LMFDB - Embedded newform 114.4.e.d.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,4,Mod(7,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("114.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	114.e (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:	$6.72621774065$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.627014547.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 26x^{4} + 169x^{2} + 147 $ x^6 + 26x^4 + 169x^2 + 147
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.2
Root			$-4.00355i$ of defining polynomial
Character	$\chi$	$=$	114.7
Dual form			114.4.e.d.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.09405 - 3.62701i) q^{5} +(3.00000 - 5.19615i) q^{6} +3.18810 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.09405 - 3.62701i) q^{5} +(3.00000 - 5.19615i) q^{6} +3.18810 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-4.18810 + 7.25401i) q^{10} +69.4003 q^{11} -12.0000 q^{12} +(4.06431 - 7.03960i) q^{13} +(-3.18810 - 5.52196i) q^{14} +(6.28216 - 10.8810i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(53.0418 + 91.8711i) q^{17} +18.0000 q^{18} +(42.6656 + 70.9834i) q^{19} +16.7524 q^{20} +(4.78216 + 8.28294i) q^{21} +(-69.4003 - 120.205i) q^{22} +(88.2468 - 152.848i) q^{23} +(12.0000 + 20.7846i) q^{24} +(53.7299 - 93.0629i) q^{25} -16.2573 q^{26} -27.0000 q^{27} +(-6.37621 + 11.0439i) q^{28} +(33.1109 - 57.3498i) q^{29} -25.1286 q^{30} -140.915 q^{31} +(-16.0000 + 27.7128i) q^{32} +(104.100 + 180.307i) q^{33} +(106.084 - 183.742i) q^{34} +(-6.67606 - 11.5633i) q^{35} +(-18.0000 - 31.1769i) q^{36} -156.003 q^{37} +(80.2814 - 144.882i) q^{38} +24.3859 q^{39} +(-16.7524 - 29.0160i) q^{40} +(207.281 + 359.022i) q^{41} +(9.56431 - 16.5659i) q^{42} +(-57.9252 - 100.329i) q^{43} +(-138.801 + 240.410i) q^{44} +37.6929 q^{45} -352.987 q^{46} +(-310.141 + 537.181i) q^{47} +(24.0000 - 41.5692i) q^{48} -332.836 q^{49} -214.920 q^{50} +(-159.125 + 275.613i) q^{51} +(16.2573 + 28.1584i) q^{52} +(185.993 - 322.149i) q^{53} +(27.0000 + 46.7654i) q^{54} +(-145.328 - 251.715i) q^{55} +25.5048 q^{56} +(-120.422 + 217.324i) q^{57} -132.444 q^{58} +(-45.8465 - 79.4084i) q^{59} +(25.1286 + 43.5241i) q^{60} +(-109.310 + 189.331i) q^{61} +(140.915 + 244.072i) q^{62} +(-14.3465 + 24.8488i) q^{63} +64.0000 q^{64} -34.0436 q^{65} +(208.201 - 360.615i) q^{66} +(72.6712 - 125.870i) q^{67} -424.334 q^{68} +529.481 q^{69} +(-13.3521 + 23.1265i) q^{70} +(-443.915 - 768.883i) q^{71} +(-36.0000 + 62.3538i) q^{72} +(-99.5081 - 172.353i) q^{73} +(156.003 + 270.205i) q^{74} +322.379 q^{75} +(-331.225 + 5.83100i) q^{76} +221.255 q^{77} +(-24.3859 - 42.2376i) q^{78} +(194.779 + 337.367i) q^{79} +(-33.5048 + 58.0321i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(414.563 - 718.044i) q^{82} +380.039 q^{83} -38.2573 q^{84} +(222.145 - 384.766i) q^{85} +(-115.850 + 200.659i) q^{86} +198.666 q^{87} +555.202 q^{88} +(212.899 - 368.753i) q^{89} +(-37.6929 - 65.2861i) q^{90} +(12.9575 - 22.4430i) q^{91} +(352.987 + 611.392i) q^{92} +(-211.372 - 366.107i) q^{93} +1240.57 q^{94} +(168.113 - 303.391i) q^{95} -96.0000 q^{96} +(-209.923 - 363.597i) q^{97} +(332.836 + 576.489i) q^{98} +(-312.301 + 540.922i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 10 q^{5} + 18 q^{6} + 14 q^{7} + 48 q^{8} - 27 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 9 * q^3 - 12 * q^4 - 10 * q^5 + 18 * q^6 + 14 * q^7 + 48 * q^8 - 27 * q^9	\( 6 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 10 q^{5} + 18 q^{6} + 14 q^{7} + 48 q^{8} - 27 q^{9} - 20 q^{10} - 88 q^{11} - 72 q^{12} + 9 q^{13} - 14 q^{14} + 30 q^{15} - 48 q^{16} + 84 q^{17} + 108 q^{18} + 32 q^{19} + 80 q^{20} + 21 q^{21} + 88 q^{22} + 2 q^{23} + 72 q^{24} + 83 q^{25} - 36 q^{26} - 162 q^{27} - 28 q^{28} - 92 q^{29} - 120 q^{30} - 218 q^{31} - 96 q^{32} - 132 q^{33} + 168 q^{34} - 282 q^{35} - 108 q^{36} + 490 q^{37} - 74 q^{38} + 54 q^{39} - 80 q^{40} + 688 q^{41} + 42 q^{42} + 103 q^{43} + 176 q^{44} + 180 q^{45} - 8 q^{46} - 322 q^{47} + 144 q^{48} - 1508 q^{49} - 332 q^{50} - 252 q^{51} + 36 q^{52} + 1322 q^{53} + 162 q^{54} + 248 q^{55} + 112 q^{56} + 111 q^{57} + 368 q^{58} - 252 q^{59} + 120 q^{60} + 435 q^{61} + 218 q^{62} - 63 q^{63} + 384 q^{64} - 3164 q^{65} - 264 q^{66} + 719 q^{67} - 672 q^{68} + 12 q^{69} - 564 q^{70} + 62 q^{71} - 216 q^{72} + 581 q^{73} - 490 q^{74} + 498 q^{75} + 20 q^{76} - 408 q^{77} - 54 q^{78} + 489 q^{79} - 160 q^{80} - 243 q^{81} + 1376 q^{82} + 4992 q^{83} - 168 q^{84} - 1632 q^{85} + 206 q^{86} - 552 q^{87} - 704 q^{88} - 1584 q^{89} - 180 q^{90} + 1573 q^{91} + 8 q^{92} - 327 q^{93} + 1288 q^{94} + 2362 q^{95} - 576 q^{96} - 974 q^{97} + 1508 q^{98} + 396 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 9 * q^3 - 12 * q^4 - 10 * q^5 + 18 * q^6 + 14 * q^7 + 48 * q^8 - 27 * q^9 - 20 * q^10 - 88 * q^11 - 72 * q^12 + 9 * q^13 - 14 * q^14 + 30 * q^15 - 48 * q^16 + 84 * q^17 + 108 * q^18 + 32 * q^19 + 80 * q^20 + 21 * q^21 + 88 * q^22 + 2 * q^23 + 72 * q^24 + 83 * q^25 - 36 * q^26 - 162 * q^27 - 28 * q^28 - 92 * q^29 - 120 * q^30 - 218 * q^31 - 96 * q^32 - 132 * q^33 + 168 * q^34 - 282 * q^35 - 108 * q^36 + 490 * q^37 - 74 * q^38 + 54 * q^39 - 80 * q^40 + 688 * q^41 + 42 * q^42 + 103 * q^43 + 176 * q^44 + 180 * q^45 - 8 * q^46 - 322 * q^47 + 144 * q^48 - 1508 * q^49 - 332 * q^50 - 252 * q^51 + 36 * q^52 + 1322 * q^53 + 162 * q^54 + 248 * q^55 + 112 * q^56 + 111 * q^57 + 368 * q^58 - 252 * q^59 + 120 * q^60 + 435 * q^61 + 218 * q^62 - 63 * q^63 + 384 * q^64 - 3164 * q^65 - 264 * q^66 + 719 * q^67 - 672 * q^68 + 12 * q^69 - 564 * q^70 + 62 * q^71 - 216 * q^72 + 581 * q^73 - 490 * q^74 + 498 * q^75 + 20 * q^76 - 408 * q^77 - 54 * q^78 + 489 * q^79 - 160 * q^80 - 243 * q^81 + 1376 * q^82 + 4992 * q^83 - 168 * q^84 - 1632 * q^85 + 206 * q^86 - 552 * q^87 - 704 * q^88 - 1584 * q^89 - 180 * q^90 + 1573 * q^91 + 8 * q^92 - 327 * q^93 + 1288 * q^94 + 2362 * q^95 - 576 * q^96 - 974 * q^97 + 1508 * q^98 + 396 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−2.09405	−	3.62701i	−0.187298	−	0.324409i	0.757051	−	0.653356i	$-0.226640\pi$
$5$	−2.09405	−	3.62701i	−0.187298	−	0.324409i	−0.944348	+	0.328947i	$0.893306\pi$
$6$	3.00000	−	5.19615i	0.204124	−	0.353553i
$7$	3.18810			0.172141			0.0860707	−	0.996289i	$-0.472569\pi$
$7$	3.18810			0.172141			0.0860707	+	0.996289i	$0.472569\pi$
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−4.18810	+	7.25401i	−0.132440	+	0.229392i
$11$	69.4003			1.90227			0.951135	−	0.308774i	$-0.0999187\pi$
$11$	69.4003			1.90227			0.951135	+	0.308774i	$0.0999187\pi$
$12$	−12.0000			−0.288675
$13$	4.06431	−	7.03960i	0.0867106	−	0.150187i	−0.819408	−	0.573210i	$-0.805698\pi$
$13$	4.06431	−	7.03960i	0.0867106	−	0.150187i	0.906119	+	0.423023i	$0.139031\pi$
$14$	−3.18810	−	5.52196i	−0.0608612	−	0.105415i
$15$	6.28216	−	10.8810i	0.108136	−	0.187298i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	53.0418	+	91.8711i	0.756737	+	1.31071i	0.944506	+	0.328493i	$0.106541\pi$
$17$	53.0418	+	91.8711i	0.756737	+	1.31071i	−0.187770	+	0.982213i	$0.560126\pi$
$18$	18.0000			0.235702
$19$	42.6656	+	70.9834i	0.515166	+	0.857090i
$19$	42.6656	+	70.9834i	0.515166	+	0.857090i
$20$	16.7524			0.187298
$21$	4.78216	+	8.28294i	0.0496930	+	0.0860707i
$22$	−69.4003	−	120.205i	−0.672554	−	1.16490i
$23$	88.2468	−	152.848i	0.800031	−	1.38570i	−0.119563	−	0.992827i	$-0.538149\pi$
$23$	88.2468	−	152.848i	0.800031	−	1.38570i	0.919595	−	0.392869i	$-0.128517\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	53.7299	−	93.0629i	0.429839	−	0.744503i
$26$	−16.2573			−0.122627
$27$	−27.0000			−0.192450
$28$	−6.37621	+	11.0439i	−0.0430354	+	0.0745394i
$29$	33.1109	−	57.3498i	0.212019	−	0.367227i	−0.740327	−	0.672247i	$-0.765330\pi$
$29$	33.1109	−	57.3498i	0.212019	−	0.367227i	0.952346	+	0.305019i	$0.0986628\pi$
$30$	−25.1286			−0.152928
$31$	−140.915			−0.816421			−0.408210	−	0.912888i	$-0.633847\pi$
$31$	−140.915			−0.816421			−0.408210	+	0.912888i	$0.633847\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	104.100	+	180.307i	0.549138	+	0.951135i
$34$	106.084	−	183.742i	0.535094	−	0.926809i
$35$	−6.67606	−	11.5633i	−0.0322417	−	0.0558443i
$36$	−18.0000	−	31.1769i	−0.0833333	−	0.144338i
$37$	−156.003			−0.693156			−0.346578	−	0.938021i	$-0.612656\pi$
$37$	−156.003			−0.693156			−0.346578	+	0.938021i	$0.612656\pi$
$38$	80.2814	−	144.882i	0.342720	−	0.618501i
$39$	24.3859			0.100125
$40$	−16.7524	−	29.0160i	−0.0662198	−	0.114696i
$41$	207.281	+	359.022i	0.789559	+	1.36756i	0.926238	+	0.376940i	$0.123024\pi$
$41$	207.281	+	359.022i	0.789559	+	1.36756i	−0.136679	+	0.990615i	$0.543643\pi$
$42$	9.56431	−	16.5659i	0.0351382	−	0.0608612i
$43$	−57.9252	−	100.329i	−0.205430	−	0.355816i	0.744839	−	0.667244i	$-0.232526\pi$
$43$	−57.9252	−	100.329i	−0.205430	−	0.355816i	−0.950270	+	0.311428i	$0.899193\pi$
$44$	−138.801	+	240.410i	−0.475568	+	0.823707i
$45$	37.6929			0.124865
$46$	−352.987			−1.13142
$47$	−310.141	+	537.181i	−0.962527	+	1.66715i	−0.246410	+	0.969166i	$0.579251\pi$
$47$	−310.141	+	537.181i	−0.962527	+	1.66715i	−0.716117	+	0.697980i	$0.754082\pi$
$48$	24.0000	−	41.5692i	0.0721688	−	0.125000i
$49$	−332.836			−0.970367
$50$	−214.920			−0.607884
$51$	−159.125	+	275.613i	−0.436902	+	0.756737i
$52$	16.2573	+	28.1584i	0.0433553	+	0.0750936i
$53$	185.993	−	322.149i	0.482039	−	0.834916i	−0.517748	−	0.855533i	$-0.673230\pi$
$53$	185.993	−	322.149i	0.482039	−	0.834916i	0.999787	+	0.0206167i	$0.00656296\pi$
$54$	27.0000	+	46.7654i	0.0680414	+	0.117851i
$55$	−145.328	−	251.715i	−0.356291	−	0.617114i
$56$	25.5048			0.0608612
$57$	−120.422	+	217.324i	−0.279830	+	0.505004i
$58$	−132.444			−0.299840
$59$	−45.8465	−	79.4084i	−0.101164	−	0.175222i	0.811000	−	0.585046i	$-0.198923\pi$
$59$	−45.8465	−	79.4084i	−0.101164	−	0.175222i	−0.912165	+	0.409824i	$0.865590\pi$
$60$	25.1286	+	43.5241i	0.0540682	+	0.0936489i
$61$	−109.310	+	189.331i	−0.229438	+	0.397399i	−0.957642	−	0.287962i	$-0.907022\pi$
$61$	−109.310	+	189.331i	−0.229438	+	0.397399i	0.728203	+	0.685361i	$0.240356\pi$
$62$	140.915	+	244.072i	0.288648	+	0.499954i
$63$	−14.3465	+	24.8488i	−0.0286902	+	0.0496930i
$64$	64.0000			0.125000
$65$	−34.0436			−0.0649628
$66$	208.201	−	360.615i	0.388299	−	0.672554i
$67$	72.6712	−	125.870i	0.132510	−	0.229515i	−0.792133	−	0.610348i	$-0.791030\pi$
$67$	72.6712	−	125.870i	0.132510	−	0.229515i	0.924644	+	0.380833i	$0.124363\pi$
$68$	−424.334			−0.756737
$69$	529.481			0.923797
$70$	−13.3521	+	23.1265i	−0.0227983	+	0.0394879i
$71$	−443.915	−	768.883i	−0.742014	−	1.28521i	−0.951577	−	0.307410i	$-0.900538\pi$
$71$	−443.915	−	768.883i	−0.742014	−	1.28521i	0.209563	−	0.977795i	$-0.432796\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	−99.5081	−	172.353i	−0.159542	−	0.276334i	0.775162	−	0.631763i	$-0.217668\pi$
$73$	−99.5081	−	172.353i	−0.159542	−	0.276334i	−0.934703	+	0.355429i	$0.884335\pi$
$74$	156.003	+	270.205i	0.245067	+	0.424469i
$75$	322.379			0.496335
$76$	−331.225	+	5.83100i	−0.499923	+	0.00880082i
$77$	221.255			0.327460
$78$	−24.3859	−	42.2376i	−0.0353995	−	0.0613137i
$79$	194.779	+	337.367i	0.277397	+	0.480465i	0.970737	−	0.240145i	$-0.0771951\pi$
$79$	194.779	+	337.367i	0.277397	+	0.480465i	−0.693340	+	0.720610i	$0.743862\pi$
$80$	−33.5048	+	58.0321i	−0.0468244	+	0.0811023i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	414.563	−	718.044i	0.558302	−	0.967008i
$83$	380.039			0.502586			0.251293	−	0.967911i	$-0.419144\pi$
$83$	380.039			0.502586			0.251293	+	0.967911i	$0.419144\pi$
$84$	−38.2573			−0.0496930
$85$	222.145	−	384.766i	0.283470	−	0.490985i
$86$	−115.850	+	200.659i	−0.145261	+	0.251600i
$87$	198.666			0.244818
$88$	555.202			0.672554
$89$	212.899	−	368.753i	0.253565	−	0.439188i	−0.710940	−	0.703253i	$-0.751730\pi$
$89$	212.899	−	368.753i	0.253565	−	0.439188i	0.964505	+	0.264065i	$0.0850635\pi$
$90$	−37.6929	−	65.2861i	−0.0441465	−	0.0764640i
$91$	12.9575	−	22.4430i	0.0149265	−	0.0258534i
$92$	352.987	+	611.392i	0.400016	+	0.692848i
$93$	−211.372	−	366.107i	−0.235680	−	0.408210i
$94$	1240.57			1.36122
$95$	168.113	−	303.391i	0.181559	−	0.327656i
$96$	−96.0000			−0.102062
$97$	−209.923	−	363.597i	−0.219736	−	0.380595i	0.734991	−	0.678077i	$-0.237186\pi$
$97$	−209.923	−	363.597i	−0.219736	−	0.380595i	−0.954727	+	0.297482i	$0.903853\pi$
$98$	332.836	+	576.489i	0.343077	+	0.594226i
$99$	−312.301	+	540.922i	−0.317045	+	0.549138i
$100$	214.920	+	372.252i	0.214920	+	0.372252i
$101$	620.855	−	1075.35i	0.611657	−	1.05942i	−0.379304	−	0.925272i	$-0.623836\pi$
$101$	620.855	−	1075.35i	0.611657	−	1.05942i	0.990961	−	0.134150i	$-0.0428302\pi$
$102$	636.501			0.617873
$103$	−593.606			−0.567862			−0.283931	−	0.958845i	$-0.591639\pi$
$103$	−593.606			−0.567862			−0.283931	+	0.958845i	$0.591639\pi$
$104$	32.5145	−	56.3168i	0.0306568	−	0.0530992i
$105$	20.0282	−	34.6898i	0.0186148	−	0.0322417i
$106$	−743.971			−0.681706
$107$	−1778.56			−1.60691			−0.803457	−	0.595363i	$-0.797008\pi$
$107$	−1778.56			−1.60691			−0.803457	+	0.595363i	$0.797008\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	534.995	+	926.639i	0.470121	+	0.814274i	0.999416	−	0.0341638i	$-0.0108768\pi$
$109$	534.995	+	926.639i	0.470121	+	0.814274i	−0.529295	+	0.848438i	$0.677543\pi$
$110$	−290.656	+	503.431i	−0.251936	+	0.436366i
$111$	−234.005	−	405.308i	−0.200097	−	0.346578i
$112$	−25.5048	−	44.1757i	−0.0215177	−	0.0372697i
$113$	583.197			0.485510			0.242755	−	0.970088i	$-0.421949\pi$
$113$	583.197			0.485510			0.242755	+	0.970088i	$0.421949\pi$
$114$	496.837	−	8.74651i	0.408185	−	0.00718584i
$115$	−739.173			−0.599376
$116$	132.444	+	229.399i	0.106009	+	0.183614i
$117$	36.5788	+	63.3564i	0.0289035	+	0.0500624i
$118$	−91.6929	+	158.817i	−0.0715341	+	0.123901i
$119$	169.103	+	292.895i	0.130266	+	0.225627i
$120$	50.2573	−	87.0481i	0.0382320	−	0.0662198i
$121$	3485.40			2.61863
$122$	437.241			0.324475
$123$	−621.844	+	1077.07i	−0.455852	+	0.789559i
$124$	281.830	−	488.143i	0.204105	−	0.353521i
$125$	−973.566			−0.696627
$126$	57.3859			0.0405741
$127$	−829.677	+	1437.04i	−0.579700	+	1.00407i	0.415814	+	0.909450i	$0.363497\pi$
$127$	−829.677	+	1437.04i	−0.579700	+	1.00407i	−0.995513	+	0.0946199i	$0.969836\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	173.776	−	300.988i	0.118605	−	0.205430i
$130$	34.0436	+	58.9652i	0.0229678	+	0.0397814i
$131$	−298.773	−	517.490i	−0.199267	−	0.345140i	0.749024	−	0.662543i	$-0.230523\pi$
$131$	−298.773	−	517.490i	−0.199267	−	0.345140i	−0.948291	+	0.317403i	$0.897189\pi$
$132$	−832.804			−0.549138
$133$	136.022	+	226.303i	0.0886814	+	0.147541i
$134$	−290.685			−0.187398
$135$	56.5394	+	97.9291i	0.0360455	+	0.0624326i
$136$	424.334	+	734.969i	0.267547	+	0.463405i
$137$	888.654	−	1539.19i	0.554182	−	0.959871i	−0.443785	−	0.896133i	$-0.646365\pi$
$137$	888.654	−	1539.19i	0.554182	−	0.959871i	0.997967	−	0.0637373i	$-0.0203020\pi$
$138$	−529.481	−	917.087i	−0.326611	−	0.565708i
$139$	−81.7836	+	141.653i	−0.0499050	+	0.0864379i	−0.889899	−	0.456158i	$-0.849225\pi$
$139$	−81.7836	+	141.653i	−0.0499050	+	0.0864379i	0.839994	+	0.542596i	$0.182559\pi$
$140$	53.4085			0.0322417
$141$	−1860.85			−1.11143
$142$	−887.829	+	1537.77i	−0.524683	+	0.908778i
$143$	282.065	−	488.550i	0.164947	−	0.285697i
$144$	144.000			0.0833333
$145$	−277.344			−0.158843
$146$	−199.016	+	344.706i	−0.112813	+	0.195398i
$147$	−499.254	−	864.733i	−0.280121	−	0.485184i
$148$	312.006	−	540.411i	0.173289	−	0.300145i
$149$	559.899	+	969.774i	0.307844	+	0.533201i	0.977890	−	0.209118i	$-0.0670592\pi$
$149$	559.899	+	969.774i	0.307844	+	0.533201i	−0.670047	+	0.742319i	$0.733726\pi$
$150$	−322.379	−	558.377i	−0.175481	−	0.303942i
$151$	−2807.15			−1.51286			−0.756432	−	0.654073i	$-0.773059\pi$
$151$	−2807.15			−1.51286			−0.756432	+	0.654073i	$0.773059\pi$
$152$	341.325	+	567.868i	0.182139	+	0.303027i
$153$	−954.752			−0.504491
$154$	−221.255	−	383.226i	−0.115774	−	0.200527i
$155$	295.083	+	511.099i	0.152914	+	0.264854i
$156$	−48.7718	+	84.4752i	−0.0250312	+	0.0433553i
$157$	−501.971	−	869.439i	−0.255170	−	0.441967i	0.709772	−	0.704432i	$-0.248798\pi$
$157$	−501.971	−	869.439i	−0.255170	−	0.441967i	−0.964942	+	0.262465i	$0.915465\pi$
$158$	389.558	−	674.734i	0.196149	−	0.339740i
$159$	1115.96			0.556611
$160$	134.019			0.0662198
$161$	281.340	−	487.295i	0.137719	−	0.238536i
$162$	−81.0000	+	140.296i	−0.0392837	+	0.0680414i
$163$	1271.99			0.611225			0.305612	−	0.952156i	$-0.401139\pi$
$163$	1271.99			0.611225			0.305612	+	0.952156i	$0.401139\pi$
$164$	−1658.25			−0.789559
$165$	435.984	−	755.146i	0.205705	−	0.356291i
$166$	−380.039	−	658.246i	−0.177691	−	0.307770i
$167$	1492.49	−	2585.07i	0.691572	−	1.19784i	−0.279751	−	0.960073i	$-0.590252\pi$
$167$	1492.49	−	2585.07i	0.691572	−	1.19784i	0.971323	−	0.237765i	$-0.0764149\pi$
$168$	38.2573	+	66.2635i	0.0175691	+	0.0304306i
$169$	1065.46	+	1845.44i	0.484963	+	0.839980i
$170$	−888.578			−0.400887
$171$	−745.256	+	13.1198i	−0.333282	+	0.00586721i
$172$	463.402			0.205430
$173$	−28.3873	−	49.1683i	−0.0124754	−	0.0216081i	0.859720	−	0.510765i	$-0.170638\pi$
$173$	−28.3873	−	49.1683i	−0.0124754	−	0.0216081i	−0.872196	+	0.489157i	$0.837304\pi$
$174$	−198.666	−	344.099i	−0.0865563	−	0.149920i
$175$	171.297	−	296.694i	0.0739931	−	0.128160i
$176$	−555.202	−	961.639i	−0.237784	−	0.411854i
$177$	137.539	−	238.225i	0.0584073	−	0.101164i
$178$	−851.598			−0.358595
$179$	−4640.98			−1.93790			−0.968948	−	0.247266i	$-0.920468\pi$
$179$	−4640.98			−1.93790			−0.968948	+	0.247266i	$0.920468\pi$
$180$	−75.3859	+	130.572i	−0.0312163	+	0.0540682i
$181$	−1887.70	+	3269.60i	−0.775204	+	1.34269i	0.159476	+	0.987202i	$0.449020\pi$
$181$	−1887.70	+	3269.60i	−0.775204	+	1.34269i	−0.934680	+	0.355491i	$0.884314\pi$
$182$	−51.8298			−0.0211093
$183$	−655.862			−0.264933
$184$	705.974	−	1222.78i	0.282854	−	0.489917i
$185$	326.679	+	565.824i	0.129826	+	0.224866i
$186$	−422.744	+	732.215i	−0.166651	+	0.288648i
$187$	3681.12	+	6375.88i	1.43952	+	2.49332i
$188$	−1240.57	−	2148.72i	−0.481264	−	0.833573i
$189$	−86.0788			−0.0331286
$190$	−693.603	+	12.2104i	−0.264838	+	0.00466230i
$191$	−2762.53			−1.04654			−0.523271	−	0.852166i	$-0.675288\pi$
$191$	−2762.53			−1.04654			−0.523271	+	0.852166i	$0.675288\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	−1030.76	−	1785.32i	−0.384433	−	0.665857i	0.607258	−	0.794505i	$-0.292270\pi$
$193$	−1030.76	−	1785.32i	−0.384433	−	0.665857i	−0.991690	+	0.128648i	$0.958936\pi$
$194$	−419.846	+	727.194i	−0.155377	+	0.269121i
$195$	−51.0653	−	88.4477i	−0.0187531	−	0.0324814i
$196$	665.672	−	1152.98i	0.242592	−	0.420181i
$197$	2094.82			0.757614			0.378807	−	0.925476i	$-0.376334\pi$
$197$	2094.82			0.757614			0.378807	+	0.925476i	$0.376334\pi$
$198$	1249.21			0.448370
$199$	858.681	−	1487.28i	0.305881	−	0.529801i	−0.671576	−	0.740935i	$-0.734382\pi$
$199$	858.681	−	1487.28i	0.305881	−	0.529801i	0.977457	+	0.211134i	$0.0677158\pi$
$200$	429.839	−	744.503i	0.151971	−	0.263222i
$201$	436.027			0.153010
$202$	−2483.42			−0.865014
$203$	105.561	−	182.837i	0.0364972	−	0.0632151i
$204$	−636.501	−	1102.45i	−0.218451	−	0.378368i
$205$	868.116	−	1503.62i	0.295765	−	0.512280i
$206$	593.606	+	1028.16i	0.200769	+	0.347743i
$207$	794.221	+	1375.63i	0.266677	+	0.461898i
$208$	−130.058			−0.0433553
$209$	2961.00	+	4926.27i	0.979985	+	1.63042i
$210$	−80.1127			−0.0263252
$211$	1145.53	+	1984.11i	0.373750	+	0.647354i	0.990139	−	0.140088i	$-0.0447384\pi$
$211$	1145.53	+	1984.11i	0.373750	+	0.647354i	−0.616389	+	0.787442i	$0.711405\pi$
$212$	743.971	+	1288.60i	0.241020	+	0.417458i
$213$	1331.74	−	2306.65i	0.428402	−	0.742014i
$214$	1778.56	+	3080.55i	0.568130	+	0.984030i
$215$	−242.597	+	420.190i	−0.0769533	+	0.133287i
$216$	−216.000			−0.0680414
$217$	−449.251			−0.140540
$218$	1069.99	−	1853.28i	0.332426	−	0.575779i
$219$	298.524	−	517.059i	0.0921114	−	0.159542i
$220$	1162.62			0.356291
$221$	862.314			0.262468
$222$	−468.009	+	810.616i	−0.141490	+	0.245067i
$223$	−1628.09	−	2819.94i	−0.488902	−	0.846804i	0.511016	−	0.859571i	$-0.329269\pi$
$223$	−1628.09	−	2819.94i	−0.488902	−	0.846804i	−0.999918	+	0.0127673i	$0.995936\pi$
$224$	−51.0097	+	88.3514i	−0.0152153	+	0.0263537i
$225$	483.569	+	837.566i	0.143280	+	0.248168i
$226$	−583.197	−	1010.13i	−0.171654	−	0.297313i
$227$	−998.044			−0.291817			−0.145909	−	0.989298i	$-0.546611\pi$
$227$	−998.044			−0.291817			−0.145909	+	0.989298i	$0.546611\pi$
$228$	−511.987	−	851.801i	−0.148716	−	0.247421i
$229$	−1028.59			−0.296816			−0.148408	−	0.988926i	$-0.547415\pi$
$229$	−1028.59			−0.296816			−0.148408	+	0.988926i	$0.547415\pi$
$230$	739.173	+	1280.29i	0.211912	+	0.367042i
$231$	331.883	+	574.838i	0.0945295	+	0.163730i
$232$	264.887	−	458.799i	0.0749600	−	0.129835i
$233$	62.7431	+	108.674i	0.0176414	+	0.0305557i	0.874711	−	0.484644i	$-0.161051\pi$
$233$	62.7431	+	108.674i	0.0176414	+	0.0305557i	−0.857070	+	0.515200i	$0.827718\pi$
$234$	73.1577	−	126.713i	0.0204379	−	0.0353995i
$235$	2597.81			0.721117
$236$	366.772			0.101164
$237$	−584.337	+	1012.10i	−0.160155	+	0.277397i
$238$	338.206	−	585.789i	0.0921118	−	0.159542i
$239$	3591.03			0.971901			0.485950	−	0.873986i	$-0.338474\pi$
$239$	3591.03			0.971901			0.485950	+	0.873986i	$0.338474\pi$
$240$	−201.029			−0.0540682
$241$	1845.92	−	3197.23i	0.493386	−	0.854570i	−0.506585	−	0.862190i	$-0.669092\pi$
$241$	1845.92	−	3197.23i	0.493386	−	0.854570i	0.999971	+	0.00762002i	$0.00242555\pi$
$242$	−3485.40	−	6036.89i	−0.925827	−	1.60358i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−437.241	−	757.324i	−0.114719	−	0.198700i
$245$	696.976	+	1207.20i	0.181748	+	0.314796i
$246$	2487.38			0.644672
$247$	673.101	−	11.8495i	0.173394	−	0.00305250i
$248$	−1127.32			−0.288648
$249$	570.058	+	987.369i	0.145084	+	0.251293i
$250$	973.566	+	1686.27i	0.246295	+	0.426595i
$251$	−3647.44	+	6317.55i	−0.917228	+	1.58869i	−0.113622	+	0.993524i	$0.536245\pi$
$251$	−3647.44	+	6317.55i	−0.917228	+	1.58869i	−0.803606	+	0.595162i	$0.797088\pi$
$252$	−57.3859	−	99.3953i	−0.0143451	−	0.0248465i
$253$	6124.35	−	10607.7i	1.52188	−	2.63597i
$254$	3318.71			0.819820
$255$	1332.87			0.327323
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1151.60	+	1994.63i	−0.279513	+	0.484131i	−0.971264	−	0.238006i	$-0.923506\pi$
$257$	−1151.60	+	1994.63i	−0.279513	+	0.484131i	0.691751	+	0.722136i	$0.256840\pi$
$258$	−695.102			−0.167733
$259$	−497.354			−0.119321
$260$	68.0871	−	117.930i	0.0162407	−	0.0281297i
$261$	297.998	+	516.148i	0.0706730	+	0.122409i
$262$	−597.546	+	1034.98i	−0.140903	+	0.244051i
$263$	−3569.19	−	6182.01i	−0.836827	−	1.44943i	−0.892534	−	0.450980i	$-0.851075\pi$
$263$	−3569.19	−	6182.01i	−0.836827	−	1.44943i	0.0557070	−	0.998447i	$-0.482259\pi$
$264$	832.804	+	1442.46i	0.194150	+	0.336277i
$265$	−1557.91			−0.361139
$266$	255.945	−	461.900i	0.0589963	−	0.106470i
$267$	1277.40			0.292792
$268$	290.685	+	503.481i	0.0662552	+	0.114757i
$269$	2723.33	+	4716.95i	0.617265	+	1.06913i	0.989983	+	0.141190i	$0.0450928\pi$
$269$	2723.33	+	4716.95i	0.617265	+	1.06913i	−0.372717	+	0.927945i	$0.621574\pi$
$270$	113.079	−	195.858i	0.0254880	−	0.0441465i
$271$	1701.84	+	2947.67i	0.381474	+	0.660732i	0.991273	−	0.131824i	$-0.0420834\pi$
$271$	1701.84	+	2947.67i	0.381474	+	0.660732i	−0.609799	+	0.792556i	$0.708750\pi$
$272$	848.669	−	1469.94i	0.189184	−	0.327677i
$273$	77.7448			0.0172356
$274$	−3554.62			−0.783731
$275$	3728.87	−	6458.59i	0.817670	−	1.41625i
$276$	−1058.96	+	1834.17i	−0.230949	+	0.400016i
$277$	−5131.93			−1.11317			−0.556584	−	0.830791i	$-0.687888\pi$
$277$	−5131.93			−1.11317			−0.556584	+	0.830791i	$0.687888\pi$
$278$	327.134			0.0705763
$279$	634.117	−	1098.32i	0.136070	−	0.235680i
$280$	−53.4085	−	92.5062i	−0.0113992	−	0.0197439i
$281$	−1683.34	+	2915.63i	−0.357365	+	0.618975i	−0.987520	−	0.157495i	$-0.949658\pi$
$281$	−1683.34	+	2915.63i	−0.357365	+	0.618975i	0.630154	+	0.776470i	$0.282992\pi$
$282$	1860.85	+	3223.08i	0.392950	+	0.680609i
$283$	−3342.88	−	5790.04i	−0.702168	−	1.21619i	−0.967704	−	0.252090i	$-0.918882\pi$
$283$	−3342.88	−	5790.04i	−0.702168	−	1.21619i	0.265535	−	0.964101i	$-0.414451\pi$
$284$	3551.32			0.742014
$285$	1040.40	−	18.3156i	0.216239	−	0.00380675i
$286$	−1128.26			−0.233270
$287$	660.835	+	1144.60i	0.135916	+	0.235413i
$288$	−144.000	−	249.415i	−0.0294628	−	0.0510310i
$289$	−3170.36	+	5491.23i	−0.645301	+	1.11769i
$290$	277.344	+	480.374i	0.0561593	+	0.0972708i
$291$	629.768	−	1090.79i	0.126865	−	0.219736i
$292$	796.065			0.159542
$293$	−5625.93			−1.12174			−0.560871	−	0.827903i	$-0.689534\pi$
$293$	−5625.93			−1.12174			−0.560871	+	0.827903i	$0.689534\pi$
$294$	−998.508	+	1729.47i	−0.198075	+	0.343077i
$295$	−192.010	+	332.571i	−0.0378957	+	0.0656374i
$296$	−1248.02			−0.245067
$297$	−1873.81			−0.366092
$298$	1119.80	−	1939.55i	0.217678	−	0.377030i
$299$	−717.325	−	1242.44i	−0.138742	−	0.240309i
$300$	−644.759	+	1116.75i	−0.124084	+	0.214920i
$301$	−184.672	−	319.861i	−0.0353631	−	0.0612507i
$302$	2807.15	+	4862.12i	0.534878	+	0.926436i
$303$	3725.13			0.706281
$304$	642.251	−	1159.06i	0.121170	−	0.218673i
$305$	915.606			0.171893
$306$	954.752	+	1653.68i	0.178365	+	0.308936i
$307$	−2801.77	−	4852.81i	−0.520865	−	0.902164i	−0.999706	−	0.0242627i	$-0.992276\pi$
$307$	−2801.77	−	4852.81i	−0.520865	−	0.902164i	0.478841	−	0.877902i	$-0.341057\pi$
$308$	−442.511	+	766.451i	−0.0818649	+	0.141794i
$309$	−890.409	−	1542.23i	−0.163928	−	0.283931i
$310$	590.166	−	1022.20i	0.108126	−	0.187280i
$311$	6668.20			1.21582			0.607908	−	0.794008i	$-0.292009\pi$
$311$	6668.20			1.21582			0.607908	+	0.794008i	$0.292009\pi$
$312$	195.087			0.0353995
$313$	−2245.70	+	3889.67i	−0.405541	+	0.702418i	−0.994384	−	0.105829i	$-0.966250\pi$
$313$	−2245.70	+	3889.67i	−0.405541	+	0.702418i	0.588843	+	0.808247i	$0.299584\pi$
$314$	−1003.94	+	1738.88i	−0.180432	+	0.312518i
$315$	120.169			0.0214945
$316$	−1558.23			−0.277397
$317$	633.023	−	1096.43i	0.112158	−	0.194264i	−0.804482	−	0.593977i	$-0.797557\pi$
$317$	633.023	−	1096.43i	0.112158	−	0.194264i	0.916640	+	0.399713i	$0.130890\pi$
$318$	−1115.96	−	1932.89i	−0.196792	−	0.340853i
$319$	2297.91	−	3980.10i	0.403317	−	0.698566i
$320$	−134.019	−	232.128i	−0.0234122	−	0.0405512i
$321$	−2667.84	−	4620.83i	−0.463876	−	0.803457i
$322$	−1125.36			−0.194764
$323$	−4258.27	+	7684.82i	−0.733549	+	1.32382i
$324$	324.000			0.0555556
$325$	−436.750	−	756.474i	−0.0745432	−	0.129113i
$326$	−1271.99	−	2203.14i	−0.216101	−	0.374297i
$327$	−1604.99	+	2779.92i	−0.271425	+	0.470121i
$328$	1658.25	+	2872.17i	0.279151	+	0.483504i
$329$	−988.763	+	1712.59i	−0.165691	+	0.286985i
$330$	−1743.93			−0.290910
$331$	−5068.09			−0.841594			−0.420797	−	0.907155i	$-0.638249\pi$
$331$	−5068.09			−0.841594			−0.420797	+	0.907155i	$0.638249\pi$
$332$	−760.077	+	1316.49i	−0.125647	+	0.217626i
$333$	702.014	−	1215.92i	0.115526	−	0.200097i
$334$	−5969.97			−0.978031
$335$	−608.709			−0.0992757
$336$	76.5145	−	132.527i	0.0124232	−	0.0215177i
$337$	−5372.06	−	9304.68i	−0.868352	−	1.50403i	−0.863680	−	0.504041i	$-0.831846\pi$
$337$	−5372.06	−	9304.68i	−0.868352	−	1.50403i	−0.00467268	−	0.999989i	$-0.501487\pi$
$338$	2130.93	−	3690.87i	0.342920	−	0.593955i
$339$	874.796	+	1515.19i	0.140155	+	0.242755i
$340$	888.578	+	1539.06i	0.141735	+	0.245492i
$341$	−9779.53			−1.55305
$342$	767.980	+	1277.70i	0.121426	+	0.202018i
$343$	−2154.64			−0.339182
$344$	−463.402	−	802.635i	−0.0726306	−	0.125800i
$345$	−1108.76	−	1920.43i	−0.173025	−	0.299688i
$346$	−56.7747	+	98.3367i	−0.00882146	+	0.0152792i
$347$	2425.67	+	4201.38i	0.375264	+	0.649977i	0.990367	−	0.138471i	$-0.0442186\pi$
$347$	2425.67	+	4201.38i	0.375264	+	0.649977i	−0.615102	+	0.788447i	$0.710885\pi$
$348$	−397.331	+	688.198i	−0.0612046	+	0.106009i
$349$	−7611.35			−1.16741			−0.583705	−	0.811966i	$-0.698398\pi$
$349$	−7611.35			−1.16741			−0.583705	+	0.811966i	$0.698398\pi$
$350$	−685.186			−0.104642
$351$	−109.736	+	190.069i	−0.0166875	+	0.0289035i
$352$	−1110.40	+	1923.28i	−0.168139	+	0.291225i
$353$	5567.64			0.839477			0.419739	−	0.907645i	$-0.362122\pi$
$353$	5567.64			0.839477			0.419739	+	0.907645i	$0.362122\pi$
$354$	−550.158			−0.0826004
$355$	−1859.16	+	3220.16i	−0.277955	+	0.481432i
$356$	851.598	+	1475.01i	0.126783	+	0.219594i
$357$	−507.308	+	878.684i	−0.0752090	+	0.130266i
$358$	4640.98	+	8038.42i	0.685149	+	1.18671i
$359$	−2170.66	−	3759.69i	−0.319116	−	0.552726i	0.661187	−	0.750221i	$-0.270053\pi$
$359$	−2170.66	−	3759.69i	−0.319116	−	0.552726i	−0.980304	+	0.197495i	$0.936719\pi$
$360$	301.544			0.0441465
$361$	−3218.30	+	6057.10i	−0.469208	+	0.883088i
$362$	7550.82			1.09630
$363$	5228.10	+	9055.34i	0.755935	+	1.30932i
$364$	51.8298	+	89.7719i	0.00746325	+	0.0129267i
$365$	−416.750	+	721.833i	−0.0597636	+	0.103514i
$366$	655.862	+	1135.99i	0.0936679	+	0.162238i
$367$	4482.24	−	7763.47i	0.637524	−	1.10422i	−0.348451	−	0.937327i	$-0.613292\pi$
$367$	4482.24	−	7763.47i	0.637524	−	1.10422i	0.985974	−	0.166896i	$-0.0533745\pi$
$368$	−2823.90			−0.400016
$369$	−3731.06			−0.526372
$370$	653.357	−	1131.65i	0.0918012	−	0.159004i
$371$	592.965	−	1027.04i	0.0829789	−	0.143724i
$372$	1690.98			0.235680
$373$	5048.11			0.700755			0.350377	−	0.936609i	$-0.386053\pi$
$373$	5048.11			0.700755			0.350377	+	0.936609i	$0.386053\pi$
$374$	7362.23	−	12751.8i	1.01789	−	1.76304i
$375$	−1460.35	−	2529.40i	−0.201099	−	0.348314i
$376$	−2481.13	+	4297.45i	−0.340305	+	0.589425i
$377$	−269.147	−	466.175i	−0.0367686	−	0.0636850i
$378$	86.0788	+	149.093i	0.0117127	+	0.0202871i
$379$	−9290.41			−1.25915			−0.629573	−	0.776941i	$-0.716770\pi$
$379$	−9290.41			−1.25915			−0.629573	+	0.776941i	$0.716770\pi$
$380$	714.752	+	1189.14i	0.0964894	+	0.160531i
$381$	−4978.06			−0.669380
$382$	2762.53	+	4784.84i	0.370009	+	0.640874i
$383$	−2081.13	−	3604.62i	−0.277652	−	0.480907i	0.693149	−	0.720794i	$-0.256223\pi$
$383$	−2081.13	−	3604.62i	−0.277652	−	0.480907i	−0.970801	+	0.239887i	$0.922890\pi$
$384$	192.000	−	332.554i	0.0255155	−	0.0441942i
$385$	−463.320	−	802.495i	−0.0613325	−	0.106231i
$386$	−2061.51	+	3570.65i	−0.271835	+	0.470832i
$387$	1042.65			0.136954
$388$	1679.38			0.219736
$389$	−2092.61	+	3624.51i	−0.272750	+	0.472417i	−0.969565	−	0.244834i	$-0.921267\pi$
$389$	−2092.61	+	3624.51i	−0.272750	+	0.472417i	0.696815	+	0.717251i	$0.254600\pi$
$390$	−102.131	+	176.895i	−0.0132605	+	0.0229678i
$391$	18723.1			2.42165
$392$	−2662.69			−0.343077
$393$	896.320	−	1552.47i	0.115047	−	0.199267i
$394$	−2094.82	−	3628.34i	−0.267857	−	0.463942i
$395$	815.754	−	1412.93i	0.103912	−	0.179980i
$396$	−1249.21	−	2163.69i	−0.158523	−	0.274569i
$397$	2264.88	+	3922.89i	0.286325	+	0.495930i	0.972930	−	0.231101i	$-0.0742329\pi$
$397$	2264.88	+	3922.89i	0.286325	+	0.495930i	−0.686605	+	0.727031i	$0.740900\pi$
$398$	−3434.72			−0.432581
$399$	−383.918	+	692.850i	−0.0481703	+	0.0869321i
$400$	−1719.36			−0.214920
$401$	4748.53	+	8224.69i	0.591347	+	1.02424i	0.994051	+	0.108913i	$0.0347370\pi$
$401$	4748.53	+	8224.69i	0.591347	+	1.02424i	−0.402704	+	0.915330i	$0.631930\pi$
$402$	−436.027	−	755.221i	−0.0540972	−	0.0936991i
$403$	−572.722	+	991.984i	−0.0707924	+	0.122616i
$404$	2483.42	+	4301.41i	0.305829	+	0.529711i
$405$	−169.618	+	293.787i	−0.0208109	+	0.0360455i
$406$	−422.245			−0.0516149
$407$	−10826.7			−1.31857
$408$	−1273.00	+	2204.91i	−0.154468	+	0.267547i
$409$	2677.22	−	4637.08i	0.323667	−	0.560608i	−0.657574	−	0.753390i	$-0.728417\pi$
$409$	2677.22	−	4637.08i	0.323667	−	0.560608i	0.981242	+	0.192781i	$0.0617508\pi$
$410$	−3472.46			−0.418275
$411$	5331.93			0.639914
$412$	1187.21	−	2056.31i	0.141965	−	0.245891i
$413$	−146.163	−	253.162i	−0.0174146	−	0.0301630i
$414$	1588.44	−	2751.26i	0.188569	−	0.326611i
$415$	−795.821	−	1378.40i	−0.0941333	−	0.163044i
$416$	130.058	+	225.267i	0.0153284	+	0.0265496i
$417$	−490.701			−0.0576253
$418$	5571.55	−	10054.9i	0.651946	−	1.17656i
$419$	14506.1			1.69134			0.845668	−	0.533709i	$-0.179202\pi$
$419$	14506.1			1.69134			0.845668	+	0.533709i	$0.179202\pi$
$420$	80.1127	+	138.759i	0.00930738	+	0.0161209i
$421$	631.724	+	1094.18i	0.0731315	+	0.126667i	0.900272	−	0.435327i	$-0.143367\pi$
$421$	631.724	+	1094.18i	0.0731315	+	0.126667i	−0.827141	+	0.561995i	$0.810034\pi$
$422$	2291.05	−	3968.22i	0.264281	−	0.457749i
$423$	−2791.27	−	4834.63i	−0.320842	−	0.555715i
$424$	1487.94	−	2577.19i	0.170427	−	0.295187i
$425$	11399.7			1.30110
$426$	−5326.98			−0.605852
$427$	−348.493	+	603.607i	−0.0394959	+	0.0684089i
$428$	3557.12	−	6161.11i	0.401729	−	0.695814i
$429$	1692.39			0.190464
$430$	970.387			0.108828
$431$	4093.81	−	7090.69i	0.457522	−	0.792451i	−0.541308	−	0.840825i	$-0.682071\pi$
$431$	4093.81	−	7090.69i	0.457522	−	0.792451i	0.998829	+	0.0483738i	$0.0154039\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	4621.47	−	8004.63i	0.512919	−	0.888401i	−0.486969	−	0.873419i	$-0.661898\pi$
$433$	4621.47	−	8004.63i	0.512919	−	0.888401i	0.999888	−	0.0149820i	$-0.00476910\pi$
$434$	449.251	+	778.126i	0.0496884	+	0.0860628i
$435$	−416.016	−	720.561i	−0.0458539	−	0.0794213i
$436$	−4279.96			−0.470121
$437$	14614.8	−	257.284i	1.59982	−	0.0281637i
$438$	−1194.10			−0.130265
$439$	1021.52	+	1769.33i	0.111059	+	0.192359i	0.916197	−	0.400727i	$-0.131243\pi$
$439$	1021.52	+	1769.33i	0.111059	+	0.192359i	−0.805139	+	0.593086i	$0.797909\pi$
$440$	−1162.62	−	2013.72i	−0.125968	−	0.218183i
$441$	1497.76	−	2594.20i	0.161728	−	0.280121i
$442$	−862.314	−	1493.57i	−0.0927966	−	0.160728i
$443$	4834.57	−	8373.71i	0.518504	−	0.898075i	−0.481265	−	0.876575i	$-0.659823\pi$
$443$	4834.57	−	8373.71i	0.518504	−	0.898075i	0.999769	−	0.0214998i	$-0.00684413\pi$
$444$	1872.04			0.200097
$445$	−1783.29			−0.189969
$446$	−3256.19	+	5639.88i	−0.345706	+	0.598781i
$447$	−1679.70	+	2909.32i	−0.177734	+	0.307844i
$448$	204.039			0.0215177
$449$	−13227.2			−1.39027			−0.695134	−	0.718881i	$-0.744655\pi$
$449$	−13227.2			−1.39027			−0.695134	+	0.718881i	$0.744655\pi$
$450$	967.138	−	1675.13i	0.101314	−	0.175481i
$451$	14385.4	+	24916.2i	1.50195	+	2.60146i
$452$	−1166.39	+	2020.26i	−0.121377	+	0.210232i
$453$	−4210.72	−	7293.18i	−0.436726	−	0.756432i
$454$	998.044	+	1728.66i	0.103173	+	0.178701i
$455$	−108.534			−0.0111828
$456$	−963.376	+	1738.59i	−0.0989347	+	0.178546i
$457$	−5380.98			−0.550791			−0.275396	−	0.961331i	$-0.588809\pi$
$457$	−5380.98			−0.550791			−0.275396	+	0.961331i	$0.588809\pi$
$458$	1028.59	+	1781.56i	0.104940	+	0.181762i
$459$	−1432.13	−	2480.52i	−0.145634	−	0.252246i
$460$	1478.35	−	2560.57i	0.149844	−	0.259538i
$461$	1422.33	+	2463.55i	0.143698	+	0.248892i	0.928886	−	0.370365i	$-0.120767\pi$
$461$	1422.33	+	2463.55i	0.143698	+	0.248892i	−0.785189	+	0.619257i	$0.787434\pi$
$462$	663.766	−	1149.68i	0.0668424	−	0.115774i
$463$	6625.39			0.665028			0.332514	−	0.943098i	$-0.392103\pi$
$463$	6625.39			0.665028			0.332514	+	0.943098i	$0.392103\pi$
$464$	−1059.55			−0.106009
$465$	−885.249	+	1533.30i	−0.0882848	+	0.152914i
$466$	125.486	−	217.348i	0.0124743	−	0.0216062i
$467$	−18635.1			−1.84653			−0.923264	−	0.384167i	$-0.874489\pi$
$467$	−18635.1			−1.84653			−0.923264	+	0.384167i	$0.874489\pi$
$468$	−292.631			−0.0289035
$469$	231.683	−	401.288i	0.0228106	−	0.0395090i
$470$	−2597.81	−	4499.54i	−0.254953	−	0.441592i
$471$	1505.91	−	2608.32i	0.147322	−	0.255170i
$472$	−366.772	−	635.267i	−0.0357670	−	0.0619503i
$473$	−4020.03	−	6962.89i	−0.390784	−	0.676858i
$474$	2337.35			0.226493
$475$	8898.34	−	156.650i	0.859545	−	0.0151317i
$476$	−1352.82			−0.130266
$477$	1673.94	+	2899.34i	0.160680	+	0.278305i
$478$	−3591.03	−	6219.84i	−0.343619	−	0.595165i
$479$	−778.310	+	1348.07i	−0.0742420	+	0.128591i	−0.900756	−	0.434325i	$-0.856987\pi$
$479$	−778.310	+	1348.07i	−0.0742420	+	0.128591i	0.826514	+	0.562916i	$0.190320\pi$
$480$	201.029	+	348.192i	0.0191160	+	0.0331099i
$481$	−634.046	+	1098.20i	−0.0601039	+	0.104103i
$482$	−7383.68			−0.697754
$483$	1688.04			0.159024
$484$	−6970.80	+	12073.8i	−0.654659	+	1.13390i
$485$	−879.179	+	1522.78i	−0.0823123	+	0.142569i
$486$	−486.000			−0.0453609
$487$	19339.5			1.79950			0.899751	−	0.436405i	$-0.143748\pi$
$487$	19339.5			1.79950			0.899751	+	0.436405i	$0.143748\pi$
$488$	−874.482	+	1514.65i	−0.0811188	+	0.140502i
$489$	1907.98	+	3304.72i	0.176445	+	0.305612i
$490$	1393.95	−	2414.40i	0.128515	−	0.222594i
$491$	3419.12	+	5922.10i	0.314262	+	0.544319i	0.979280	−	0.202509i	$-0.0649095\pi$
$491$	3419.12	+	5922.10i	0.314262	+	0.544319i	−0.665018	+	0.746827i	$0.731576\pi$
$492$	−2487.38	−	4308.26i	−0.227926	−	0.394779i
$493$	7025.05			0.641770
$494$	−693.625	−	1154.00i	−0.0631734	−	0.105103i
$495$	2615.90			0.237527
$496$	1127.32	+	1952.57i	0.102053	+	0.176760i
$497$	−1415.25	−	2451.28i	−0.127731	−	0.221237i
$498$	1140.12	−	1974.74i	0.102590	−	0.177691i
$499$	9057.49	+	15688.0i	0.812563	+	1.40740i	0.911065	+	0.412263i	$0.135262\pi$
$499$	9057.49	+	15688.0i	0.812563	+	1.40740i	−0.0985021	+	0.995137i	$0.531405\pi$
$500$	1947.13	−	3372.53i	0.174157	−	0.301648i
$501$	8954.95			0.798559
$502$	14589.8			1.29716
$503$	2915.92	−	5050.53i	0.258478	−	0.447698i	−0.707356	−	0.706857i	$-0.750112\pi$
$503$	2915.92	−	5050.53i	0.258478	−	0.447698i	0.965834	+	0.259160i	$0.0834456\pi$
$504$	−114.772	+	198.791i	−0.0101435	+	0.0175691i
$505$	−5200.41			−0.458248
$506$	−24497.4			−2.15226
$507$	−3196.39	+	5536.31i	−0.279993	+	0.484963i
$508$	−3318.71	−	5748.17i	−0.289850	−	0.502035i
$509$	−4957.32	+	8586.34i	−0.431689	+	0.747707i	−0.997019	−	0.0771579i	$-0.975415\pi$
$509$	−4957.32	+	8586.34i	−0.431689	+	0.747707i	0.565330	+	0.824865i	$0.308749\pi$
$510$	−1332.87	−	2308.59i	−0.115726	−	0.200444i
$511$	−317.242	−	549.480i	−0.0274637	−	0.0475686i
$512$	512.000			0.0441942
$513$	−1151.97	−	1916.55i	−0.0991437	−	0.164947i
$514$	4606.40			0.395291
$515$	1243.04	+	2153.01i	0.106359	+	0.184220i
$516$	695.102	+	1203.95i	0.0593027	+	0.102715i
$517$	−21523.9	+	37280.5i	−1.83099	+	3.17136i
$518$	497.354	+	861.443i	0.0421863	+	0.0730688i
$519$	85.1620	−	147.505i	0.00720269	−	0.0124754i
$520$	−272.348			−0.0229678
$521$	−5851.91			−0.492086			−0.246043	−	0.969259i	$-0.579131\pi$
$521$	−5851.91			−0.492086			−0.246043	+	0.969259i	$0.579131\pi$
$522$	595.997	−	1032.30i	0.0499733	−	0.0865563i
$523$	−3447.05	+	5970.46i	−0.288200	+	0.499178i	−0.973380	−	0.229196i	$-0.926390\pi$
$523$	−3447.05	+	5970.46i	−0.288200	+	0.499178i	0.685180	+	0.728374i	$0.259724\pi$
$524$	2390.19			0.199267
$525$	1027.78			0.0854399
$526$	−7138.38	+	12364.0i	−0.591726	+	1.02490i
$527$	−7474.37	−	12946.0i	−0.617816	−	1.07009i
$528$	1665.61	−	2884.92i	0.137285	−	0.237784i
$529$	−9491.49	−	16439.7i	−0.780101	−	1.35117i
$530$	1557.91	+	2698.39i	0.127682	+	0.221152i
$531$	825.236			0.0674430
$532$	−1055.98	+	18.5899i	−0.0860574	+	0.00151499i
$533$	3369.83			0.273853
$534$	−1277.40	−	2212.52i	−0.103518	−	0.179298i
$535$	3724.40	+	6450.84i	0.300971	+	0.521298i
$536$	581.370	−	1006.96i	0.0468495	−	0.0811458i
$537$	−6961.47	−	12057.6i	−0.559422	−	0.968948i
$538$	5446.66	−	9433.89i	0.436472	−	0.755992i
$539$	−23098.9			−1.84590
$540$	−452.315			−0.0360455
$541$	2812.50	−	4871.39i	0.223509	−	0.387130i	−0.732362	−	0.680916i	$-0.761582\pi$
$541$	2812.50	−	4871.39i	0.223509	−	0.387130i	0.955871	+	0.293786i	$0.0949153\pi$
$542$	3403.68	−	5895.34i	0.269743	−	0.467208i
$543$	−11326.2			−0.895129
$544$	−3394.67			−0.267547
$545$	2240.62	−	3880.86i	0.176105	−	0.305023i
$546$	−77.7448	−	134.658i	−0.00609372	−	0.0105546i
$547$	−1798.07	+	3114.35i	−0.140548	+	0.243437i	−0.927703	−	0.373319i	$-0.878220\pi$
$547$	−1798.07	+	3114.35i	−0.140548	+	0.243437i	0.787155	+	0.616755i	$0.211553\pi$
$548$	3554.62	+	6156.78i	0.277091	+	0.479935i
$549$	−983.793	−	1703.98i	−0.0764795	−	0.132466i
$550$	−14915.5			−1.15636
$551$	5483.59	−	96.5350i	0.423972	−	0.00746376i
$552$	4235.85			0.326611
$553$	620.975	+	1075.56i	0.0477515	+	0.0827080i
$554$	5131.93	+	8888.76i	0.393564	+	0.681674i
$555$	−980.036	+	1697.47i	−0.0749553	+	0.129826i
$556$	−327.134	−	566.613i	−0.0249525	−	0.0432190i
$557$	−9190.73	+	15918.8i	−0.699145	+	1.21095i	0.269618	+	0.962967i	$0.413103\pi$
$557$	−9190.73	+	15918.8i	−0.699145	+	1.21095i	−0.968763	+	0.247987i	$0.920231\pi$
$558$	−2536.47			−0.192432
$559$	−941.705			−0.0712520
$560$	−106.817	+	185.012i	−0.00806043	+	0.0139611i
$561$	−11043.3	+	19127.6i	−0.831106	+	1.43952i
$562$	6733.36			0.505391
$563$	5578.33			0.417582			0.208791	−	0.977960i	$-0.433047\pi$
$563$	5578.33			0.417582			0.208791	+	0.977960i	$0.433047\pi$
$564$	3721.70	−	6446.17i	0.277858	−	0.481264i
$565$	−1221.25	−	2115.26i	−0.0909349	−	0.157504i
$566$	−6685.76	+	11580.1i	−0.496508	+	0.859977i
$567$	−129.118	−	223.639i	−0.00956342	−	0.0165643i
$568$	−3551.32	−	6151.06i	−0.262341	−	0.454389i
$569$	16981.3			1.25113			0.625564	−	0.780173i	$-0.284869\pi$
$569$	16981.3			1.25113			0.625564	+	0.780173i	$0.284869\pi$
$570$	−1072.13	−	1783.72i	−0.0787833	−	0.131073i
$571$	−19520.5			−1.43066			−0.715332	−	0.698785i	$-0.753724\pi$
$571$	−19520.5			−1.43066			−0.715332	+	0.698785i	$0.753724\pi$
$572$	1128.26	+	1954.20i	0.0824735	+	0.142848i
$573$	−4143.79	−	7177.26i	−0.302111	−	0.523271i
$574$	1321.67	−	2289.20i	0.0961070	−	0.166462i
$575$	−9482.98	−	16425.0i	−0.687770	−	1.19125i
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	6371.35			0.459693			0.229846	−	0.973227i	$-0.426178\pi$
$577$	6371.35			0.459693			0.229846	+	0.973227i	$0.426178\pi$
$578$	12681.4			0.912593
$579$	3092.27	−	5355.97i	0.221952	−	0.384433i
$580$	554.688	−	960.748i	0.0397107	−	0.0687809i
$581$	1211.60			0.0865159
$582$	−2519.07			−0.179414
$583$	12908.0	−	22357.2i	0.916969	−	1.58824i
$584$	−796.065	−	1378.82i	−0.0564065	−	0.0976989i
$585$	153.196	−	265.343i	0.0108271	−	0.0187531i
$586$	5625.93	+	9744.39i	0.396596	+	0.686924i
$587$	−5379.52	−	9317.61i	−0.378257	−	0.655160i	0.612552	−	0.790430i	$-0.290143\pi$
$587$	−5379.52	−	9317.61i	−0.378257	−	0.655160i	−0.990809	+	0.135271i	$0.956810\pi$
$588$	3994.03			0.280121
$589$	−6012.21	−	10002.6i	−0.420592	−	0.699747i
$590$	768.039			0.0535927
$591$	3142.23	+	5442.51i	0.218704	+	0.378807i
$592$	1248.02	+	2161.64i	0.0866444	+	0.150073i
$593$	−1805.88	+	3127.87i	−0.125057	+	0.216604i	−0.921755	−	0.387773i	$-0.873245\pi$
$593$	−1805.88	+	3127.87i	−0.125057	+	0.216604i	0.796698	+	0.604377i	$0.206578\pi$
$594$	1873.81	+	3245.53i	0.129433	+	0.224185i
$595$	708.220	−	1226.67i	0.0487970	−	0.0845188i
$596$	−4479.19			−0.307844
$597$	5152.09			0.353201
$598$	−1434.65	+	2484.89i	−0.0981057	+	0.169924i
$599$	4590.12	−	7950.31i	0.313100	−	0.542306i	−0.665932	−	0.746013i	$-0.731966\pi$
$599$	4590.12	−	7950.31i	0.313100	−	0.542306i	0.979032	+	0.203707i	$0.0652991\pi$
$600$	2579.03			0.175481
$601$	12700.4			0.862000			0.431000	−	0.902352i	$-0.358161\pi$
$601$	12700.4			0.862000			0.431000	+	0.902352i	$0.358161\pi$
$602$	−369.343	+	639.721i	−0.0250055	+	0.0433108i
$603$	654.041	+	1132.83i	0.0441702	+	0.0765050i
$604$	5614.29	−	9724.24i	0.378216	−	0.655089i
$605$	−7298.61	−	12641.6i	−0.490464	−	0.849509i
$606$	−3725.13	−	6452.12i	−0.249708	−	0.432507i
$607$	−24227.5			−1.62004			−0.810019	−	0.586404i	$-0.800543\pi$
$607$	−24227.5			−1.62004			−0.810019	+	0.586404i	$0.800543\pi$
$608$	−2649.80	+	46.6480i	−0.176749	+	0.00311156i
$609$	633.367			0.0421434
$610$	−915.606	−	1585.88i	−0.0607734	−	0.105263i
$611$	2521.02	+	4366.54i	0.166923	+	0.289119i
$612$	1909.50	−	3307.36i	0.126123	−	0.218451i
$613$	8106.74	+	14041.3i	0.534141	+	0.925159i	0.999204	+	0.0398814i	$0.0126980\pi$
$613$	8106.74	+	14041.3i	0.534141	+	0.925159i	−0.465064	+	0.885277i	$0.653969\pi$
$614$	−5603.54	+	9705.62i	−0.368307	+	0.637927i
$615$	5208.70			0.341520
$616$	1770.04			0.115774
$617$	10757.7	−	18632.8i	0.701924	−	1.21577i	−0.265866	−	0.964010i	$-0.585658\pi$
$617$	10757.7	−	18632.8i	0.701924	−	1.21577i	0.967790	−	0.251758i	$-0.0810087\pi$
$618$	−1780.82	+	3084.47i	−0.115914	+	0.200769i
$619$	−15878.5			−1.03103			−0.515516	−	0.856880i	$-0.672400\pi$
$619$	−15878.5			−1.03103			−0.515516	+	0.856880i	$0.672400\pi$
$620$	−2360.66			−0.152914
$621$	−2382.66	+	4126.89i	−0.153966	+	0.266677i
$622$	−6668.20	−	11549.7i	−0.429856	−	0.744532i
$623$	678.746	−	1175.62i	0.0436491	−	0.0756024i
$624$	−195.087	−	337.901i	−0.0125156	−	0.0216777i
$625$	−4677.54	−	8101.73i	−0.299362	−	0.518511i
$626$	8982.80			0.573522
$627$	−8357.32	+	15082.3i	−0.532312	+	0.960654i
$628$	4015.77			0.255170
$629$	−8274.68	−	14332.2i	−0.524536	−	0.908523i
$630$	−120.169	−	208.139i	−0.00759944	−	0.0131626i
$631$	−2779.87	+	4814.88i	−0.175380	+	0.303768i	−0.940293	−	0.340366i	$-0.889449\pi$
$631$	−2779.87	+	4814.88i	−0.175380	+	0.303768i	0.764912	+	0.644134i	$0.222782\pi$
$632$	1558.23	+	2698.94i	0.0980745	+	0.169870i
$633$	−3436.58	+	5952.33i	−0.215785	+	0.373750i
$634$	−2532.09			−0.158616
$635$	6949.55			0.434306
$636$	−2231.91	+	3865.79i	−0.139153	+	0.241020i
$637$	−1352.75	+	2343.03i	−0.0841412	+	0.145737i
$638$	−9191.64			−0.570377
$639$	7990.46			0.494676
$640$	−268.039	+	464.257i	−0.0165549	+	0.0286740i
$641$	10243.5	+	17742.2i	0.631190	+	1.09325i	0.987309	+	0.158812i	$0.0507665\pi$
$641$	10243.5	+	17742.2i	0.631190	+	1.09325i	−0.356119	+	0.934441i	$0.615900\pi$
$642$	−5335.68	+	9241.66i	−0.328010	+	0.568130i
$643$	2051.15	+	3552.69i	0.125800	+	0.217892i	0.922045	−	0.387082i	$-0.126517\pi$
$643$	2051.15	+	3552.69i	0.125800	+	0.217892i	−0.796245	+	0.604974i	$0.793184\pi$
$644$	1125.36	+	1949.18i	0.0688593	+	0.119268i
$645$	−1455.58			−0.0888580
$646$	17568.8	−	309.287i	1.07002	−	0.0188370i
$647$	22860.4			1.38908			0.694539	−	0.719455i	$-0.255608\pi$
$647$	22860.4			1.38908			0.694539	+	0.719455i	$0.255608\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	−3181.76	−	5510.97i	−0.192442	−	0.333320i
$650$	−873.501	+	1512.95i	−0.0527100	+	0.0912964i
$651$	−673.877	−	1167.19i	−0.0405704	−	0.0702700i
$652$	−2543.97	+	4406.29i	−0.152806	+	0.264668i
$653$	26388.5			1.58141			0.790706	−	0.612197i	$-0.209714\pi$
$653$	26388.5			1.58141			0.790706	+	0.612197i	$0.209714\pi$
$654$	6419.94			0.383853
$655$	−1251.29	+	2167.30i	−0.0746444	+	0.129288i
$656$	3316.50	−	5744.35i	0.197390	−	0.341889i
$657$	1791.15			0.106361
$658$	3955.05			0.234322
$659$	−1611.65	+	2791.45i	−0.0952668	+	0.165007i	−0.909720	−	0.415222i	$-0.863704\pi$
$659$	−1611.65	+	2791.45i	−0.0952668	+	0.165007i	0.814453	+	0.580229i	$0.197037\pi$
$660$	1743.93	+	3020.58i	0.102852	+	0.178146i
$661$	13740.1	−	23798.5i	0.808513	−	1.40039i	−0.105381	−	0.994432i	$-0.533606\pi$
$661$	13740.1	−	23798.5i	0.808513	−	1.40039i	0.913894	−	0.405953i	$-0.133060\pi$
$662$	5068.09	+	8778.19i	0.297548	+	0.515369i
$663$	1293.47	+	2240.36i	0.0757681	+	0.131234i
$664$	3040.31			0.177691
$665$	535.963	−	967.243i	0.0312538	−	0.0564031i
$666$	−2808.06			−0.163378
$667$	−5843.87	−	10121.9i	−0.339244	−	0.587587i
$668$	5969.97	+	10340.3i	0.345786	+	0.598919i
$669$	4884.28	−	8459.82i	0.282268	−	0.488902i
$670$	608.709	+	1054.32i	0.0350992	+	0.0607937i
$671$	−7586.17	+	13139.6i	−0.436454	+	0.755961i
$672$	−306.058			−0.0175691
$673$	−2165.00			−0.124004			−0.0620020	−	0.998076i	$-0.519749\pi$
$673$	−2165.00			−0.124004			−0.0620020	+	0.998076i	$0.519749\pi$
$674$	−10744.1	+	18609.4i	−0.614018	+	1.06351i
$675$	−1450.71	+	2512.70i	−0.0827226	+	0.143280i
$676$	−8523.70			−0.484963
$677$	11999.0			0.681179			0.340589	−	0.940212i	$-0.389373\pi$
$677$	11999.0			0.681179			0.340589	+	0.940212i	$0.389373\pi$
$678$	1749.59	−	3030.38i	0.0991043	−	0.171654i
$679$	−669.256	−	1159.19i	−0.0378258	−	0.0655161i
$680$	1777.16	−	3078.13i	0.100222	−	0.173589i
$681$	−1497.07	−	2593.00i	−0.0842404	−	0.145909i
$682$	9779.53	+	16938.6i	0.549087	+	0.951047i
$683$	5234.35			0.293246			0.146623	−	0.989192i	$-0.453160\pi$
$683$	5234.35			0.293246			0.146623	+	0.989192i	$0.453160\pi$
$684$	1445.06	−	2607.88i	0.0807798	−	0.145782i
$685$	−7443.56			−0.415188
$686$	2154.64	+	3731.94i	0.119919	+	0.207706i
$687$	−1542.88	−	2672.34i	−0.0856834	−	0.148408i
$688$	−926.803	+	1605.27i	−0.0513576	+	0.0889540i
$689$	−1511.87	−	2618.63i	−0.0835958	−	0.144792i
$690$	−2217.52	+	3840.86i	−0.122347	+	0.211912i
$691$	−5160.63			−0.284109			−0.142055	−	0.989859i	$-0.545371\pi$
$691$	−5160.63			−0.284109			−0.142055	+	0.989859i	$0.545371\pi$
$692$	227.099			0.0124754
$693$	−995.649	+	1724.52i	−0.0545766	+	0.0945295i
$694$	4851.34	−	8402.76i	0.265352	−	0.459603i
$695$	685.036			0.0373884
$696$	1589.32			0.0865563
$697$	−21989.1	+	38086.3i	−1.19498	+	2.06976i
$698$	7611.35	+	13183.2i	0.412742	+	0.714890i
$699$	−188.229	+	326.023i	−0.0101852	+	0.0176414i
$700$	685.186	+	1186.78i	0.0369966	+	0.0640799i
$701$	1657.51	+	2870.90i	0.0893059	+	0.154682i	0.907218	−	0.420661i	$-0.138202\pi$
$701$	1657.51	+	2870.90i	0.0893059	+	0.154682i	−0.817912	+	0.575343i	$0.804868\pi$
$702$	438.946			0.0235996
$703$	−6655.96	−	11073.6i	−0.357090	−	0.594097i
$704$	4441.62			0.237784
$705$	3896.71	+	6749.31i	0.208168	+	0.360558i
$706$	−5567.64	−	9643.43i	−0.296800	−	0.514073i
$707$	1979.35	−	3428.34i	0.105292	−	0.182370i
$708$	550.158	+	952.901i	0.0292037	+	0.0505822i
$709$	9166.60	−	15877.0i	0.485555	−	0.841007i	−0.514307	−	0.857606i	$-0.671951\pi$
$709$	9166.60	−	15877.0i	0.485555	−	0.841007i	0.999862	+	0.0165995i	$0.00528404\pi$
$710$	7436.64			0.393088
$711$	−3506.02			−0.184931
$712$	1703.20	−	2950.02i	0.0896488	−	0.155276i
$713$	−12435.3	+	21538.5i	−0.653162	+	1.13131i
$714$	2029.23			0.106362
$715$	−2362.63			−0.123577
$716$	9281.96	−	16076.8i	0.484474	−	0.839133i
$717$	5386.54	+	9329.76i	0.280564	+	0.485950i
$718$	−4341.31	+	7519.37i	−0.225649	+	0.390836i
$719$	−4873.50	−	8441.15i	−0.252783	−	0.437833i	0.711508	−	0.702678i	$-0.248013\pi$
$719$	−4873.50	−	8441.15i	−0.252783	−	0.437833i	−0.964291	+	0.264845i	$0.914679\pi$
$720$	−301.544	−	522.289i	−0.0156081	−	0.0270341i
$721$	−1892.48			−0.0977526
$722$	13709.5	−	482.844i	0.706669	−	0.0248886i
$723$	11075.5			0.569713
$724$	−7550.82	−	13078.4i	−0.387602	−	0.671346i
$725$	−3558.09	−	6162.80i	−0.182268	−	0.315697i
$726$	10456.2	−	18110.7i	0.534526	−	0.925827i
$727$	−16361.8	−	28339.4i	−0.834697	−	1.44574i	−0.894277	−	0.447515i	$-0.852309\pi$
$727$	−16361.8	−	28339.4i	−0.834697	−	1.44574i	0.0595791	−	0.998224i	$-0.481024\pi$
$728$	103.660	−	179.544i	0.00527731	−	0.00914057i
$729$	729.000			0.0370370
$730$	1667.00			0.0845185
$731$	6144.91	−	10643.3i	0.310914	−	0.538518i
$732$	1311.72	−	2271.97i	0.0662332	−	0.114719i
$733$	36938.2			1.86131			0.930657	−	0.365894i	$-0.119237\pi$
$733$	36938.2			1.86131			0.930657	+	0.365894i	$0.119237\pi$
$734$	−17929.0			−0.901594
$735$	−2090.93	+	3621.59i	−0.104932	+	0.181748i
$736$	2823.90	+	4891.13i	0.141427	+	0.244959i
$737$	5043.40	−	8735.43i	0.252071	−	0.436599i
$738$	3731.06	+	6462.39i	0.186101	+	0.322336i
$739$	4993.60	+	8649.16i	0.248569	+	0.430534i	0.963129	−	0.269040i	$-0.0867064\pi$
$739$	4993.60	+	8649.16i	0.248569	+	0.430534i	−0.714560	+	0.699574i	$0.753373\pi$
$740$	−2613.43			−0.129826
$741$	1040.44	+	1730.99i	0.0515809	+	0.0858160i
$742$	−2371.86			−0.117350
$743$	−10869.9	−	18827.2i	−0.536713	−	0.929615i	−0.999078	−	0.0429249i	$-0.986332\pi$
$743$	−10869.9	−	18827.2i	−0.536713	−	0.929615i	0.462365	−	0.886690i	$-0.347001\pi$
$744$	−1690.98	−	2928.86i	−0.0833256	−	0.144324i
$745$	2344.92	−	4061.51i	0.115317	−	0.199735i
$746$	−5048.11	−	8743.59i	−0.247754	−	0.429123i
$747$	−1710.17	+	2962.11i	−0.0837644	+	0.145084i
$748$	−29448.9			−1.43952
$749$	−5670.23			−0.276617
$750$	−2920.70	+	5058.80i	−0.142198	+	0.246295i
$751$	19033.7	−	32967.3i	0.924833	−	1.60186i	0.133003	−	0.991116i	$-0.457538\pi$
$751$	19033.7	−	32967.3i	0.924833	−	1.60186i	0.791830	−	0.610742i	$-0.209129\pi$
$752$	9924.53			0.481264
$753$	−21884.6			−1.05912
$754$	−538.293	+	932.351i	−0.0259993	+	0.0450321i
$755$	5878.31	+	10181.5i	0.283356	+	0.490787i
$756$	172.158	−	298.186i	0.00828216	−	0.0143451i
$757$	5682.61	+	9842.58i	0.272838	+	0.472569i	0.969587	−	0.244746i	$-0.0787045\pi$
$757$	5682.61	+	9842.58i	0.272838	+	0.472569i	−0.696750	+	0.717314i	$0.745371\pi$
$758$	9290.41	+	16091.5i	0.445176	+	0.771067i
$759$	36746.1			1.75731
$760$	1344.91	−	2427.13i	0.0641907	−	0.115844i
$761$	24549.3			1.16940			0.584699	−	0.811250i	$-0.301213\pi$
$761$	24549.3			1.16940			0.584699	+	0.811250i	$0.301213\pi$
$762$	4978.06	+	8622.25i	0.236662	+	0.409910i
$763$	1705.62	+	2954.22i	0.0809274	+	0.140170i
$764$	5525.06	−	9569.68i	0.261636	−	0.453166i
$765$	1999.30	+	3462.89i	0.0944900	+	0.163662i
$766$	−4162.26	+	7209.24i	−0.196330	+	0.340053i
$767$	−745.338			−0.0350881
$768$	−768.000			−0.0360844
$769$	−7111.27	+	12317.1i	−0.333471	+	0.577588i	−0.983190	−	0.182586i	$-0.941553\pi$
$769$	−7111.27	+	12317.1i	−0.333471	+	0.577588i	0.649719	+	0.760174i	$0.274886\pi$
$770$	−926.641	+	1604.99i	−0.0433686	+	0.0751166i
$771$	−6909.60			−0.322754
$772$	8246.06			0.384433
$773$	−8041.29	+	13927.9i	−0.374159	+	0.648063i	−0.990201	−	0.139651i	$-0.955402\pi$
$773$	−8041.29	+	13927.9i	−0.374159	+	0.648063i	0.616041	+	0.787714i	$0.288735\pi$
$774$	−1042.65	−	1805.93i	−0.0484204	−	0.0838666i
$775$	−7571.34	+	13113.9i	−0.350930	+	0.607828i
$776$	−1679.38	−	2908.78i	−0.0776886	−	0.134561i
$777$	−746.031	−	1292.16i	−0.0344450	−	0.0596604i
$778$	8370.46			0.385727
$779$	−16640.8	+	30031.4i	−0.765365	+	1.38124i
$780$	408.523			0.0187531
$781$	−30807.8	−	53360.7i	−1.41151	−	2.44481i
$782$	−18723.1	−	32429.3i	−0.856183	−	1.48295i
$783$	−893.995	+	1548.45i	−0.0408030	+	0.0706730i
$784$	2662.69	+	4611.91i	0.121296	+	0.210091i
$785$	−2102.31	+	3641.30i	−0.0955854	+	0.165559i
$786$	−3585.28			−0.162701
$787$	30058.0			1.36144			0.680720	−	0.732544i	$-0.261667\pi$
$787$	30058.0			1.36144			0.680720	+	0.732544i	$0.261667\pi$
$788$	−4189.64	+	7256.68i	−0.189403	+	0.328056i
$789$	10707.6	−	18546.0i	0.483142	−	0.836827i
$790$	−3263.02			−0.146953
$791$	1859.29			0.0835764
$792$	−2498.41	+	4327.37i	−0.112092	+	0.194150i
$793$	888.543	+	1539.00i	0.0397895	+	0.0689174i
$794$	4529.76	−	7845.77i	0.202462	−	0.350675i
$795$	−2336.87	−	4047.58i	−0.104252	−	0.180570i
$796$	3434.72	+	5949.12i	0.152940	+	0.264901i
$797$	−20008.2			−0.889243			−0.444621	−	0.895719i	$-0.646662\pi$
$797$	−20008.2			−0.889243			−0.444621	+	0.895719i	$0.646662\pi$
$798$	1583.97	−	27.8848i	0.0702656	−	0.00123698i
$799$	−65801.8			−2.91352
$800$	1719.36	+	2978.01i	0.0759855	+	0.131611i
$801$	1916.09	+	3318.77i	0.0845217	+	0.146396i
$802$	9497.05	−	16449.4i	0.418145	−	0.724249i
$803$	−6905.89	−	11961.4i	−0.303491	−	0.525662i
$804$	−872.055	+	1510.44i	−0.0382525	+	0.0662552i
$805$	−2356.56			−0.103178
$806$	2290.89			0.100116
$807$	−8169.99	+	14150.8i	−0.356378	+	0.617265i
$808$	4966.84	−	8602.82i	0.216254	−	0.374562i
$809$	35302.3			1.53419			0.767097	−	0.641532i	$-0.221701\pi$
$809$	35302.3			1.53419			0.767097	+	0.641532i	$0.221701\pi$
$810$	678.473			0.0294310
$811$	−5490.38	+	9509.61i	−0.237723	+	0.411748i	−0.960060	−	0.279793i	$-0.909734\pi$
$811$	−5490.38	+	9509.61i	−0.237723	+	0.411748i	0.722338	+	0.691540i	$0.243068\pi$
$812$	422.245	+	731.349i	0.0182486	+	0.0316075i
$813$	−5105.52	+	8843.02i	−0.220244	+	0.381474i
$814$	10826.7	+	18752.3i	0.466185	+	0.807456i
$815$	−2663.60	−	4613.50i	−0.114481	−	0.198287i
$816$	5092.01			0.218451
$817$	4650.31	−	8392.34i	0.199136	−	0.359377i
$818$	−10708.9			−0.457735
$819$	116.617	+	201.987i	0.00497550	+	0.00861782i
$820$	3472.46	+	6014.48i	0.147883	+	0.256140i
$821$	2813.34	−	4872.85i	0.119594	−	0.207142i	−0.800013	−	0.599983i	$-0.795174\pi$
$821$	2813.34	−	4872.85i	0.119594	−	0.207142i	0.919607	+	0.392840i	$0.128508\pi$
$822$	−5331.93	−	9235.17i	−0.226244	−	0.391866i
$823$	−14383.1	+	24912.3i	−0.609191	+	1.05515i	0.382183	+	0.924087i	$0.375172\pi$
$823$	−14383.1	+	24912.3i	−0.609191	+	1.05515i	−0.991374	+	0.131063i	$0.958161\pi$
$824$	−4748.85			−0.200769
$825$	22373.2			0.944164
$826$	−292.327	+	506.325i	−0.0123140	+	0.0213284i
$827$	−22241.2	+	38522.9i	−0.935191	+	1.61980i	−0.160897	+	0.986971i	$0.551439\pi$
$827$	−22241.2	+	38522.9i	−0.935191	+	1.61980i	−0.774294	+	0.632827i	$0.781895\pi$
$828$	−6353.77			−0.266677
$829$	23302.5			0.976271			0.488136	−	0.872768i	$-0.337677\pi$
$829$	23302.5			0.976271			0.488136	+	0.872768i	$0.337677\pi$
$830$	−1591.64	+	2756.80i	−0.0665623	+	0.115289i
$831$	−7697.89	−	13333.1i	−0.321344	−	0.556584i
$832$	260.116	−	450.534i	0.0108388	−	0.0187734i
$833$	−17654.2	−	30578.0i	−0.734312	−	1.27187i
$834$	490.701	+	849.920i	0.0203736	+	0.0352881i
$835$	−12501.4			−0.518120
$836$	−22987.1	+	404.673i	−0.950988	+	0.0167415i
$837$	3804.70			0.157120
$838$	−14506.1	−	25125.3i	−0.597978	−	1.03573i
$839$	13841.8	+	23974.8i	0.569575	+	0.986533i	0.996608	+	0.0822969i	$0.0262256\pi$
$839$	13841.8	+	23974.8i	0.569575	+	0.986533i	−0.427033	+	0.904236i	$0.640441\pi$
$840$	160.225	−	277.519i	0.00658131	−	0.0113992i
$841$	10001.8	+	17323.7i	0.410096	+	0.710307i
$842$	1263.45	−	2188.36i	0.0517118	−	0.0895674i
$843$	−10100.0			−0.412650
$844$	−9164.21			−0.373750
$845$	4462.27	−	7728.88i	0.181665	−	0.314653i
$846$	−5582.55	+	9669.25i	−0.226870	+	0.392950i
$847$	11111.8			0.450776
$848$	−5951.77			−0.241020
$849$	10028.6	−	17370.1i	0.405397	−	0.702168i
$850$	−11399.7	−	19744.9i	−0.460008	−	0.796758i
$851$	−13766.8	+	23844.7i	−0.554546	+	0.960502i
$852$	5326.98	+	9226.59i	0.214201	+	0.371007i
$853$	15304.7	+	26508.6i	0.614331	+	1.06405i	0.990502	+	0.137502i	$0.0439072\pi$
$853$	15304.7	+	26508.6i	0.614331	+	1.06405i	−0.376171	+	0.926550i	$0.622759\pi$
$854$	1393.97			0.0558556
$855$	1608.19	+	2675.57i	0.0643263	+	0.107021i
$856$	−14228.5			−0.568130
$857$	−5459.14	−	9455.50i	−0.217597	−	0.376889i	0.736476	−	0.676464i	$-0.236488\pi$
$857$	−5459.14	−	9455.50i	−0.217597	−	0.376889i	−0.954073	+	0.299575i	$0.903155\pi$
$858$	−1692.39	−	2931.30i	−0.0673394	−	0.116635i
$859$	−7319.75	+	12678.2i	−0.290741	+	0.503578i	−0.973985	−	0.226612i	$-0.927235\pi$
$859$	−7319.75	+	12678.2i	−0.290741	+	0.503578i	0.683244	+	0.730190i	$0.260569\pi$
$860$	−970.387	−	1680.76i	−0.0384767	−	0.0666435i
$861$	−1982.50	+	3433.80i	−0.0784710	+	0.135916i
$862$	−16375.2			−0.647033
$863$	−22775.2			−0.898353			−0.449176	−	0.893443i	$-0.648283\pi$
$863$	−22775.2			−0.898353			−0.449176	+	0.893443i	$0.648283\pi$
$864$	432.000	−	748.246i	0.0170103	−	0.0294628i
$865$	−118.889	+	205.922i	−0.00467324	+	0.00809429i
$866$	−18485.9			−0.725377
$867$	−19022.2			−0.745129
$868$	898.502	−	1556.25i	0.0351350	−	0.0608556i
$869$	13517.7	+	23413.4i	0.527684	+	0.913975i
$870$	−832.032	+	1441.12i	−0.0324236	+	0.0561593i
$871$	−590.717	−	1023.15i	−0.0229801	−	0.0398028i
$872$	4279.96	+	7413.11i	0.166213	+	0.287889i
$873$	3778.61			0.146491
$874$	−15060.4	−	25056.2i	−0.582867	−	0.969725i
$875$	−3103.83			−0.119918
$876$	1194.10	+	2068.24i	0.0460557	+	0.0797708i
$877$	−402.954	−	697.937i	−0.0155152	−	0.0268730i	0.858164	−	0.513376i	$-0.171605\pi$
$877$	−402.954	−	697.937i	−0.0155152	−	0.0268730i	−0.873679	+	0.486503i	$0.838272\pi$
$878$	2043.05	−	3538.67i	0.0785303	−	0.136018i
$879$	−8438.89	−	14616.6i	−0.323819	−	0.560871i
$880$	−2325.25	+	4027.44i	−0.0890728	+	0.154279i
$881$	−901.690			−0.0344821			−0.0172410	−	0.999851i	$-0.505488\pi$
$881$	−901.690			−0.0344821			−0.0172410	+	0.999851i	$0.505488\pi$
$882$	−5991.05			−0.228718
$883$	12703.2	−	22002.5i	0.484140	−	0.838554i	−0.515695	−	0.856773i	$-0.672466\pi$
$883$	12703.2	−	22002.5i	0.484140	−	0.838554i	0.999834	+	0.0182183i	$0.00579938\pi$
$884$	−1724.63	+	2987.14i	−0.0656171	+	0.113652i
$885$	−1152.06			−0.0437582
$886$	−19338.3			−0.733275
$887$	−14280.2	+	24734.1i	−0.540568	+	0.936291i	0.458304	+	0.888796i	$0.348457\pi$
$887$	−14280.2	+	24734.1i	−0.540568	+	0.936291i	−0.998871	+	0.0474953i	$0.984876\pi$
$888$	−1872.04	−	3242.46i	−0.0707449	−	0.122534i
$889$	−2645.10	+	4581.44i	−0.0997904	+	0.172842i
$890$	1783.29	+	3088.75i	0.0671641	+	0.116332i
$891$	−2810.71	−	4868.30i	−0.105682	−	0.183046i
$892$	13024.8			0.488902
$893$	−51363.3	+	904.218i	−1.92476	+	0.0338841i
$894$	6718.79			0.251353
$895$	9718.46	+	16832.9i	0.362963	+	0.628671i
$896$	−204.039	−	353.405i	−0.00760765	−	0.0131768i
$897$	2151.98	−	3727.33i	0.0801030	−	0.138742i
$898$	13227.2	+	22910.2i	0.491534	+	0.851361i
$899$	−4665.82	+	8081.44i	−0.173097	+	0.299812i
$900$	−3868.55			−0.143280
$901$	39461.6			1.45911
$902$	28770.8	−	49832.4i	1.06204	−	1.83951i
$903$	554.015	−	959.582i	0.0204169	−	0.0353631i
$904$	4665.58			0.171654
$905$	15811.8			0.580776
$906$	−8421.44	+	14586.4i	−0.308812	+	0.534878i
$907$	20452.7	+	35425.1i	0.748755	+	1.29688i	0.948420	+	0.317017i	$0.102681\pi$
$907$	20452.7	+	35425.1i	0.748755	+	1.29688i	−0.199665	+	0.979864i	$0.563985\pi$
$908$	1996.09	−	3457.33i	0.0729543	−	0.126361i
$909$	5587.70	+	9678.17i	0.203886	+	0.353141i
$910$	108.534	+	187.987i	0.00395372	+	0.00684804i
$911$	30047.9			1.09279			0.546395	−	0.837527i	$-0.316000\pi$
$911$	30047.9			1.09279			0.546395	+	0.837527i	$0.316000\pi$
$912$	3974.70	−	69.9721i	0.144315	−	0.00254058i
$913$	26374.8			0.956055
$914$	5380.98	+	9320.13i	0.194734	+	0.337289i
$915$	1373.41	+	2378.81i	0.0496213	+	0.0859466i
$916$	2057.17	−	3563.12i	0.0742040	−	0.128525i
$917$	−952.520	−	1649.81i	−0.0343021	−	0.0594129i
$918$	−2864.26	+	4961.04i	−0.102979	+	0.178365i
$919$	−49600.1			−1.78036			−0.890182	−	0.455605i	$-0.849423\pi$
$919$	−49600.1			−1.78036			−0.890182	+	0.455605i	$0.849423\pi$
$920$	−5913.39			−0.211912
$921$	8405.31	−	14558.4i	0.300721	−	0.520865i
$922$	2844.67	−	4927.11i	0.101610	−	0.175993i
$923$	−7216.84			−0.257362
$924$	−2655.07			−0.0945295
$925$	−8382.03	+	14518.1i	−0.297945	+	0.516057i
$926$	−6625.39	−	11475.5i	−0.235123	−	0.407245i
$927$	2671.23	−	4626.70i	0.0946436	−	0.163928i
$928$	1059.55	+	1835.19i	0.0374800	+	0.0649173i
$929$	−13778.4	−	23864.8i	−0.486603	−	0.842821i	0.513279	−	0.858222i	$-0.328431\pi$
$929$	−13778.4	−	23864.8i	−0.486603	−	0.842821i	−0.999881	+	0.0154015i	$0.995097\pi$
$930$	3541.00			0.124854
$931$	−14200.6	−	23625.8i	−0.499900	−	0.831693i
$932$	−501.945			−0.0176414
$933$	10002.3	+	17324.5i	0.350976	+	0.607908i
$934$	18635.1	+	32276.9i	0.652846	+	1.13076i
$935$	15416.9	−	26702.9i	0.539237	−	0.933986i
$936$	292.631	+	506.851i	0.0102189	+	0.0176997i
$937$	13440.4	−	23279.5i	0.468601	−	0.811641i	−0.530755	−	0.847525i	$-0.678092\pi$
$937$	13440.4	−	23279.5i	0.468601	−	0.811641i	0.999356	+	0.0358846i	$0.0114249\pi$
$938$	−926.734			−0.0322590
$939$	−13474.2			−0.468279
$940$	−5195.62	+	8999.08i	−0.180279	+	0.312253i
$941$	3205.67	−	5552.38i	0.111054	−	0.192351i	−0.805142	−	0.593083i	$-0.797911\pi$
$941$	3205.67	−	5552.38i	0.111054	−	0.192351i	0.916195	+	0.400732i	$0.131244\pi$
$942$	−6023.65			−0.208345
$943$	73167.6			2.52669
$944$	−733.544	+	1270.53i	−0.0252911	+	0.0438055i
$945$	180.254	+	312.208i	0.00620492	+	0.0107472i
$946$	−8040.05	+	13925.8i	−0.276326	+	0.478611i
$947$	994.915	+	1723.24i	0.0341398	+	0.0591319i	0.882590	−	0.470143i	$-0.155798\pi$
$947$	994.915	+	1723.24i	0.0341398	+	0.0591319i	−0.848451	+	0.529274i	$0.822464\pi$
$948$	−2337.35	−	4048.40i	−0.0800775	−	0.138698i
$949$	−1617.73			−0.0553358
$950$	−9169.67	−	15255.7i	−0.313161	−	0.521012i
$951$	3798.14			0.129509
$952$	1352.82	+	2343.16i	0.0460559	+	0.0797712i
$953$	19133.2	+	33139.7i	0.650351	+	1.12644i	0.983038	+	0.183404i	$0.0587117\pi$
$953$	19133.2	+	33139.7i	0.650351	+	1.12644i	−0.332686	+	0.943038i	$0.607955\pi$
$954$	3347.87	−	5798.68i	0.113618	−	0.196792i
$955$	5784.88	+	10019.7i	0.196015	+	0.339508i
$956$	−7182.05	+	12439.7i	−0.242975	+	0.420845i
$957$	13787.5			0.465711
$958$	3113.24			0.104994
$959$	2833.12	−	4907.11i	0.0953976	−	0.165234i
$960$	402.058	−	696.385i	0.0135171	−	0.0234122i
$961$	−9934.01			−0.333457
$962$	2536.18			0.0849998
$963$	8003.52	−	13862.5i	0.267819	−	0.463876i
$964$	7383.68	+	12788.9i	0.246693	+	0.427285i
$965$	−4316.92	+	7477.12i	−0.144007	+	0.249427i
$966$	−1688.04	−	2923.77i	−0.0562234	−	0.0973818i
$967$	−110.058	−	190.626i	−0.00366001	−	0.00633932i	0.864190	−	0.503166i	$-0.167832\pi$
$967$	−110.058	−	190.626i	−0.00366001	−	0.00633932i	−0.867850	+	0.496827i	$0.834498\pi$
$968$	27883.2			0.925827
$969$	−26353.1	+	463.930i	−0.873669	+	0.0153804i
$970$	3516.72			0.116407
$971$	−1087.68	−	1883.91i	−0.0359478	−	0.0622633i	0.847492	−	0.530809i	$-0.178112\pi$
$971$	−1087.68	−	1883.91i	−0.0359478	−	0.0622633i	−0.883440	+	0.468545i	$0.844778\pi$
$972$	486.000	+	841.777i	0.0160375	+	0.0277778i
$973$	−260.735	+	451.606i	−0.00859072	+	0.0148796i
$974$	−19339.5	−	33497.0i	−0.636220	−	1.10196i
$975$	1310.25	−	2269.42i	0.0430376	−	0.0745432i
$976$	3497.93			0.114719
$977$	13707.7			0.448872			0.224436	−	0.974489i	$-0.427946\pi$
$977$	13707.7			0.448872			0.224436	+	0.974489i	$0.427946\pi$
$978$	3815.96	−	6609.43i	0.124766	−	0.216101i
$979$	14775.3	−	25591.5i	0.482350	−	0.835454i
$980$	−5575.81			−0.181748
$981$	−9629.91			−0.313414
$982$	6838.25	−	11844.2i	0.222217	−	0.384891i
$983$	9442.87	+	16355.5i	0.306389	+	0.530682i	0.977570	−	0.210612i	$-0.0675457\pi$
$983$	9442.87	+	16355.5i	0.306389	+	0.530682i	−0.671180	+	0.741294i	$0.734212\pi$
$984$	−4974.75	+	8616.52i	−0.161168	+	0.279151i
$985$	−4386.67	−	7597.93i	−0.141899	−	0.245777i
$986$	−7025.05	−	12167.7i	−0.226900	−	0.393002i
$987$	−5932.58			−0.191323
$988$	−1305.15	+	2355.39i	−0.0420268	+	0.0758451i
$989$	−20446.8			−0.657403
$990$	−2615.90	−	4530.87i	−0.0839786	−	0.145455i
$991$	20327.5	+	35208.3i	0.651589	+	1.12858i	0.982737	+	0.185006i	$0.0592305\pi$
$991$	20327.5	+	35208.3i	0.651589	+	1.12858i	−0.331149	+	0.943579i	$0.607436\pi$
$992$	2254.64	−	3905.15i	0.0721621	−	0.124988i
$993$	−7602.14	−	13167.3i	−0.242947	−	0.420797i
$994$	−2830.49	+	4902.56i	−0.0903197	+	0.156438i
$995$	−7192.49			−0.229163
$996$	−4560.46			−0.145084
$997$	8216.65	−	14231.7i	0.261007	−	0.452077i	−0.705503	−	0.708707i	$-0.749279\pi$
$997$	8216.65	−	14231.7i	0.261007	−	0.452077i	0.966510	+	0.256630i	$0.0826121\pi$
$998$	18115.0	−	31376.1i	0.574569	−	0.995182i
$999$	4212.08			0.133398

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.e.d.7.2	✓	6
3.2	odd	2		342.4.g.h.235.2		6
19.7	even	3		2166.4.a.u.1.2		3
19.11	even	3	inner	114.4.e.d.49.2	yes	6
19.12	odd	6		2166.4.a.t.1.2		3
57.11	odd	6		342.4.g.h.163.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.e.d.7.2	✓	6	1.1	even	1	trivial
114.4.e.d.49.2	yes	6	19.11	even	3	inner
342.4.g.h.163.2		6	57.11	odd	6
342.4.g.h.235.2		6	3.2	odd	2
2166.4.a.t.1.2		3	19.12	odd	6
2166.4.a.u.1.2		3	19.7	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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	114.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.09405 - 3.62701i) q^{5} +(3.00000 - 5.19615i) q^{6} +3.18810 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.09405 - 3.62701i) q^{5} +(3.00000 - 5.19615i) q^{6} +3.18810 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-4.18810 + 7.25401i) q^{10} +69.4003 q^{11} -12.0000 q^{12} +(4.06431 - 7.03960i) q^{13} +(-3.18810 - 5.52196i) q^{14} +(6.28216 - 10.8810i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(53.0418 + 91.8711i) q^{17} +18.0000 q^{18} +(42.6656 + 70.9834i) q^{19} +16.7524 q^{20} +(4.78216 + 8.28294i) q^{21} +(-69.4003 - 120.205i) q^{22} +(88.2468 - 152.848i) q^{23} +(12.0000 + 20.7846i) q^{24} +(53.7299 - 93.0629i) q^{25} -16.2573 q^{26} -27.0000 q^{27} +(-6.37621 + 11.0439i) q^{28} +(33.1109 - 57.3498i) q^{29} -25.1286 q^{30} -140.915 q^{31} +(-16.0000 + 27.7128i) q^{32} +(104.100 + 180.307i) q^{33} +(106.084 - 183.742i) q^{34} +(-6.67606 - 11.5633i) q^{35} +(-18.0000 - 31.1769i) q^{36} -156.003 q^{37} +(80.2814 - 144.882i) q^{38} +24.3859 q^{39} +(-16.7524 - 29.0160i) q^{40} +(207.281 + 359.022i) q^{41} +(9.56431 - 16.5659i) q^{42} +(-57.9252 - 100.329i) q^{43} +(-138.801 + 240.410i) q^{44} +37.6929 q^{45} -352.987 q^{46} +(-310.141 + 537.181i) q^{47} +(24.0000 - 41.5692i) q^{48} -332.836 q^{49} -214.920 q^{50} +(-159.125 + 275.613i) q^{51} +(16.2573 + 28.1584i) q^{52} +(185.993 - 322.149i) q^{53} +(27.0000 + 46.7654i) q^{54} +(-145.328 - 251.715i) q^{55} +25.5048 q^{56} +(-120.422 + 217.324i) q^{57} -132.444 q^{58} +(-45.8465 - 79.4084i) q^{59} +(25.1286 + 43.5241i) q^{60} +(-109.310 + 189.331i) q^{61} +(140.915 + 244.072i) q^{62} +(-14.3465 + 24.8488i) q^{63} +64.0000 q^{64} -34.0436 q^{65} +(208.201 - 360.615i) q^{66} +(72.6712 - 125.870i) q^{67} -424.334 q^{68} +529.481 q^{69} +(-13.3521 + 23.1265i) q^{70} +(-443.915 - 768.883i) q^{71} +(-36.0000 + 62.3538i) q^{72} +(-99.5081 - 172.353i) q^{73} +(156.003 + 270.205i) q^{74} +322.379 q^{75} +(-331.225 + 5.83100i) q^{76} +221.255 q^{77} +(-24.3859 - 42.2376i) q^{78} +(194.779 + 337.367i) q^{79} +(-33.5048 + 58.0321i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(414.563 - 718.044i) q^{82} +380.039 q^{83} -38.2573 q^{84} +(222.145 - 384.766i) q^{85} +(-115.850 + 200.659i) q^{86} +198.666 q^{87} +555.202 q^{88} +(212.899 - 368.753i) q^{89} +(-37.6929 - 65.2861i) q^{90} +(12.9575 - 22.4430i) q^{91} +(352.987 + 611.392i) q^{92} +(-211.372 - 366.107i) q^{93} +1240.57 q^{94} +(168.113 - 303.391i) q^{95} -96.0000 q^{96} +(-209.923 - 363.597i) q^{97} +(332.836 + 576.489i) q^{98} +(-312.301 + 540.922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 10 q^{5} + 18 q^{6} + 14 q^{7} + 48 q^{8} - 27 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 9 * q^3 - 12 * q^4 - 10 * q^5 + 18 * q^6 + 14 * q^7 + 48 * q^8 - 27 * q^9	\( 6 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 10 q^{5} + 18 q^{6} + 14 q^{7} + 48 q^{8} - 27 q^{9} - 20 q^{10} - 88 q^{11} - 72 q^{12} + 9 q^{13} - 14 q^{14} + 30 q^{15} - 48 q^{16} + 84 q^{17} + 108 q^{18} + 32 q^{19} + 80 q^{20} + 21 q^{21} + 88 q^{22} + 2 q^{23} + 72 q^{24} + 83 q^{25} - 36 q^{26} - 162 q^{27} - 28 q^{28} - 92 q^{29} - 120 q^{30} - 218 q^{31} - 96 q^{32} - 132 q^{33} + 168 q^{34} - 282 q^{35} - 108 q^{36} + 490 q^{37} - 74 q^{38} + 54 q^{39} - 80 q^{40} + 688 q^{41} + 42 q^{42} + 103 q^{43} + 176 q^{44} + 180 q^{45} - 8 q^{46} - 322 q^{47} + 144 q^{48} - 1508 q^{49} - 332 q^{50} - 252 q^{51} + 36 q^{52} + 1322 q^{53} + 162 q^{54} + 248 q^{55} + 112 q^{56} + 111 q^{57} + 368 q^{58} - 252 q^{59} + 120 q^{60} + 435 q^{61} + 218 q^{62} - 63 q^{63} + 384 q^{64} - 3164 q^{65} - 264 q^{66} + 719 q^{67} - 672 q^{68} + 12 q^{69} - 564 q^{70} + 62 q^{71} - 216 q^{72} + 581 q^{73} - 490 q^{74} + 498 q^{75} + 20 q^{76} - 408 q^{77} - 54 q^{78} + 489 q^{79} - 160 q^{80} - 243 q^{81} + 1376 q^{82} + 4992 q^{83} - 168 q^{84} - 1632 q^{85} + 206 q^{86} - 552 q^{87} - 704 q^{88} - 1584 q^{89} - 180 q^{90} + 1573 q^{91} + 8 q^{92} - 327 q^{93} + 1288 q^{94} + 2362 q^{95} - 576 q^{96} - 974 q^{97} + 1508 q^{98} + 396 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 9 * q^3 - 12 * q^4 - 10 * q^5 + 18 * q^6 + 14 * q^7 + 48 * q^8 - 27 * q^9 - 20 * q^10 - 88 * q^11 - 72 * q^12 + 9 * q^13 - 14 * q^14 + 30 * q^15 - 48 * q^16 + 84 * q^17 + 108 * q^18 + 32 * q^19 + 80 * q^20 + 21 * q^21 + 88 * q^22 + 2 * q^23 + 72 * q^24 + 83 * q^25 - 36 * q^26 - 162 * q^27 - 28 * q^28 - 92 * q^29 - 120 * q^30 - 218 * q^31 - 96 * q^32 - 132 * q^33 + 168 * q^34 - 282 * q^35 - 108 * q^36 + 490 * q^37 - 74 * q^38 + 54 * q^39 - 80 * q^40 + 688 * q^41 + 42 * q^42 + 103 * q^43 + 176 * q^44 + 180 * q^45 - 8 * q^46 - 322 * q^47 + 144 * q^48 - 1508 * q^49 - 332 * q^50 - 252 * q^51 + 36 * q^52 + 1322 * q^53 + 162 * q^54 + 248 * q^55 + 112 * q^56 + 111 * q^57 + 368 * q^58 - 252 * q^59 + 120 * q^60 + 435 * q^61 + 218 * q^62 - 63 * q^63 + 384 * q^64 - 3164 * q^65 - 264 * q^66 + 719 * q^67 - 672 * q^68 + 12 * q^69 - 564 * q^70 + 62 * q^71 - 216 * q^72 + 581 * q^73 - 490 * q^74 + 498 * q^75 + 20 * q^76 - 408 * q^77 - 54 * q^78 + 489 * q^79 - 160 * q^80 - 243 * q^81 + 1376 * q^82 + 4992 * q^83 - 168 * q^84 - 1632 * q^85 + 206 * q^86 - 552 * q^87 - 704 * q^88 - 1584 * q^89 - 180 * q^90 + 1573 * q^91 + 8 * q^92 - 327 * q^93 + 1288 * q^94 + 2362 * q^95 - 576 * q^96 - 974 * q^97 + 1508 * q^98 + 396 * q^99

Introduction

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