858i	0.197023	−	0.735300i	0.991734	−	0.128312i	$-0.0409559\pi$
$878$	−56.6391	−	15.1764i	−0.0645093	−	0.0172852i
$879$	364.550	−	364.550i	0.414733	−	0.414733i
$880$	203.138	+	351.846i	0.230839	+	0.399825i
$881$	−880.173	−	508.168i	−0.999061	−	0.576808i	−0.0910907	−	0.995843i	$-0.529035\pi$
$881$	−880.173	−	508.168i	−0.999061	−	0.576808i	−0.907970	+	0.419034i	$0.862369\pi$
$882$	−46.4500	−	173.354i	−0.0526644	−	0.196546i
$883$		−	785.277i		−	0.889328i	−0.895697	−	0.444664i	$-0.853323\pi$
$883$		−	785.277i		−	0.889328i	0.895697	−	0.444664i	$-0.146677\pi$
$884$			131.867i			0.149170i
$885$	−709.261			−0.801425
$886$	27.2820	−	7.31020i	0.0307924	−	0.00825079i
$887$	−642.531	+	1112.90i	−0.724386	+	1.25467i	0.234840	+	0.972034i	$0.424543\pi$
$887$	−642.531	+	1112.90i	−0.724386	+	1.25467i	−0.959226	+	0.282640i	$0.908790\pi$
$888$	217.061	−	125.321i	0.244439	−	0.141127i
$889$	−327.311	−	327.311i	−0.368179	−	0.368179i
$890$	170.985	−	638.123i	0.192117	−	0.716992i
$891$	131.942	+	35.3538i	0.148083	+	0.0396788i
$892$	−65.0615	+	65.0615i	−0.0729389	+	0.0729389i
$893$	153.804	+	266.396i	0.172233	+	0.298316i
$894$	−336.631	−	194.354i	−0.376544	−	0.217398i
$895$	−86.9845	−	324.631i	−0.0971894	−	0.362716i
$896$		−	29.2820i		−	0.0326808i
$897$	358.650	−	621.200i	0.399833	−	0.692531i
$898$	−186.613			−0.207809
$899$	−729.449	+	195.455i	−0.811400	+	0.217414i
$900$	59.3538	−	102.804i	0.0659487	−	0.114226i
$901$	−429.015	+	247.692i	−0.476155	+	0.274908i
$902$	−649.261	−	649.261i	−0.719802	−	0.719802i
$903$	−37.8942	+	141.423i	−0.0419648	+	0.156615i
$904$	−237.100	−	63.5307i	−0.262279	−	0.0702774i
$905$	1430.75	−	1430.75i	1.58094	−	1.58094i
$906$	−275.329	−	476.885i	−0.303896	−	0.526363i
$907$	−241.501	−	139.431i	−0.266264	−	0.153727i	0.360925	−	0.932595i	$-0.382461\pi$
$907$	−241.501	−	139.431i	−0.266264	−	0.153727i	−0.627189	+	0.778867i	$0.715794\pi$
$908$	−7.11027	−	26.5359i	−0.00783070	−	0.0292246i
$909$			416.438i			0.458128i
$910$	−307.583	−	82.4167i	−0.338004	−	0.0905678i
$911$	86.7668			0.0952434			0.0476217	−	0.998865i	$-0.484836\pi$
$911$	86.7668			0.0952434			0.0476217	+	0.998865i	$0.484836\pi$
$912$	24.6795	−	6.61285i	0.0270608	−	0.00725093i
$913$	225.015	−	389.738i	0.246457	−	0.426876i
$914$	361.165	−	208.519i	0.395147	−	0.228138i
$915$	649.965	+	649.965i	0.710345	+	0.710345i
$916$	210.329	−	784.960i	0.229617	−	0.856943i
$917$	−134.090	−	35.9292i	−0.146226	−	0.0391813i
$918$	−26.3538	+	26.3538i	−0.0287079	+	0.0287079i
$919$	−288.431	−	499.577i	−0.313853	−	0.543609i	0.665340	−	0.746540i	$-0.268287\pi$
$919$	−288.431	−	499.577i	−0.313853	−	0.543609i	−0.979193	+	0.202931i	$0.934953\pi$
$920$	522.200	+	301.492i	0.567609	+	0.327709i
$921$	44.4217	+	165.784i	0.0482320	+	0.180004i
$922$			664.246i			0.720440i
$923$	180.566	+	673.883i	0.195630	+	0.730101i
$924$	136.077			0.147269
$925$	977.727	−	261.981i	1.05700	−	0.283223i
$926$	−462.599	+	801.245i	−0.499567	+	0.865276i
$927$	−278.677	+	160.894i	−0.300622	+	0.173564i
$928$	−69.2820	−	69.2820i	−0.0746574	−	0.0746574i
$929$	3.85917	−	14.4026i	0.00415411	−	0.0155034i	−0.963818	−	0.266562i	$-0.914112\pi$
$929$	3.85917	−	14.4026i	0.00415411	−	0.0155034i	0.967972	+	0.251059i	$0.0807788\pi$
$930$	690.358	+	184.981i	0.742320	+	0.198904i
$931$	110.309	−	110.309i	0.118484	−	0.118484i
$932$	27.3308	+	47.3384i	0.0293249	+	0.0507922i
$933$	210.358	+	121.450i	0.225464	+	0.130172i
$934$	145.183	+	541.832i	0.155443	+	0.580120i
$935$		−	515.138i		−	0.550950i
$936$	106.550	−	28.5500i	0.113835	−	0.0305021i
$937$	700.477			0.747574			0.373787	−	0.927515i	$-0.378059\pi$
$937$	700.477			0.747574			0.373787	+	0.927515i	$0.378059\pi$
$938$	−233.695	+	62.6185i	−0.249142	+	0.0667575i
$939$	−476.561	+	825.429i	−0.507520	+	0.879051i
$940$	−966.831	+	558.200i	−1.02854	+	0.593830i
$941$	−1147.05	−	1147.05i	−1.21897	−	1.21897i	−0.967992	−	0.250983i	$-0.919246\pi$
$941$	−1147.05	−	1147.05i	−1.21897	−	1.21897i	−0.250983	−	0.967992i	$-0.580754\pi$
$942$	−87.8494	+	327.858i	−0.0932583	+	0.348045i
$943$	−1316.32	−	352.708i	−1.39589	−	0.374027i
$944$	173.072	−	173.072i	0.183339	−	0.183339i
$945$	−45.0000	−	77.9423i	−0.0476190	−	0.0824786i
$946$	607.104	+	350.512i	0.641759	+	0.370520i
$947$	317.902	+	1186.43i	0.335694	+	1.25283i	0.903115	+	0.429400i	$0.141275\pi$
$947$	317.902	+	1186.43i	0.335694	+	1.25283i	−0.567420	+	0.823428i	$0.692059\pi$
$948$		−	125.138i		−	0.132003i
$949$	−131.241	+	489.800i	−0.138295	+	0.516122i
$950$	103.184			0.108615
$951$	−74.0385	+	19.8385i	−0.0778533	+	0.0208607i
$952$	−18.5641	+	32.1539i	−0.0195001	+	0.0337751i
$953$	−941.038	+	543.309i	−0.987449	+	0.570104i	−0.904511	−	0.426451i	$-0.859764\pi$
$953$	−941.038	+	543.309i	−0.987449	+	0.570104i	−0.0829379	+	0.996555i	$0.526430\pi$
$954$	293.023	+	293.023i	0.307152	+	0.307152i
$955$	−281.769	+	1051.58i	−0.295046	+	1.10113i
$956$	−2.35383	−	0.630707i	−0.00246216	−	0.000659735i
$957$	321.962	−	321.962i	0.336428	−	0.336428i
$958$	−254.536	−	440.869i	−0.265695	−	0.460197i
$959$	277.250	+	160.070i	0.289103	+	0.166914i
$960$	24.0000	+	89.5692i	0.0250000	+	0.0933013i
$961$			939.993i			0.978141i
$962$	814.583	+	470.300i	0.846760	+	0.488877i
$963$	16.5077			0.0171420
$964$	164.406	−	44.0526i	0.170546	−	0.0456977i
$965$	275.172	−	476.611i	0.285152	−	0.493898i
$966$	174.904	−	100.981i	0.181060	−	0.104535i
$967$	827.831	+	827.831i	0.856081	+	0.856081i	0.990874	−	0.134793i	$-0.0430368\pi$
$967$	827.831	+	827.831i	0.856081	+	0.856081i	−0.134793	+	0.990874i	$0.543037\pi$
$968$	80.0526	−	298.760i	0.0826989	−	0.308637i
$969$	−31.2923	−	8.38476i	−0.0322934	−	0.00865300i
$970$	122.918	−	122.918i	0.126719	−	0.126719i
$971$	571.850	+	990.473i	0.588929	+	1.02005i	0.994373	+	0.105935i	$0.0337835\pi$
$971$	571.850	+	990.473i	0.588929	+	1.02005i	−0.405444	+	0.914120i	$0.632883\pi$
$972$	27.0000	+	15.5885i	0.0277778	+	0.0160375i
$973$	102.965	+	384.269i	0.105822	+	0.394932i
$974$		−	274.000i		−	0.281314i
$975$	445.483			0.456906
$976$	−317.205			−0.325005
$977$	331.990	−	88.9564i	0.339805	−	0.0910505i	−0.0848811	−	0.996391i	$-0.527051\pi$
$977$	331.990	−	88.9564i	0.339805	−	0.0910505i	0.424686	+	0.905341i	$0.360384\pi$
$978$	−343.547	+	595.040i	−0.351275	+	0.608426i
$979$	−917.507	+	529.723i	−0.937188	+	0.541086i
$980$	400.344	+	400.344i	0.408514	+	0.408514i
$981$	119.483	−	445.915i	0.121797	−	0.454552i
$982$	−31.5167	−	8.44486i	−0.0320944	−	0.00859966i
$983$	630.073	−	630.073i	0.640970	−	0.640970i	−0.309824	−	0.950794i	$-0.600270\pi$
$983$	630.073	−	630.073i	0.640970	−	0.640970i	0.950794	+	0.309824i	$0.100270\pi$
$984$	−104.785	−	181.492i	−0.106488	−	0.184443i
$985$	−1565.11	−	903.615i	−1.58894	−	0.917376i
$986$	32.1539	+	120.000i	0.0326104	+	0.121704i
$987$			373.923i			0.378848i
$988$	67.8001	+	67.8001i	0.0686236	+	0.0686236i
$989$	1040.44			1.05201
$990$	−416.238	+	111.531i	−0.420443	+	0.112657i
$991$	478.369	−	828.560i	0.482714	−	0.836085i	−0.517089	−	0.855931i	$-0.672985\pi$
$991$	478.369	−	828.560i	0.482714	−	0.836085i	0.999803	+	0.0198468i	$0.00631784\pi$
$992$	−213.597	+	123.321i	−0.215320	+	0.124315i
$993$	494.715	+	494.715i	0.498202	+	0.498202i
$994$	−50.8399	+	189.737i	−0.0511468	+	0.190883i
$995$	412.310	+	110.478i	0.414382	+	0.111033i
$996$	72.6307	−	72.6307i	0.0729224	−	0.0729224i
$997$	83.5845	+	144.773i	0.0838360	+	0.145208i	0.904895	−	0.425636i	$-0.139949\pi$
$997$	83.5845	+	144.773i	0.0838360	+	0.145208i	−0.821059	+	0.570844i	$0.806616\pi$
$998$	278.460	+	160.769i	0.279018	+	0.161091i
$999$	68.8057	+	256.786i	0.0688746	+	0.257044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.3.l.a.7.1	✓	4
3.2	odd	2		234.3.bb.c.163.1		4
13.2	odd	12	inner	78.3.l.a.67.1	yes	4
13.4	even	6		1014.3.f.d.775.1		4
13.6	odd	12		1014.3.f.e.577.1		4
13.7	odd	12		1014.3.f.d.577.1		4
13.9	even	3		1014.3.f.e.775.1		4
39.2	even	12		234.3.bb.c.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.a.7.1	✓	4	1.1	even	1	trivial
78.3.l.a.67.1	yes	4	13.2	odd	12	inner
234.3.bb.c.145.1		4	39.2	even	12
234.3.bb.c.163.1		4	3.2	odd	2
1014.3.f.d.577.1		4	13.7	odd	12
1014.3.f.d.775.1		4	13.4	even	6
1014.3.f.e.577.1		4	13.6	odd	12
1014.3.f.e.775.1		4	13.9	even	3

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	78.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-4.73205 - 4.73205i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(-2.50000 - 0.669873i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.36603 + 0.366025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-4.73205 - 4.73205i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(-2.50000 - 0.669873i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(8.19615 + 4.73205i) q^{10} +(-3.92820 - 14.6603i) q^{11} -3.46410i q^{12} +(11.2583 - 6.50000i) q^{13} +3.66025 q^{14} +(-11.1962 + 3.00000i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-4.39230 + 2.53590i) q^{17} +(3.00000 + 3.00000i) q^{18} +(-0.954483 + 3.56218i) q^{19} +(-12.9282 - 3.46410i) q^{20} +(-3.16987 + 3.16987i) q^{21} +(10.7321 + 18.5885i) q^{22} +(27.5885 + 15.9282i) q^{23} +(1.26795 + 4.73205i) q^{24} +19.7846i q^{25} +(-13.0000 + 13.0000i) q^{26} -5.19615 q^{27} +(-5.00000 + 1.33975i) q^{28} +(-8.66025 + 15.0000i) q^{29} +(14.1962 - 8.19615i) q^{30} +(30.8301 + 30.8301i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-25.3923 - 6.80385i) q^{33} +(5.07180 - 5.07180i) q^{34} +(8.66025 + 15.0000i) q^{35} +(-5.19615 - 3.00000i) q^{36} +(-13.2417 - 49.4186i) q^{37} -5.21539i q^{38} -22.5167i q^{39} +18.9282 q^{40} +(-41.3205 + 11.0718i) q^{41} +(3.16987 - 5.49038i) q^{42} +(28.2846 - 16.3301i) q^{43} +(-21.4641 - 21.4641i) q^{44} +(-5.19615 + 19.3923i) q^{45} +(-43.5167 - 11.6603i) q^{46} +(58.9808 - 58.9808i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-36.6340 - 21.1506i) q^{49} +(-7.24167 - 27.0263i) q^{50} +8.78461i q^{51} +(13.0000 - 22.5167i) q^{52} +97.6743 q^{53} +(7.09808 - 1.90192i) q^{54} +(-50.7846 + 87.9615i) q^{55} +(6.33975 - 3.66025i) q^{56} +(4.51666 + 4.51666i) q^{57} +(6.33975 - 23.6603i) q^{58} +(59.1051 + 15.8372i) q^{59} +(-16.3923 + 16.3923i) q^{60} +(-39.6506 - 68.6769i) q^{61} +(-53.3993 - 30.8301i) q^{62} +(2.00962 + 7.50000i) q^{63} -8.00000i q^{64} +(-84.0333 - 22.5167i) q^{65} +37.1769 q^{66} +(-63.8468 + 17.1077i) q^{67} +(-5.07180 + 8.78461i) q^{68} +(47.7846 - 27.5885i) q^{69} +(-17.3205 - 17.3205i) q^{70} +(-13.8897 + 51.8372i) q^{71} +(8.19615 + 2.19615i) q^{72} +(-27.5814 + 27.5814i) q^{73} +(36.1769 + 62.6603i) q^{74} +(29.6769 + 17.1340i) q^{75} +(1.90897 + 7.12436i) q^{76} +39.2820i q^{77} +(8.24167 + 30.7583i) q^{78} +36.1244 q^{79} +(-25.8564 + 6.92820i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(52.3923 - 30.2487i) q^{82} +(20.9667 + 20.9667i) q^{83} +(-2.32051 + 8.66025i) q^{84} +(32.7846 + 8.78461i) q^{85} +(-32.6603 + 32.6603i) q^{86} +(15.0000 + 25.9808i) q^{87} +(37.1769 + 21.4641i) q^{88} +(-18.0666 - 67.4256i) q^{89} -28.3923i q^{90} +(-32.5000 + 8.70835i) q^{91} +63.7128 q^{92} +(72.9449 - 19.5455i) q^{93} +(-58.9808 + 102.158i) q^{94} +(21.3731 - 12.3397i) q^{95} +(6.92820 + 6.92820i) q^{96} +(4.75387 - 17.7417i) q^{97} +(57.7846 + 15.4833i) q^{98} +(-32.1962 + 32.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 12 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 12 * q^5 - 6 * q^6 - 10 * q^7 - 8 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} - 12 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9} + 12 q^{10} + 12 q^{11} - 20 q^{14} - 24 q^{15} + 8 q^{16} + 24 q^{17} + 12 q^{18} + 62 q^{19} - 24 q^{20} - 30 q^{21} + 36 q^{22} + 48 q^{23} + 12 q^{24} - 52 q^{26} - 20 q^{28} + 36 q^{30} + 106 q^{31} + 8 q^{32} - 60 q^{33} + 48 q^{34} - 98 q^{37} + 48 q^{40} - 96 q^{41} + 30 q^{42} + 30 q^{43} - 72 q^{44} - 84 q^{46} + 132 q^{47} - 150 q^{49} - 74 q^{50} + 52 q^{52} + 72 q^{53} + 18 q^{54} - 120 q^{55} + 60 q^{56} - 72 q^{57} + 60 q^{58} + 84 q^{59} - 24 q^{60} - 72 q^{61} - 30 q^{62} + 60 q^{63} - 156 q^{65} + 24 q^{66} - 148 q^{67} - 48 q^{68} + 108 q^{69} + 180 q^{71} + 12 q^{72} - 190 q^{73} + 20 q^{74} - 6 q^{75} - 124 q^{76} + 78 q^{78} + 96 q^{79} - 48 q^{80} - 18 q^{81} + 168 q^{82} + 264 q^{83} + 60 q^{84} + 48 q^{85} - 96 q^{86} + 60 q^{87} + 24 q^{88} + 288 q^{89} - 130 q^{91} + 144 q^{92} + 174 q^{93} - 132 q^{94} - 60 q^{95} + 310 q^{97} + 148 q^{98} - 108 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 12 * q^5 - 6 * q^6 - 10 * q^7 - 8 * q^8 - 6 * q^9 + 12 * q^10 + 12 * q^11 - 20 * q^14 - 24 * q^15 + 8 * q^16 + 24 * q^17 + 12 * q^18 + 62 * q^19 - 24 * q^20 - 30 * q^21 + 36 * q^22 + 48 * q^23 + 12 * q^24 - 52 * q^26 - 20 * q^28 + 36 * q^30 + 106 * q^31 + 8 * q^32 - 60 * q^33 + 48 * q^34 - 98 * q^37 + 48 * q^40 - 96 * q^41 + 30 * q^42 + 30 * q^43 - 72 * q^44 - 84 * q^46 + 132 * q^47 - 150 * q^49 - 74 * q^50 + 52 * q^52 + 72 * q^53 + 18 * q^54 - 120 * q^55 + 60 * q^56 - 72 * q^57 + 60 * q^58 + 84 * q^59 - 24 * q^60 - 72 * q^61 - 30 * q^62 + 60 * q^63 - 156 * q^65 + 24 * q^66 - 148 * q^67 - 48 * q^68 + 108 * q^69 + 180 * q^71 + 12 * q^72 - 190 * q^73 + 20 * q^74 - 6 * q^75 - 124 * q^76 + 78 * q^78 + 96 * q^79 - 48 * q^80 - 18 * q^81 + 168 * q^82 + 264 * q^83 + 60 * q^84 + 48 * q^85 - 96 * q^86 + 60 * q^87 + 24 * q^88 + 288 * q^89 - 130 * q^91 + 144 * q^92 + 174 * q^93 - 132 * q^94 - 60 * q^95 + 310 * q^97 + 148 * q^98 - 108 * q^99

Introduction

L-functions

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