LMFDB - Embedded newform 170.3.e.b.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,3,Mod(13,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("170.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	170.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.63216449413$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 80 x^{14} + 2532 x^{12} + 40532 x^{10} + 346464 x^{8} + 1518752 x^{6} + 2895224 x^{4} + \cdots + 148996 $ x^16 + 80x^14 + 2532x^12 + 40532x^10 + 346464x^8 + 1518752x^6 + 2895224x^4 + 1253728*x^2 + 148996
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.1
Root			$4.98490i$ of defining polynomial
Character	$\chi$	$=$	170.157
Dual form			170.3.e.b.13.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -4.98490i q^{3} -2.00000i q^{4} +(-4.92182 + 0.880714i) q^{5} +(-4.98490 - 4.98490i) q^{6} +0.0526451i q^{7} +(-2.00000 - 2.00000i) q^{8} -15.8492 q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} -4.98490i q^{3} -2.00000i q^{4} +(-4.92182 + 0.880714i) q^{5} +(-4.98490 - 4.98490i) q^{6} +0.0526451i q^{7} +(-2.00000 - 2.00000i) q^{8} -15.8492 q^{9} +(-4.04111 + 5.80254i) q^{10} +(3.92931 + 3.92931i) q^{11} -9.96980 q^{12} +(7.50642 - 7.50642i) q^{13} +(0.0526451 + 0.0526451i) q^{14} +(4.39027 + 24.5348i) q^{15} -4.00000 q^{16} +(9.69198 - 13.9666i) q^{17} +(-15.8492 + 15.8492i) q^{18} -11.2212 q^{19} +(1.76143 + 9.84365i) q^{20} +0.262430 q^{21} +7.85862 q^{22} -12.1038 q^{23} +(-9.96980 + 9.96980i) q^{24} +(23.4487 - 8.66943i) q^{25} -15.0128i q^{26} +34.1428i q^{27} +0.105290 q^{28} +(-17.9887 - 17.9887i) q^{29} +(28.9251 + 20.1445i) q^{30} +(10.7574 - 10.7574i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(19.5872 - 19.5872i) q^{33} +(-4.27460 - 23.6586i) q^{34} +(-0.0463652 - 0.259110i) q^{35} +31.6985i q^{36} +41.9878 q^{37} +(-11.2212 + 11.2212i) q^{38} +(-37.4187 - 37.4187i) q^{39} +(11.6051 + 8.08222i) q^{40} +(-54.3180 - 54.3180i) q^{41} +(0.262430 - 0.262430i) q^{42} +(-30.8983 - 30.8983i) q^{43} +(7.85862 - 7.85862i) q^{44} +(78.0072 - 13.9586i) q^{45} +(-12.1038 + 12.1038i) q^{46} +(11.8258 + 11.8258i) q^{47} +19.9396i q^{48} +48.9972 q^{49} +(14.7793 - 32.1181i) q^{50} +(-69.6220 - 48.3136i) q^{51} +(-15.0128 - 15.0128i) q^{52} +(67.3929 + 67.3929i) q^{53} +(34.1428 + 34.1428i) q^{54} +(-22.8000 - 15.8788i) q^{55} +(0.105290 - 0.105290i) q^{56} +55.9367i q^{57} -35.9775 q^{58} +82.1345 q^{59} +(49.0696 - 8.78054i) q^{60} +(29.2095 + 29.2095i) q^{61} -21.5148i q^{62} -0.834384i q^{63} +8.00000i q^{64} +(-30.3343 + 43.5563i) q^{65} -39.1745i q^{66} +(79.4772 + 79.4772i) q^{67} +(-27.9332 - 19.3840i) q^{68} +60.3363i q^{69} +(-0.305475 - 0.212745i) q^{70} +(-83.1532 + 83.1532i) q^{71} +(31.6985 + 31.6985i) q^{72} -71.4227i q^{73} +(41.9878 - 41.9878i) q^{74} +(-43.2163 - 116.889i) q^{75} +22.4424i q^{76} +(-0.206859 + 0.206859i) q^{77} -74.8375 q^{78} +(74.9841 - 74.9841i) q^{79} +(19.6873 - 3.52285i) q^{80} +27.5552 q^{81} -108.636 q^{82} +(0.938649 + 0.938649i) q^{83} -0.524861i q^{84} +(-35.4017 + 77.2769i) q^{85} -61.7966 q^{86} +(-89.6721 + 89.6721i) q^{87} -15.7172i q^{88} +58.2677i q^{89} +(64.0485 - 91.9658i) q^{90} +(0.395176 + 0.395176i) q^{91} +24.2076i q^{92} +(-53.6246 - 53.6246i) q^{93} +23.6517 q^{94} +(55.2289 - 9.88268i) q^{95} +(19.9396 + 19.9396i) q^{96} +14.2644 q^{97} +(48.9972 - 48.9972i) q^{98} +(-62.2766 - 62.2766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9	$ 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9} - 4 q^{10} + 20 q^{11} + 4 q^{13} - 12 q^{14} + 12 q^{15} - 64 q^{16} + 36 q^{17} - 16 q^{18} - 16 q^{19} - 4 q^{20} + 40 q^{22} + 16 q^{23} + 44 q^{25} - 24 q^{28} - 20 q^{29} + 12 q^{30} + 92 q^{31} - 64 q^{32} - 60 q^{33} + 24 q^{34} - 124 q^{35} + 32 q^{37} - 16 q^{38} - 140 q^{39} - 60 q^{41} + 52 q^{43} + 40 q^{44} + 198 q^{45} + 16 q^{46} + 112 q^{47} + 136 q^{49} - 4 q^{50} - 140 q^{51} - 8 q^{52} + 48 q^{53} + 108 q^{54} + 40 q^{55} - 24 q^{56} - 40 q^{58} + 76 q^{61} - 40 q^{65} + 116 q^{67} - 24 q^{68} - 124 q^{70} - 268 q^{71} + 32 q^{72} + 32 q^{74} + 136 q^{75} - 116 q^{77} - 280 q^{78} - 88 q^{79} + 8 q^{80} - 352 q^{81} - 120 q^{82} - 160 q^{83} + 310 q^{85} + 104 q^{86} + 236 q^{87} + 260 q^{90} - 168 q^{91} + 48 q^{93} + 224 q^{94} + 264 q^{95} - 256 q^{97} + 136 q^{98} - 348 q^{99}+O(q^{100}) $ 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9 - 4 * q^10 + 20 * q^11 + 4 * q^13 - 12 * q^14 + 12 * q^15 - 64 * q^16 + 36 * q^17 - 16 * q^18 - 16 * q^19 - 4 * q^20 + 40 * q^22 + 16 * q^23 + 44 * q^25 - 24 * q^28 - 20 * q^29 + 12 * q^30 + 92 * q^31 - 64 * q^32 - 60 * q^33 + 24 * q^34 - 124 * q^35 + 32 * q^37 - 16 * q^38 - 140 * q^39 - 60 * q^41 + 52 * q^43 + 40 * q^44 + 198 * q^45 + 16 * q^46 + 112 * q^47 + 136 * q^49 - 4 * q^50 - 140 * q^51 - 8 * q^52 + 48 * q^53 + 108 * q^54 + 40 * q^55 - 24 * q^56 - 40 * q^58 + 76 * q^61 - 40 * q^65 + 116 * q^67 - 24 * q^68 - 124 * q^70 - 268 * q^71 + 32 * q^72 + 32 * q^74 + 136 * q^75 - 116 * q^77 - 280 * q^78 - 88 * q^79 + 8 * q^80 - 352 * q^81 - 120 * q^82 - 160 * q^83 + 310 * q^85 + 104 * q^86 + 236 * q^87 + 260 * q^90 - 168 * q^91 + 48 * q^93 + 224 * q^94 + 264 * q^95 - 256 * q^97 + 136 * q^98 - 348 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$		−	4.98490i		−	1.66163i	−0.556546	−	0.830817i	$-0.687874\pi$
$3$		−	4.98490i		−	1.66163i	0.556546	−	0.830817i	$-0.312126\pi$
$4$		−	2.00000i		−	0.500000i
$5$	−4.92182	+	0.880714i	−0.984365	+	0.176143i
$5$	−4.92182	+	0.880714i	−0.984365	+	0.176143i
$6$	−4.98490	−	4.98490i	−0.830817	−	0.830817i
$7$			0.0526451i			0.00752072i	0.999993	+	0.00376036i	$0.00119696\pi$
$7$			0.0526451i			0.00752072i	−0.999993	+	0.00376036i	$0.998803\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	−15.8492			−1.76103
$10$	−4.04111	+	5.80254i	−0.404111	+	0.580254i
$11$	3.92931	+	3.92931i	0.357210	+	0.357210i	0.862784	−	0.505573i	$-0.168719\pi$
$11$	3.92931	+	3.92931i	0.357210	+	0.357210i	−0.505573	+	0.862784i	$0.668719\pi$
$12$	−9.96980			−0.830817
$13$	7.50642	−	7.50642i	0.577417	−	0.577417i	−0.356774	−	0.934191i	$-0.616123\pi$
$13$	7.50642	−	7.50642i	0.577417	−	0.577417i	0.934191	+	0.356774i	$0.116123\pi$
$14$	0.0526451	+	0.0526451i	0.00376036	+	0.00376036i
$15$	4.39027	+	24.5348i	0.292685	+	1.63565i
$16$	−4.00000			−0.250000
$17$	9.69198	−	13.9666i	0.570117	−	0.821564i
$17$	9.69198	−	13.9666i	0.570117	−	0.821564i
$18$	−15.8492	+	15.8492i	−0.880513	+	0.880513i
$19$	−11.2212			−0.590591			−0.295295	−	0.955406i	$-0.595418\pi$
$19$	−11.2212			−0.590591			−0.295295	+	0.955406i	$0.595418\pi$
$20$	1.76143	+	9.84365i	0.0880714	+	0.492182i
$21$	0.262430			0.0124967
$22$	7.85862			0.357210
$23$	−12.1038			−0.526253			−0.263127	−	0.964761i	$-0.584754\pi$
$23$	−12.1038			−0.526253			−0.263127	+	0.964761i	$0.584754\pi$
$24$	−9.96980	+	9.96980i	−0.415408	+	0.415408i
$25$	23.4487	−	8.66943i	0.937947	−	0.346777i
$26$		−	15.0128i		−	0.577417i
$27$			34.1428i			1.26455i
$28$	0.105290			0.00376036
$29$	−17.9887	−	17.9887i	−0.620301	−	0.620301i	0.325307	−	0.945608i	$-0.394532\pi$
$29$	−17.9887	−	17.9887i	−0.620301	−	0.620301i	−0.945608	+	0.325307i	$0.894532\pi$
$30$	28.9251	+	20.1445i	0.964169	+	0.671484i
$31$	10.7574	−	10.7574i	0.347013	−	0.347013i	−0.511983	−	0.858996i	$-0.671089\pi$
$31$	10.7574	−	10.7574i	0.347013	−	0.347013i	0.858996	+	0.511983i	$0.171089\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	19.5872	−	19.5872i	0.593552	−	0.593552i
$34$	−4.27460	−	23.6586i	−0.125724	−	0.695840i
$35$	−0.0463652	−	0.259110i	−0.00132472	−	0.00740314i
$36$			31.6985i			0.880513i
$37$	41.9878			1.13481			0.567403	−	0.823440i	$-0.307948\pi$
$37$	41.9878			1.13481			0.567403	+	0.823440i	$0.307948\pi$
$38$	−11.2212	+	11.2212i	−0.295295	+	0.295295i
$39$	−37.4187	−	37.4187i	−0.959455	−	0.959455i
$40$	11.6051	+	8.08222i	0.290127	+	0.202055i
$41$	−54.3180	−	54.3180i	−1.32483	−	1.32483i	−0.909816	−	0.415013i	$-0.863777\pi$
$41$	−54.3180	−	54.3180i	−1.32483	−	1.32483i	−0.415013	−	0.909816i	$-0.636223\pi$
$42$	0.262430	−	0.262430i	0.00624834	−	0.00624834i
$43$	−30.8983	−	30.8983i	−0.718565	−	0.718565i	0.249746	−	0.968311i	$-0.419653\pi$
$43$	−30.8983	−	30.8983i	−0.718565	−	0.718565i	−0.968311	+	0.249746i	$0.919653\pi$
$44$	7.85862	−	7.85862i	0.178605	−	0.178605i
$45$	78.0072	−	13.9586i	1.73349	−	0.310192i
$46$	−12.1038	+	12.1038i	−0.263127	+	0.263127i
$47$	11.8258	+	11.8258i	0.251613	+	0.251613i	0.821632	−	0.570018i	$-0.193064\pi$
$47$	11.8258	+	11.8258i	0.251613	+	0.251613i	−0.570018	+	0.821632i	$0.693064\pi$
$48$			19.9396i			0.415408i
$49$	48.9972			0.999943
$50$	14.7793	−	32.1181i	0.295585	−	0.642362i
$51$	−69.6220	−	48.3136i	−1.36514	−	0.947325i
$52$	−15.0128	−	15.0128i	−0.288708	−	0.288708i
$53$	67.3929	+	67.3929i	1.27156	+	1.27156i	0.945268	+	0.326296i	$0.105801\pi$
$53$	67.3929	+	67.3929i	1.27156	+	1.27156i	0.326296	+	0.945268i	$0.394199\pi$
$54$	34.1428	+	34.1428i	0.632274	+	0.632274i
$55$	−22.8000	−	15.8788i	−0.414545	−	0.288705i
$56$	0.105290	−	0.105290i	0.00188018	−	0.00188018i
$57$			55.9367i			0.981345i
$58$	−35.9775			−0.620301
$59$	82.1345			1.39211			0.696055	−	0.717988i	$-0.254937\pi$
$59$	82.1345			1.39211			0.696055	+	0.717988i	$0.254937\pi$
$60$	49.0696	−	8.78054i	0.817827	−	0.146342i
$61$	29.2095	+	29.2095i	0.478845	+	0.478845i	0.904762	−	0.425917i	$-0.140049\pi$
$61$	29.2095	+	29.2095i	0.478845	+	0.478845i	−0.425917	+	0.904762i	$0.640049\pi$
$62$		−	21.5148i		−	0.347013i
$63$		−	0.834384i		−	0.0132442i
$64$			8.00000i			0.125000i
$65$	−30.3343	+	43.5563i	−0.466681	+	0.670096i
$66$		−	39.1745i		−	0.593552i
$67$	79.4772	+	79.4772i	1.18623	+	1.18623i	0.978102	+	0.208125i	$0.0667362\pi$
$67$	79.4772	+	79.4772i	1.18623	+	1.18623i	0.208125	+	0.978102i	$0.433264\pi$
$68$	−27.9332	−	19.3840i	−0.410782	−	0.285058i
$69$			60.3363i			0.874440i
$70$	−0.305475	−	0.212745i	−0.00436393	−	0.00303921i
$71$	−83.1532	+	83.1532i	−1.17117	+	1.17117i	−0.189242	+	0.981931i	$0.560603\pi$
$71$	−83.1532	+	83.1532i	−1.17117	+	1.17117i	−0.981931	+	0.189242i	$0.939397\pi$
$72$	31.6985	+	31.6985i	0.440257	+	0.440257i
$73$		−	71.4227i		−	0.978393i	−0.872174	−	0.489196i	$-0.837290\pi$
$73$		−	71.4227i		−	0.978393i	0.872174	−	0.489196i	$-0.162710\pi$
$74$	41.9878	−	41.9878i	0.567403	−	0.567403i
$75$	−43.2163	−	116.889i	−0.576217	−	1.55853i
$76$			22.4424i			0.295295i
$77$	−0.206859	+	0.206859i	−0.00268648	+	0.00268648i
$78$	−74.8375			−0.959455
$79$	74.9841	−	74.9841i	0.949166	−	0.949166i	−0.0496035	−	0.998769i	$-0.515796\pi$
$79$	74.9841	−	74.9841i	0.949166	−	0.949166i	0.998769	+	0.0496035i	$0.0157958\pi$
$80$	19.6873	−	3.52285i	0.246091	−	0.0440357i
$81$	27.5552			0.340188
$82$	−108.636			−1.32483
$83$	0.938649	+	0.938649i	0.0113090	+	0.0113090i	0.712739	−	0.701430i	$-0.247455\pi$
$83$	0.938649	+	0.938649i	0.0113090	+	0.0113090i	−0.701430	+	0.712739i	$0.747455\pi$
$84$		−	0.524861i		−	0.00624834i
$85$	−35.4017	+	77.2769i	−0.416490	+	0.909140i
$86$	−61.7966			−0.718565
$87$	−89.6721	+	89.6721i	−1.03071	+	1.03071i
$88$		−	15.7172i		−	0.178605i
$89$			58.2677i			0.654693i	0.944904	+	0.327347i	$0.106155\pi$
$89$			58.2677i			0.654693i	−0.944904	+	0.327347i	$0.893845\pi$
$90$	64.0485	−	91.9658i	0.711650	−	1.02184i
$91$	0.395176	+	0.395176i	0.00434259	+	0.00434259i
$92$			24.2076i			0.263127i
$93$	−53.6246	−	53.6246i	−0.576609	−	0.576609i
$94$	23.6517			0.251613
$95$	55.2289	−	9.88268i	0.581357	−	0.104028i
$96$	19.9396	+	19.9396i	0.207704	+	0.207704i
$97$	14.2644			0.147056			0.0735280	−	0.997293i	$-0.476574\pi$
$97$	14.2644			0.147056			0.0735280	+	0.997293i	$0.476574\pi$
$98$	48.9972	−	48.9972i	0.499972	−	0.499972i
$99$	−62.2766	−	62.2766i	−0.629056	−	0.629056i
$100$	−17.3389	−	46.8974i	−0.173389	−	0.468974i
$101$	183.328			1.81513			0.907563	−	0.419916i	$-0.137941\pi$
$101$	183.328			1.81513			0.907563	+	0.419916i	$0.137941\pi$
$102$	−117.936	+	21.3085i	−1.15623	+	0.208907i
$103$	4.44600	−	4.44600i	0.0431650	−	0.0431650i	−0.685195	−	0.728360i	$-0.740283\pi$
$103$	4.44600	−	4.44600i	0.0431650	−	0.0431650i	0.728360	+	0.685195i	$0.240283\pi$
$104$	−30.0257			−0.288708
$105$	−1.29164	+	0.231126i	−0.0123013	+	0.00220120i
$106$	134.786			1.27156
$107$	−54.3644			−0.508079			−0.254039	−	0.967194i	$-0.581759\pi$
$107$	−54.3644			−0.508079			−0.254039	+	0.967194i	$0.581759\pi$
$108$	68.2856			0.632274
$109$	−13.2777	+	13.2777i	−0.121814	+	0.121814i	−0.765386	−	0.643572i	$-0.777452\pi$
$109$	−13.2777	+	13.2777i	−0.121814	+	0.121814i	0.643572	+	0.765386i	$0.277452\pi$
$110$	−38.6787	+	6.92119i	−0.351625	+	0.0629200i
$111$		−	209.305i		−	1.88563i
$112$		−	0.210580i		−	0.00188018i
$113$	−124.652			−1.10312			−0.551558	−	0.834136i	$-0.685967\pi$
$113$	−124.652			−1.10312			−0.551558	+	0.834136i	$0.685967\pi$
$114$	55.9367	+	55.9367i	0.490673	+	0.490673i
$115$	59.5729	−	10.6600i	0.518025	−	0.0926956i
$116$	−35.9775	+	35.9775i	−0.310151	+	0.310151i
$117$	−118.971	+	118.971i	−1.01685	+	1.01685i
$118$	82.1345	−	82.1345i	0.696055	−	0.696055i
$119$	0.735272	+	0.510235i	0.00617875	+	0.00428769i
$120$	40.2891	−	57.8501i	0.335742	−	0.482085i
$121$		−	90.1210i		−	0.744802i
$122$	58.4191			0.478845
$123$	−270.770	+	270.770i	−2.20138	+	2.20138i
$124$	−21.5148	−	21.5148i	−0.173507	−	0.173507i
$125$	−107.775	+	63.3210i	−0.862200	+	0.506568i
$126$	−0.834384	−	0.834384i	−0.00662210	−	0.00662210i
$127$	−17.2834	+	17.2834i	−0.136090	+	0.136090i	−0.771870	−	0.635780i	$-0.780679\pi$
$127$	−17.2834	+	17.2834i	−0.136090	+	0.136090i	0.635780	+	0.771870i	$0.280679\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$	−154.025	+	154.025i	−1.19399	+	1.19399i
$130$	13.2220	+	73.8905i	0.101708	+	0.568389i
$131$	−183.918	+	183.918i	−1.40396	+	1.40396i	−0.616965	+	0.786991i	$0.711638\pi$
$131$	−183.918	+	183.918i	−1.40396	+	1.40396i	−0.786991	+	0.616965i	$0.788362\pi$
$132$	−39.1745	−	39.1745i	−0.296776	−	0.296776i
$133$		−	0.590742i		−	0.00444167i
$134$	158.954			1.18623
$135$	−30.0700	−	168.045i	−0.222741	−	1.24478i
$136$	−47.3171	+	8.54920i	−0.347920	+	0.0628618i
$137$	−11.4165	−	11.4165i	−0.0833322	−	0.0833322i	0.664212	−	0.747544i	$-0.268767\pi$
$137$	−11.4165	−	11.4165i	−0.0833322	−	0.0833322i	−0.747544	+	0.664212i	$0.768767\pi$
$138$	60.3363	+	60.3363i	0.437220	+	0.437220i
$139$	−72.2696	−	72.2696i	−0.519925	−	0.519925i	0.397624	−	0.917549i	$-0.369835\pi$
$139$	−72.2696	−	72.2696i	−0.519925	−	0.519925i	−0.917549	+	0.397624i	$0.869835\pi$
$140$	−0.518219	+	0.0927305i	−0.00370157	+	0.000662360i
$141$	58.9506	−	58.9506i	0.418089	−	0.418089i
$142$			166.306i			1.17117i
$143$	58.9901			0.412518
$144$	63.3970			0.440257
$145$	104.380	+	72.6945i	0.719864	+	0.501341i
$146$	−71.4227	−	71.4227i	−0.489196	−	0.489196i
$147$		−	244.246i		−	1.66154i
$148$		−	83.9757i		−	0.567403i
$149$		−	53.7528i		−	0.360757i	−0.983597	−	0.180379i	$-0.942268\pi$
$149$		−	53.7528i		−	0.360757i	0.983597	−	0.180379i	$-0.0577323\pi$
$150$	−160.106	−	73.6731i	−1.06737	−	0.491154i
$151$		−	89.9015i		−	0.595374i	−0.954664	−	0.297687i	$-0.903785\pi$
$151$		−	89.9015i		−	0.595374i	0.954664	−	0.297687i	$-0.0962152\pi$
$152$	22.4424	+	22.4424i	0.147648	+	0.147648i
$153$	−153.611	+	221.360i	−1.00399	+	1.44680i
$154$			0.413718i			0.00268648i
$155$	−43.4719	+	62.4203i	−0.280464	+	0.402711i
$156$	−74.8375	+	74.8375i	−0.479728	+	0.479728i
$157$	79.1837	+	79.1837i	0.504355	+	0.504355i	0.912788	−	0.408434i	$-0.133925\pi$
$157$	79.1837	+	79.1837i	0.504355	+	0.504355i	−0.408434	+	0.912788i	$0.633925\pi$
$158$		−	149.968i		−	0.949166i
$159$	335.947	−	335.947i	2.11287	−	2.11287i
$160$	16.1644	−	23.2101i	0.101028	−	0.145063i
$161$		−	0.637206i		−	0.00395780i
$162$	27.5552	−	27.5552i	0.170094	−	0.170094i
$163$	−15.5756			−0.0955557			−0.0477779	−	0.998858i	$-0.515214\pi$
$163$	−15.5756			−0.0955557			−0.0477779	+	0.998858i	$0.515214\pi$
$164$	−108.636	+	108.636i	−0.662414	+	0.662414i
$165$	−79.1541	+	113.656i	−0.479722	+	0.688822i
$166$	1.87730			0.0113090
$167$	301.191			1.80354			0.901770	−	0.432217i	$-0.142269\pi$
$167$	301.191			1.80354			0.901770	+	0.432217i	$0.142269\pi$
$168$	−0.524861	−	0.524861i	−0.00312417	−	0.00312417i
$169$			56.3074i			0.333180i
$170$	41.8753	+	112.679i	0.246325	+	0.662815i
$171$	177.848			1.04005
$172$	−61.7966	+	61.7966i	−0.359282	+	0.359282i
$173$		−	13.0435i		−	0.0753959i	−0.999289	−	0.0376980i	$-0.987998\pi$
$173$		−	13.0435i		−	0.0753959i	0.999289	−	0.0376980i	$-0.0120025\pi$
$174$			179.344i			1.03071i
$175$	0.456403	+	1.23446i	0.00260802	+	0.00705404i
$176$	−15.7172	−	15.7172i	−0.0893025	−	0.0893025i
$177$		−	409.432i		−	2.31318i
$178$	58.2677	+	58.2677i	0.327347	+	0.327347i
$179$	−280.070			−1.56464			−0.782319	−	0.622878i	$-0.785963\pi$
$179$	−280.070			−1.56464			−0.782319	+	0.622878i	$0.785963\pi$
$180$	−27.9173	−	156.014i	−0.155096	−	0.866746i
$181$	199.431	+	199.431i	1.10183	+	1.10183i	0.994190	+	0.107638i	$0.0343287\pi$
$181$	199.431	+	199.431i	1.10183	+	1.10183i	0.107638	+	0.994190i	$0.465671\pi$
$182$	0.790352			0.00434259
$183$	145.607	−	145.607i	0.795665	−	0.795665i
$184$	24.2076	+	24.2076i	0.131563	+	0.131563i
$185$	−206.657	+	36.9793i	−1.11706	+	0.199888i
$186$	−107.249			−0.576609
$187$	92.9619	−	16.7962i	0.497122	−	0.0898194i
$188$	23.6517	−	23.6517i	0.125807	−	0.125807i
$189$	−1.79745			−0.00951031
$190$	45.3462	−	65.1116i	0.238664	−	0.342692i
$191$	−275.501			−1.44241			−0.721206	−	0.692721i	$-0.756412\pi$
$191$	−275.501			−1.44241			−0.721206	+	0.692721i	$0.756412\pi$
$192$	39.8792			0.207704
$193$	162.987			0.844492			0.422246	−	0.906481i	$-0.361242\pi$
$193$	162.987			0.844492			0.422246	+	0.906481i	$0.361242\pi$
$194$	14.2644	−	14.2644i	0.0735280	−	0.0735280i
$195$	217.124	+	151.213i	1.11345	+	0.775453i
$196$		−	97.9945i		−	0.499972i
$197$			167.235i			0.848911i	0.905449	+	0.424456i	$0.139534\pi$
$197$			167.235i			0.848911i	−0.905449	+	0.424456i	$0.860466\pi$
$198$	−124.553			−0.629056
$199$	−145.676	−	145.676i	−0.732039	−	0.732039i	0.238984	−	0.971023i	$-0.423186\pi$
$199$	−145.676	−	145.676i	−0.732039	−	0.732039i	−0.971023	+	0.238984i	$0.923186\pi$
$200$	−64.2362	−	29.5585i	−0.321181	−	0.147793i
$201$	396.186	−	396.186i	1.97108	−	1.97108i
$202$	183.328	−	183.328i	0.907563	−	0.907563i
$203$	0.947019	−	0.947019i	0.00466512	−	0.00466512i
$204$	−96.6272	+	139.244i	−0.473663	+	0.682569i
$205$	315.182	+	219.505i	1.53747	+	1.07076i
$206$		−	8.89199i		−	0.0431650i
$207$	191.836			0.926746
$208$	−30.0257	+	30.0257i	−0.144354	+	0.144354i
$209$	−44.0917	−	44.0917i	−0.210965	−	0.210965i
$210$	−1.06051	+	1.52276i	−0.00505005	+	0.00725125i
$211$	164.915	+	164.915i	0.781588	+	0.781588i	0.980099	−	0.198511i	$-0.0636105\pi$
$211$	164.915	+	164.915i	0.781588	+	0.781588i	−0.198511	+	0.980099i	$0.563610\pi$
$212$	134.786	−	134.786i	0.635782	−	0.635782i
$213$	414.511	+	414.511i	1.94606	+	1.94606i
$214$	−54.3644	+	54.3644i	−0.254039	+	0.254039i
$215$	179.288	+	124.863i	0.833900	+	0.580760i
$216$	68.2856	−	68.2856i	0.316137	−	0.316137i
$217$	0.566325	+	0.566325i	0.00260979	+	0.00260979i
$218$			26.5554i			0.121814i
$219$	−356.035			−1.62573
$220$	−31.7576	+	45.5999i	−0.144353	+	0.207272i
$221$	−32.0869	−	177.591i	−0.145190	−	0.803579i
$222$	−209.305	−	209.305i	−0.942817	−	0.942817i
$223$	190.304	+	190.304i	0.853381	+	0.853381i	0.990548	−	0.137167i	$-0.0437998\pi$
$223$	190.304	+	190.304i	0.853381	+	0.853381i	−0.137167	+	0.990548i	$0.543800\pi$
$224$	−0.210580	−	0.210580i	−0.000940091	−	0.000940091i
$225$	−371.644	+	137.404i	−1.65175	+	0.610684i
$226$	−124.652	+	124.652i	−0.551558	+	0.551558i
$227$		−	117.964i		−	0.519663i	−0.965654	−	0.259832i	$-0.916333\pi$
$227$		−	117.964i		−	0.519663i	0.965654	−	0.259832i	$-0.0836671\pi$
$228$	111.873			0.490673
$229$	346.655			1.51378			0.756889	−	0.653543i	$-0.226718\pi$
$229$	346.655			1.51378			0.756889	+	0.653543i	$0.226718\pi$
$230$	48.9129	−	70.2329i	0.212665	−	0.305360i
$231$	1.03117	+	1.03117i	0.00446394	+	0.00446394i
$232$			71.9550i			0.310151i
$233$		−	339.153i		−	1.45559i	−0.685793	−	0.727797i	$-0.740544\pi$
$233$		−	339.153i		−	1.45559i	0.685793	−	0.727797i	$-0.259456\pi$
$234$			237.942i			1.01685i
$235$	−68.6198	−	47.7895i	−0.291999	−	0.203359i
$236$		−	164.269i		−	0.696055i
$237$	−373.788	−	373.788i	−1.57717	−	1.57717i
$238$	1.24551	−	0.225037i	0.00523322	−	0.000945532i
$239$			47.9740i			0.200728i	0.994951	+	0.100364i	$0.0320007\pi$
$239$			47.9740i			0.200728i	−0.994951	+	0.100364i	$0.967999\pi$
$240$	−17.5611	−	98.1392i	−0.0731712	−	0.408913i
$241$	84.7763	−	84.7763i	0.351769	−	0.351769i	−0.508999	−	0.860767i	$-0.669984\pi$
$241$	84.7763	−	84.7763i	0.351769	−	0.351769i	0.860767	+	0.508999i	$0.169984\pi$
$242$	−90.1210	−	90.1210i	−0.372401	−	0.372401i
$243$			169.925i			0.699280i
$244$	58.4191	−	58.4191i	0.239423	−	0.239423i
$245$	−241.156	+	43.1525i	−0.984309	+	0.176133i
$246$			541.539i			2.20138i
$247$	−84.2312	+	84.2312i	−0.341017	+	0.341017i
$248$	−43.0296			−0.173507
$249$	4.67907	−	4.67907i	0.0187914	−	0.0187914i
$250$	−44.4540	+	171.096i	−0.177816	+	0.684384i
$251$	−212.165			−0.845281			−0.422640	−	0.906297i	$-0.638897\pi$
$251$	−212.165			−0.845281			−0.422640	+	0.906297i	$0.638897\pi$
$252$	−1.66877			−0.00662210
$253$	−47.5597	−	47.5597i	−0.187983	−	0.187983i
$254$			34.5669i			0.136090i
$255$	385.218	+	176.474i	1.51066	+	0.692054i
$256$	16.0000			0.0625000
$257$	111.080	−	111.080i	0.432218	−	0.432218i	−0.457164	−	0.889382i	$-0.651135\pi$
$257$	111.080	−	111.080i	0.432218	−	0.432218i	0.889382	+	0.457164i	$0.151135\pi$
$258$			308.050i			1.19399i
$259$			2.21045i			0.00853457i
$260$	87.1125	+	60.6685i	0.335048	+	0.233340i
$261$	285.108	+	285.108i	1.09237	+	1.09237i
$262$			367.836i			1.40396i
$263$	−60.4840	−	60.4840i	−0.229977	−	0.229977i	0.582706	−	0.812683i	$-0.301994\pi$
$263$	−60.4840	−	60.4840i	−0.229977	−	0.229977i	−0.812683	+	0.582706i	$0.801994\pi$
$264$	−78.3489			−0.296776
$265$	−391.050	−	272.342i	−1.47566	−	1.02771i
$266$	−0.590742	−	0.590742i	−0.00222083	−	0.00222083i
$267$	290.459			1.08786
$268$	158.954	−	158.954i	0.593114	−	0.593114i
$269$	−110.689	−	110.689i	−0.411483	−	0.411483i	0.470772	−	0.882255i	$-0.343975\pi$
$269$	−110.689	−	110.689i	−0.411483	−	0.411483i	−0.882255	+	0.470772i	$0.843975\pi$
$270$	−198.115	−	137.975i	−0.733758	−	0.511017i
$271$	−321.097			−1.18486			−0.592430	−	0.805622i	$-0.701831\pi$
$271$	−321.097			−1.18486			−0.592430	+	0.805622i	$0.701831\pi$
$272$	−38.7679	+	55.8663i	−0.142529	+	0.205391i
$273$	1.96991	−	1.96991i	0.00721580	−	0.00721580i
$274$	−22.8330			−0.0833322
$275$	126.202	+	58.0723i	0.458917	+	0.211172i
$276$	120.673			0.437220
$277$	−106.687			−0.385152			−0.192576	−	0.981282i	$-0.561684\pi$
$277$	−106.687			−0.385152			−0.192576	+	0.981282i	$0.561684\pi$
$278$	−144.539			−0.519925
$279$	−170.497	+	170.497i	−0.611099	+	0.611099i
$280$	−0.425489	+	0.610950i	−0.00151960	+	0.00218196i
$281$			426.126i			1.51646i	0.651985	+	0.758232i	$0.273936\pi$
$281$			426.126i			1.51646i	−0.651985	+	0.758232i	$0.726064\pi$
$282$		−	117.901i		−	0.418089i
$283$	−30.7410			−0.108626			−0.0543128	−	0.998524i	$-0.517297\pi$
$283$	−30.7410			−0.108626			−0.0543128	+	0.998524i	$0.517297\pi$
$284$	166.306	+	166.306i	0.585586	+	0.585586i
$285$	−49.2642	−	275.310i	−0.172857	−	0.966002i
$286$	58.9901	−	58.9901i	0.206259	−	0.206259i
$287$	2.85957	−	2.85957i	0.00996367	−	0.00996367i
$288$	63.3970	−	63.3970i	0.220128	−	0.220128i
$289$	−101.131	−	270.728i	−0.349934	−	0.936774i
$290$	177.075	−	31.6859i	0.610603	−	0.109262i
$291$		−	71.1068i		−	0.244353i
$292$	−142.845			−0.489196
$293$	327.123	−	327.123i	1.11646	−	1.11646i	0.124203	−	0.992257i	$-0.460363\pi$
$293$	327.123	−	327.123i	1.11646	−	1.11646i	0.992257	−	0.124203i	$-0.0396374\pi$
$294$	−244.246	−	244.246i	−0.830770	−	0.830770i
$295$	−404.252	+	72.3370i	−1.37034	+	0.245210i
$296$	−83.9757	−	83.9757i	−0.283702	−	0.283702i
$297$	−134.158	+	134.158i	−0.451709	+	0.451709i
$298$	−53.7528	−	53.7528i	−0.180379	−	0.180379i
$299$	−90.8563	+	90.8563i	−0.303867	+	0.303867i
$300$	−233.779	+	86.4325i	−0.779263	+	0.288108i
$301$	1.62664	−	1.62664i	0.00540413	−	0.00540413i
$302$	−89.9015	−	89.9015i	−0.297687	−	0.297687i
$303$		−	913.870i		−	3.01607i
$304$	44.8849			0.147648
$305$	−169.489	−	118.039i	−0.555703	−	0.387013i
$306$	67.7492	+	374.970i	0.221403	+	1.22539i
$307$	−320.135	−	320.135i	−1.04279	−	1.04279i	−0.999043	−	0.0437439i	$-0.986071\pi$
$307$	−320.135	−	320.135i	−1.04279	−	1.04279i	−0.0437439	−	0.999043i	$-0.513929\pi$
$308$	0.413718	+	0.413718i	0.00134324	+	0.00134324i
$309$	−22.1629	−	22.1629i	−0.0717245	−	0.0717245i
$310$	18.9484	+	105.892i	0.0611238	+	0.341587i
$311$	−131.618	+	131.618i	−0.423208	+	0.423208i	−0.886307	−	0.463099i	$-0.846738\pi$
$311$	−131.618	+	131.618i	−0.423208	+	0.423208i	0.463099	+	0.886307i	$0.346738\pi$
$312$			149.675i			0.479728i
$313$	30.7871			0.0983612			0.0491806	−	0.998790i	$-0.484339\pi$
$313$	30.7871			0.0983612			0.0491806	+	0.998790i	$0.484339\pi$
$314$	158.367			0.504355
$315$	0.734854	+	4.10669i	0.00233287	+	0.0130371i
$316$	−149.968	−	149.968i	−0.474583	−	0.474583i
$317$		−	167.692i		−	0.528997i	−0.964386	−	0.264498i	$-0.914794\pi$
$317$		−	167.692i		−	0.528997i	0.964386	−	0.264498i	$-0.0852064\pi$
$318$		−	671.894i		−	2.11287i
$319$		−	141.367i		−	0.443156i
$320$	−7.04571	−	39.3746i	−0.0220178	−	0.123046i
$321$			271.001i			0.844241i
$322$	−0.637206	−	0.637206i	−0.00197890	−	0.00197890i
$323$	−108.756	+	156.722i	−0.336706	+	0.485208i
$324$		−	55.1105i		−	0.170094i
$325$	110.939	−	241.092i	0.341352	−	0.741822i
$326$	−15.5756	+	15.5756i	−0.0477779	+	0.0477779i
$327$	66.1881	+	66.1881i	0.202410	+	0.202410i
$328$			217.272i			0.662414i
$329$	−0.622572	+	0.622572i	−0.00189231	+	0.00189231i
$330$	34.5015	+	192.810i	0.104550	+	0.584272i
$331$			271.770i			0.821056i	0.911848	+	0.410528i	$0.134656\pi$
$331$			271.770i			0.821056i	−0.911848	+	0.410528i	$0.865344\pi$
$332$	1.87730	−	1.87730i	0.00565451	−	0.00565451i
$333$	−665.475			−1.99842
$334$	301.191	−	301.191i	0.901770	−	0.901770i
$335$	−461.170	−	321.176i	−1.37663	−	0.958735i
$336$	−1.04972			−0.00312417
$337$	229.785			0.681853			0.340927	−	0.940090i	$-0.389259\pi$
$337$	229.785			0.681853			0.340927	+	0.940090i	$0.389259\pi$
$338$	56.3074	+	56.3074i	0.166590	+	0.166590i
$339$			621.379i			1.83298i
$340$	154.554	+	70.8033i	0.454570	+	0.208245i
$341$	84.5384			0.247913
$342$	177.848	−	177.848i	0.520023	−	0.520023i
$343$			5.15907i			0.0150410i
$344$			123.593i			0.359282i
$345$	−53.1390	−	296.965i	−0.154026	−	0.860768i
$346$	−13.0435	−	13.0435i	−0.0376980	−	0.0376980i
$347$			379.283i			1.09304i	0.837448	+	0.546518i	$0.184047\pi$
$347$			379.283i			1.09304i	−0.837448	+	0.546518i	$0.815953\pi$
$348$	179.344	+	179.344i	0.515357	+	0.515357i
$349$	−6.00329			−0.0172014			−0.00860070	−	0.999963i	$-0.502738\pi$
$349$	−6.00329			−0.0172014			−0.00860070	+	0.999963i	$0.502738\pi$
$350$	1.69086	+	0.778055i	0.00483103	+	0.00222301i
$351$	256.290	+	256.290i	0.730171	+	0.730171i
$352$	−31.4345			−0.0893025
$353$	368.352	−	368.352i	1.04349	−	1.04349i	0.0444790	−	0.999010i	$-0.485837\pi$
$353$	368.352	−	368.352i	1.04349	−	1.04349i	0.999010	−	0.0444790i	$-0.0141628\pi$
$354$	−409.432	−	409.432i	−1.15659	−	1.15659i
$355$	336.031	−	482.500i	0.946567	−	1.35915i
$356$	116.535			0.327347
$357$	2.54347	−	3.66526i	0.00712457	−	0.0102668i
$358$	−280.070	+	280.070i	−0.782319	+	0.782319i
$359$	−84.5859			−0.235615			−0.117808	−	0.993036i	$-0.537587\pi$
$359$	−84.5859			−0.235615			−0.117808	+	0.993036i	$0.537587\pi$
$360$	−183.932	−	128.097i	−0.510921	−	0.355825i
$361$	−235.084			−0.651203
$362$	398.862			1.10183
$363$	−449.244			−1.23759
$364$	0.790352	−	0.790352i	0.00217130	−	0.00217130i
$365$	62.9029	+	351.530i	0.172337	+	0.963095i
$366$		−	291.213i		−	0.795665i
$367$			175.510i			0.478230i	0.970991	+	0.239115i	$0.0768573\pi$
$367$			175.510i			0.478230i	−0.970991	+	0.239115i	$0.923143\pi$
$368$	48.4153			0.131563
$369$	860.898	+	860.898i	2.33306	+	2.33306i
$370$	−169.677	+	243.636i	−0.458588	+	0.658476i
$371$	−3.54790	+	3.54790i	−0.00956308	+	0.00956308i
$372$	−107.249	+	107.249i	−0.288304	+	0.288304i
$373$	−292.403	+	292.403i	−0.783921	+	0.783921i	−0.980490	−	0.196569i	$-0.937020\pi$
$373$	−292.403	+	292.403i	−0.783921	+	0.783921i	0.196569	+	0.980490i	$0.437020\pi$
$374$	76.1656	−	109.758i	0.203651	−	0.293471i
$375$	315.649	+	537.248i	0.841730	+	1.43266i
$376$		−	47.3033i		−	0.125807i
$377$	−270.062			−0.716345
$378$	−1.79745	+	1.79745i	−0.00475516	+	0.00475516i
$379$	88.6402	+	88.6402i	0.233879	+	0.233879i	0.814310	−	0.580431i	$-0.197116\pi$
$379$	88.6402	+	88.6402i	0.233879	+	0.233879i	−0.580431	+	0.814310i	$0.697116\pi$
$380$	−19.7654	−	110.458i	−0.0520141	−	0.290678i
$381$	86.1562	+	86.1562i	0.226132	+	0.226132i
$382$	−275.501	+	275.501i	−0.721206	+	0.721206i
$383$	244.650	+	244.650i	0.638772	+	0.638772i	0.950253	−	0.311480i	$-0.100825\pi$
$383$	244.650	+	244.650i	0.638772	+	0.638772i	−0.311480	+	0.950253i	$0.600825\pi$
$384$	39.8792	−	39.8792i	0.103852	−	0.103852i
$385$	0.835939	−	1.20031i	0.00217127	−	0.00311768i
$386$	162.987	−	162.987i	0.422246	−	0.422246i
$387$	489.714	+	489.714i	1.26541	+	1.26541i
$388$		−	28.5289i		−	0.0735280i
$389$	220.249			0.566192			0.283096	−	0.959092i	$-0.408638\pi$
$389$	220.249			0.566192			0.283096	+	0.959092i	$0.408638\pi$
$390$	368.337	−	65.9104i	0.944454	−	0.169001i
$391$	−117.310	+	169.049i	−0.300026	+	0.432350i
$392$	−97.9945	−	97.9945i	−0.249986	−	0.249986i
$393$	916.814	+	916.814i	2.33286	+	2.33286i
$394$	167.235	+	167.235i	0.424456	+	0.424456i
$395$	−303.019	+	435.098i	−0.767136	+	1.10151i
$396$	−124.553	+	124.553i	−0.314528	+	0.314528i
$397$		−	438.414i		−	1.10432i	−0.833739	−	0.552159i	$-0.813804\pi$
$397$		−	438.414i		−	1.10432i	0.833739	−	0.552159i	$-0.186196\pi$
$398$	−291.352			−0.732039
$399$	−2.94479			−0.00738043
$400$	−93.7947	+	34.6777i	−0.234487	+	0.0866943i
$401$	−360.106	−	360.106i	−0.898020	−	0.898020i	0.0972411	−	0.995261i	$-0.468998\pi$
$401$	−360.106	−	360.106i	−0.898020	−	0.898020i	−0.995261	+	0.0972411i	$0.968998\pi$
$402$		−	792.372i		−	1.97108i
$403$		−	161.499i		−	0.400742i
$404$		−	366.655i		−	0.907563i
$405$	−135.622	+	24.2683i	−0.334869	+	0.0599216i
$406$		−	1.89404i		−	0.00466512i
$407$	164.983	+	164.983i	0.405364	+	0.405364i
$408$	42.6169	+	235.871i	0.104453	+	0.578116i
$409$		−	189.446i		−	0.463194i	−0.972812	−	0.231597i	$-0.925605\pi$
$409$		−	189.446i		−	0.463194i	0.972812	−	0.231597i	$-0.0743951\pi$
$410$	534.687	−	95.6771i	1.30411	−	0.233359i
$411$	−56.9102	+	56.9102i	−0.138468	+	0.138468i
$412$	−8.89199	−	8.89199i	−0.0215825	−	0.0215825i
$413$			4.32398i			0.0104697i
$414$	191.836	−	191.836i	0.463373	−	0.463373i
$415$	−5.44654	−	3.79318i	−0.0131242	−	0.00914020i
$416$			60.0513i			0.144354i
$417$	−360.257	+	360.257i	−0.863925	+	0.863925i
$418$	−88.1833			−0.210965
$419$	320.376	−	320.376i	0.764622	−	0.764622i	−0.212532	−	0.977154i	$-0.568171\pi$
$419$	320.376	−	320.376i	0.764622	−	0.764622i	0.977154	+	0.212532i	$0.0681711\pi$
$420$	0.462252	+	2.58327i	0.00110060	+	0.00615065i
$421$	−44.7427			−0.106277			−0.0531385	−	0.998587i	$-0.516922\pi$
$421$	−44.7427			−0.106277			−0.0531385	+	0.998587i	$0.516922\pi$
$422$	329.830			0.781588
$423$	−187.430	−	187.430i	−0.443098	−	0.443098i
$424$		−	269.571i		−	0.635782i
$425$	106.182	−	411.522i	0.249840	−	0.968287i
$426$	829.021			1.94606
$427$	−1.53774	+	1.53774i	−0.00360126	+	0.00360126i
$428$			108.729i			0.254039i
$429$		−	294.060i		−	0.685454i
$430$	304.152	−	54.4251i	0.707330	−	0.126570i
$431$	178.147	+	178.147i	0.413334	+	0.413334i	0.882898	−	0.469565i	$-0.155589\pi$
$431$	178.147	+	178.147i	0.413334	+	0.413334i	−0.469565	+	0.882898i	$0.655589\pi$
$432$		−	136.571i		−	0.316137i
$433$	149.748	+	149.748i	0.345839	+	0.345839i	0.858557	−	0.512718i	$-0.171361\pi$
$433$	149.748	+	149.748i	0.345839	+	0.345839i	−0.512718	+	0.858557i	$0.671361\pi$
$434$	1.13265			0.00260979
$435$	362.375	−	520.326i	0.833045	−	1.19615i
$436$	26.5554	+	26.5554i	0.0609070	+	0.0609070i
$437$	135.820			0.310800
$438$	−356.035	+	356.035i	−0.812865	+	0.812865i
$439$	−198.498	−	198.498i	−0.452159	−	0.452159i	0.443911	−	0.896071i	$-0.353591\pi$
$439$	−198.498	−	198.498i	−0.452159	−	0.452159i	−0.896071	+	0.443911i	$0.853591\pi$
$440$	13.8424	+	77.3575i	0.0314600	+	0.175812i
$441$	−776.569			−1.76093
$442$	−209.678	−	145.504i	−0.474385	−	0.329195i
$443$	231.871	−	231.871i	0.523410	−	0.523410i	−0.395190	−	0.918600i	$-0.629321\pi$
$443$	231.871	−	231.871i	0.523410	−	0.523410i	0.918600	+	0.395190i	$0.129321\pi$
$444$	−418.611			−0.942817
$445$	−51.3172	−	286.783i	−0.115319	−	0.644457i
$446$	380.608			0.853381
$447$	−267.953			−0.599447
$448$	−0.421161			−0.000940091
$449$	−520.191	+	520.191i	−1.15855	+	1.15855i	−0.173767	+	0.984787i	$0.555594\pi$
$449$	−520.191	+	520.191i	−1.15855	+	1.15855i	−0.984787	+	0.173767i	$0.944406\pi$
$450$	−234.240	+	509.048i	−0.520533	+	1.13122i
$451$		−	426.864i		−	0.946484i
$452$			249.304i			0.551558i
$453$	−448.150			−0.989294
$454$	−117.964	−	117.964i	−0.259832	−	0.259832i
$455$	−2.29302	−	1.59695i	−0.00503961	−	0.00350978i
$456$	111.873	−	111.873i	0.245336	−	0.245336i
$457$	354.768	−	354.768i	0.776297	−	0.776297i	−0.202902	−	0.979199i	$-0.565037\pi$
$457$	354.768	−	354.768i	0.776297	−	0.776297i	0.979199	+	0.202902i	$0.0650372\pi$
$458$	346.655	−	346.655i	0.756889	−	0.756889i
$459$	476.858	+	330.911i	1.03891	+	0.720940i
$460$	−21.3200	−	119.146i	−0.0463478	−	0.259012i
$461$		−	433.035i		−	0.939337i	−0.882843	−	0.469669i	$-0.844373\pi$
$461$		−	433.035i		−	0.939337i	0.882843	−	0.469669i	$-0.155627\pi$
$462$	2.06234			0.00446394
$463$	100.046	−	100.046i	0.216081	−	0.216081i	−0.590763	−	0.806845i	$-0.701173\pi$
$463$	100.046	−	100.046i	0.216081	−	0.216081i	0.806845	+	0.590763i	$0.201173\pi$
$464$	71.9550	+	71.9550i	0.155075	+	0.155075i
$465$	311.159	+	216.703i	0.669159	+	0.466028i
$466$	−339.153	−	339.153i	−0.727797	−	0.727797i
$467$	258.356	−	258.356i	0.553224	−	0.553224i	−0.374146	−	0.927370i	$-0.622064\pi$
$467$	258.356	−	258.356i	0.553224	−	0.553224i	0.927370	+	0.374146i	$0.122064\pi$
$468$	237.942	+	237.942i	0.508423	+	0.508423i
$469$	−4.18409	+	4.18409i	−0.00892129	+	0.00892129i
$470$	−116.409	+	20.8303i	−0.247679	+	0.0443199i
$471$	394.723	−	394.723i	0.838052	−	0.838052i
$472$	−164.269	−	164.269i	−0.348028	−	0.348028i
$473$		−	242.818i		−	0.513357i
$474$	−747.576			−1.57717
$475$	−263.123	+	97.2816i	−0.553943	+	0.204803i
$476$	1.02047	−	1.47054i	0.00214385	−	0.00308938i
$477$	−1068.13	−	1068.13i	−2.23926	−	2.23926i
$478$	47.9740	+	47.9740i	0.100364	+	0.100364i
$479$	299.436	+	299.436i	0.625127	+	0.625127i	0.946838	−	0.321711i	$-0.104258\pi$
$479$	299.436	+	299.436i	0.625127	+	0.625127i	−0.321711	+	0.946838i	$0.604258\pi$
$480$	−115.700	−	80.5781i	−0.241042	−	0.167871i
$481$	315.178	−	315.178i	0.655256	−	0.655256i
$482$		−	169.553i		−	0.351769i
$483$	−3.17641			−0.00657642
$484$	−180.242			−0.372401
$485$	−70.2070	+	12.5629i	−0.144757	+	0.0259029i
$486$	169.925	+	169.925i	0.349640	+	0.349640i
$487$			430.743i			0.884483i	0.896896	+	0.442242i	$0.145817\pi$
$487$			430.743i			0.884483i	−0.896896	+	0.442242i	$0.854183\pi$
$488$		−	116.838i		−	0.239423i
$489$			77.6427i			0.158779i
$490$	−198.003	+	284.308i	−0.404088	+	0.580221i
$491$			435.187i			0.886328i	0.896441	+	0.443164i	$0.146144\pi$
$491$			435.187i			0.886328i	−0.896441	+	0.443164i	$0.853856\pi$
$492$	541.539	+	541.539i	1.10069	+	1.10069i
$493$	−425.588	+	76.8947i	−0.863261	+	0.155973i
$494$			168.462i			0.341017i
$495$	361.362	+	251.667i	0.730025	+	0.508417i
$496$	−43.0296	+	43.0296i	−0.0867533	+	0.0867533i
$497$	−4.37761	−	4.37761i	−0.00880806	−	0.00880806i
$498$		−	9.35814i		−	0.0187914i
$499$	199.073	−	199.073i	0.398945	−	0.398945i	−0.478916	−	0.877861i	$-0.658970\pi$
$499$	199.073	−	199.073i	0.398945	−	0.398945i	0.877861	+	0.478916i	$0.158970\pi$
$500$	126.642	+	215.550i	0.253284	+	0.431100i
$501$		−	1501.41i		−	2.99682i
$502$	−212.165	+	212.165i	−0.422640	+	0.422640i
$503$	877.046			1.74363			0.871815	−	0.489835i	$-0.162943\pi$
$503$	877.046			1.74363			0.871815	+	0.489835i	$0.162943\pi$
$504$	−1.66877	+	1.66877i	−0.00331105	+	0.00331105i
$505$	−902.307	+	161.459i	−1.78675	+	0.319721i
$506$	−95.1193			−0.187983
$507$	280.687			0.553623
$508$	34.5669	+	34.5669i	0.0680450	+	0.0680450i
$509$			788.072i			1.54828i	0.633017	+	0.774138i	$0.281816\pi$
$509$			788.072i			1.54828i	−0.633017	+	0.774138i	$0.718184\pi$
$510$	561.692	−	208.744i	1.10136	−	0.409302i
$511$	3.76005			0.00735822
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		−	383.124i		−	0.746830i
$514$		−	222.160i		−	0.432218i
$515$	−17.9668	+	25.7981i	−0.0348869	+	0.0500933i
$516$	308.050	+	308.050i	0.596996	+	0.596996i
$517$			92.9347i			0.179758i
$518$	2.21045	+	2.21045i	0.00426728	+	0.00426728i
$519$	−65.0205			−0.125280
$520$	147.781	−	26.4440i	0.284194	−	0.0508539i
$521$	226.738	+	226.738i	0.435198	+	0.435198i	0.890392	−	0.455194i	$-0.150430\pi$
$521$	226.738	+	226.738i	0.435198	+	0.435198i	−0.455194	+	0.890392i	$0.650430\pi$
$522$	570.216			1.09237
$523$	−477.269	+	477.269i	−0.912561	+	0.912561i	−0.996473	−	0.0839125i	$-0.973258\pi$
$523$	−477.269	+	477.269i	−0.912561	+	0.912561i	0.0839125	+	0.996473i	$0.473258\pi$
$524$	367.836	+	367.836i	0.701978	+	0.701978i
$525$	6.15365	−	2.27512i	0.0117212	−	0.00433357i
$526$	−120.968			−0.229977
$527$	−45.9836	−	254.505i	−0.0872555	−	0.482931i
$528$	−78.3489	+	78.3489i	−0.148388	+	0.148388i
$529$	−382.498			−0.723058
$530$	−663.392	+	118.708i	−1.25168	+	0.223977i
$531$	−1301.77			−2.45154
$532$	−1.18148			−0.00222083
$533$	−815.466			−1.52996
$534$	290.459	−	290.459i	0.543930	−	0.543930i
$535$	267.572	−	47.8795i	0.500135	−	0.0894944i
$536$		−	317.909i		−	0.593114i
$537$			1396.12i			2.59986i
$538$	−221.378			−0.411483
$539$	192.525	+	192.525i	0.357190	+	0.357190i
$540$	−336.089	+	60.1400i	−0.622388	+	0.111370i
$541$	−382.329	+	382.329i	−0.706707	+	0.706707i	−0.965841	−	0.259134i	$-0.916563\pi$
$541$	−382.329	+	382.329i	−0.706707	+	0.706707i	0.259134	+	0.965841i	$0.416563\pi$
$542$	−321.097	+	321.097i	−0.592430	+	0.592430i
$543$	994.143	−	994.143i	1.83083	−	1.83083i
$544$	17.0984	+	94.6343i	0.0314309	+	0.173960i
$545$	53.6567	−	77.0445i	0.0984527	−	0.141366i
$546$		−	3.93983i		−	0.00721580i
$547$	224.401			0.410240			0.205120	−	0.978737i	$-0.434242\pi$
$547$	224.401			0.410240			0.205120	+	0.978737i	$0.434242\pi$
$548$	−22.8330	+	22.8330i	−0.0416661	+	0.0416661i
$549$	−462.949	−	462.949i	−0.843259	−	0.843259i
$550$	184.274	−	68.1298i	0.335044	−	0.123872i
$551$	201.856	+	201.856i	0.366344	+	0.366344i
$552$	120.673	−	120.673i	0.218610	−	0.218610i
$553$	3.94754	+	3.94754i	0.00713841	+	0.00713841i
$554$	−106.687	+	106.687i	−0.192576	+	0.192576i
$555$	184.338	+	1030.16i	0.332141	+	1.85615i
$556$	−144.539	+	144.539i	−0.259962	+	0.259962i
$557$	335.493	+	335.493i	0.602321	+	0.602321i	0.940928	−	0.338607i	$-0.109956\pi$
$557$	335.493	+	335.493i	0.602321	+	0.602321i	−0.338607	+	0.940928i	$0.609956\pi$
$558$			340.993i			0.611099i
$559$	−463.871			−0.829823
$560$	0.185461	+	1.03644i	0.000331180	+	0.00185078i
$561$	−83.7276	−	463.406i	−0.149247	−	0.826035i
$562$	426.126	+	426.126i	0.758232	+	0.758232i
$563$	325.004	+	325.004i	0.577271	+	0.577271i	0.934150	−	0.356880i	$-0.116159\pi$
$563$	325.004	+	325.004i	0.577271	+	0.577271i	−0.356880	+	0.934150i	$0.616159\pi$
$564$	−117.901	−	117.901i	−0.209045	−	0.209045i
$565$	613.516	−	109.783i	1.08587	−	0.194306i
$566$	−30.7410	+	30.7410i	−0.0543128	+	0.0543128i
$567$			1.45065i			0.00255846i
$568$	332.613			0.585586
$569$	−259.344			−0.455790			−0.227895	−	0.973686i	$-0.573184\pi$
$569$	−259.344			−0.455790			−0.227895	+	0.973686i	$0.573184\pi$
$570$	−324.575	−	226.046i	−0.569429	−	0.396572i
$571$	−55.2081	−	55.2081i	−0.0966867	−	0.0966867i	0.657109	−	0.753796i	$-0.271779\pi$
$571$	−55.2081	−	55.2081i	−0.0966867	−	0.0966867i	−0.753796	+	0.657109i	$0.771779\pi$
$572$		−	117.980i		−	0.206259i
$573$			1373.34i			2.39676i
$574$		−	5.71915i		−	0.00996367i
$575$	−283.819	+	104.933i	−0.493598	+	0.182493i
$576$		−	126.794i		−	0.220128i
$577$	−269.016	−	269.016i	−0.466232	−	0.466232i	0.434460	−	0.900691i	$-0.356939\pi$
$577$	−269.016	−	269.016i	−0.466232	−	0.466232i	−0.900691	+	0.434460i	$0.856939\pi$
$578$	−371.859	−	169.597i	−0.643354	−	0.293420i
$579$		−	812.474i		−	1.40324i
$580$	145.389	−	208.761i	0.250671	−	0.359932i
$581$	−0.0494152	+	0.0494152i	−8.50520e−5	+	8.50520e-5i
$582$	−71.1068	−	71.1068i	−0.122177	−	0.122177i
$583$			529.615i			0.908431i
$584$	−142.845	+	142.845i	−0.244598	+	0.244598i
$585$	480.775	−	690.334i	0.821837	−	1.18006i
$586$		−	654.245i		−	1.11646i
$587$	−571.775	+	571.775i	−0.974063	+	0.974063i	−0.999672	−	0.0256088i	$-0.991848\pi$
$587$	−571.775	+	571.775i	−0.974063	+	0.974063i	0.0256088	+	0.999672i	$0.491848\pi$
$588$	−488.493			−0.830770
$589$	−120.711	+	120.711i	−0.204943	+	0.204943i
$590$	−331.915	+	476.589i	−0.562567	+	0.807777i
$591$	833.652			1.41058
$592$	−167.951			−0.283702
$593$	−384.281	−	384.281i	−0.648028	−	0.648028i	0.304488	−	0.952516i	$-0.401515\pi$
$593$	−384.281	−	384.281i	−0.648028	−	0.648028i	−0.952516	+	0.304488i	$0.901515\pi$
$594$			268.315i			0.451709i
$595$	−4.06825	−	1.86372i	−0.00683739	−	0.00313231i
$596$	−107.506			−0.180379
$597$	−726.179	+	726.179i	−1.21638	+	1.21638i
$598$			181.713i			0.303867i
$599$		−	235.502i		−	0.393159i	−0.980488	−	0.196580i	$-0.937017\pi$
$599$		−	235.502i		−	0.393159i	0.980488	−	0.196580i	$-0.0629834\pi$
$600$	−147.346	+	320.211i	−0.245577	+	0.533686i
$601$	662.707	+	662.707i	1.10267	+	1.10267i	0.994087	+	0.108587i	$0.0346327\pi$
$601$	662.707	+	662.707i	1.10267	+	1.10267i	0.108587	+	0.994087i	$0.465367\pi$
$602$		−	3.25329i		−	0.00540413i
$603$	−1259.65	−	1259.65i	−2.08898	−	2.08898i
$604$	−179.803			−0.297687
$605$	79.3708	+	443.560i	0.131191	+	0.733157i
$606$	−913.870	−	913.870i	−1.50804	−	1.50804i
$607$	−1019.75			−1.67999			−0.839994	−	0.542596i	$-0.817441\pi$
$607$	−1019.75			−1.67999			−0.839994	+	0.542596i	$0.817441\pi$
$608$	44.8849	−	44.8849i	0.0738238	−	0.0738238i
$609$	−4.72079	−	4.72079i	−0.00775171	−	0.00775171i
$610$	−287.528	+	51.4505i	−0.471358	+	0.0843451i
$611$	177.539			0.290572
$612$	442.719	+	307.221i	0.723398	+	0.501995i
$613$	−643.228	+	643.228i	−1.04931	+	1.04931i	−0.0505921	+	0.998719i	$0.516111\pi$
$613$	−643.228	+	643.228i	−1.04931	+	1.04931i	−0.998719	+	0.0505921i	$0.983889\pi$
$614$	−640.271			−1.04279
$615$	1094.21	−	1571.15i	1.77920	−	2.55472i
$616$	0.827435			0.00134324
$617$	975.682			1.58133			0.790666	−	0.612248i	$-0.209735\pi$
$617$	975.682			1.58133			0.790666	+	0.612248i	$0.209735\pi$
$618$	−44.3257			−0.0717245
$619$	−742.980	+	742.980i	−1.20029	+	1.20029i	−0.226214	+	0.974078i	$0.572635\pi$
$619$	−742.980	+	742.980i	−1.20029	+	1.20029i	−0.974078	+	0.226214i	$0.927365\pi$
$620$	124.841	+	86.9437i	0.201356	+	0.140232i
$621$		−	413.258i		−	0.665472i
$622$			263.235i			0.423208i
$623$	−3.06751			−0.00492377
$624$	149.675	+	149.675i	0.239864	+	0.239864i
$625$	474.682	−	406.574i	0.759491	−	0.650518i
$626$	30.7871	−	30.7871i	0.0491806	−	0.0491806i
$627$	−219.793	+	219.793i	−0.350546	+	0.350546i
$628$	158.367	−	158.367i	0.252177	−	0.252177i
$629$	406.946	−	586.427i	0.646972	−	0.932316i
$630$	4.84155	+	3.37184i	0.00768499	+	0.00535212i
$631$		−	263.265i		−	0.417219i	−0.977999	−	0.208610i	$-0.933106\pi$
$631$		−	263.265i		−	0.417219i	0.977999	−	0.208610i	$-0.0668938\pi$
$632$	−299.936			−0.474583
$633$	822.085	−	822.085i	1.29871	−	1.29871i
$634$	−167.692	−	167.692i	−0.264498	−	0.264498i
$635$	69.8443	−	100.288i	0.109991	−	0.157934i
$636$	−671.894	−	671.894i	−1.05644	−	1.05644i
$637$	367.794	−	367.794i	0.577384	−	0.577384i
$638$	−141.367	−	141.367i	−0.221578	−	0.221578i
$639$	1317.92	−	1317.92i	2.06247	−	2.06247i
$640$	−46.4203	−	32.3289i	−0.0725317	−	0.0505139i
$641$	23.3139	−	23.3139i	0.0363712	−	0.0363712i	−0.688687	−	0.725058i	$-0.741813\pi$
$641$	23.3139	−	23.3139i	0.0363712	−	0.0363712i	0.725058	+	0.688687i	$0.241813\pi$
$642$	271.001	+	271.001i	0.422120	+	0.422120i
$643$			255.330i			0.397092i	0.980092	+	0.198546i	$0.0636218\pi$
$643$			255.330i			0.397092i	−0.980092	+	0.198546i	$0.936378\pi$
$644$	−1.27441			−0.00197890
$645$	622.432	−	893.735i	0.965010	−	1.38564i
$646$	47.9662	+	265.478i	0.0742512	+	0.410957i
$647$	93.5864	+	93.5864i	0.144647	+	0.144647i	0.775722	−	0.631075i	$-0.217386\pi$
$647$	93.5864	+	93.5864i	0.144647	+	0.144647i	−0.631075	+	0.775722i	$0.717386\pi$
$648$	−55.1105	−	55.1105i	−0.0850470	−	0.0850470i
$649$	322.732	+	322.732i	0.497276	+	0.497276i
$650$	−130.153	−	352.031i	−0.200235	−	0.541587i
$651$	2.82307	−	2.82307i	0.00433652	−	0.00433652i
$652$			31.1512i			0.0477779i
$653$	118.236			0.181066			0.0905329	−	0.995893i	$-0.471143\pi$
$653$	118.236			0.181066			0.0905329	+	0.995893i	$0.471143\pi$
$654$	132.376			0.202410
$655$	743.234	−	1067.19i	1.13471	−	1.62930i
$656$	217.272	+	217.272i	0.331207	+	0.331207i
$657$			1131.99i			1.72298i
$658$			1.24514i			0.00189231i
$659$		−	355.919i		−	0.540089i	−0.962848	−	0.270044i	$-0.912962\pi$
$659$		−	355.919i		−	0.540089i	0.962848	−	0.270044i	$-0.0870384\pi$
$660$	227.311	+	158.308i	0.344411	+	0.239861i
$661$			476.248i			0.720497i	0.932856	+	0.360248i	$0.117308\pi$
$661$			476.248i			0.720497i	−0.932856	+	0.360248i	$0.882692\pi$
$662$	271.770	+	271.770i	0.410528	+	0.410528i
$663$	−885.274	+	159.950i	−1.33525	+	0.241252i
$664$		−	3.75459i		−	0.00565451i
$665$	0.520275	+	2.90753i	0.000782368	+	0.00437222i
$666$	−665.475	+	665.475i	−0.999212	+	0.999212i
$667$	217.732	+	217.732i	0.326435	+	0.326435i
$668$		−	602.382i		−	0.901770i
$669$	948.646	−	948.646i	1.41801	−	1.41801i
$670$	−782.346	+	139.993i	−1.16768	+	0.208945i
$671$			229.547i			0.342097i
$672$	−1.04972	+	1.04972i	−0.00156209	+	0.00156209i
$673$	−322.358			−0.478987			−0.239493	−	0.970898i	$-0.576981\pi$
$673$	−322.358			−0.478987			−0.239493	+	0.970898i	$0.576981\pi$
$674$	229.785	−	229.785i	0.340927	−	0.340927i
$675$	295.999	+	800.603i	0.438516	+	1.18608i
$676$	112.615			0.166590
$677$	−579.701			−0.856279			−0.428140	−	0.903713i	$-0.640831\pi$
$677$	−579.701			−0.856279			−0.428140	+	0.903713i	$0.640831\pi$
$678$	621.379	+	621.379i	0.916488	+	0.916488i
$679$			0.750952i			0.00110597i
$680$	225.357	−	83.7505i	0.331408	−	0.123163i
$681$	−588.037			−0.863490
$682$	84.5384	−	84.5384i	0.123957	−	0.123957i
$683$		−	123.550i		−	0.180894i	−0.995901	−	0.0904468i	$-0.971170\pi$
$683$		−	123.550i		−	0.180894i	0.995901	−	0.0904468i	$-0.0288295\pi$
$684$		−	355.696i		−	0.520023i
$685$	66.2448	+	46.1354i	0.0967077	+	0.0673509i
$686$	5.15907	+	5.15907i	0.00752051	+	0.00752051i
$687$		−	1728.04i		−	2.51534i
$688$	123.593	+	123.593i	0.179641	+	0.179641i
$689$	1011.76			1.46844
$690$	−350.104	−	243.826i	−0.507397	−	0.353371i
$691$	780.383	+	780.383i	1.12935	+	1.12935i	0.990282	+	0.139071i	$0.0444118\pi$
$691$	780.383	+	780.383i	1.12935	+	1.12935i	0.139071	+	0.990282i	$0.455588\pi$
$692$	−26.0870			−0.0376980
$693$	3.27856	−	3.27856i	0.00473096	−	0.00473096i
$694$	379.283	+	379.283i	0.546518	+	0.546518i
$695$	419.347	+	292.049i	0.603377	+	0.420215i
$696$	358.688			0.515357
$697$	−1285.09	+	232.188i	−1.84374	+	0.333124i
$698$	−6.00329	+	6.00329i	−0.00860070	+	0.00860070i
$699$	−1690.65			−2.41866
$700$	2.46892	−	0.912806i	0.00352702	−	0.00130401i
$701$	−531.128			−0.757671			−0.378836	−	0.925464i	$-0.623675\pi$
$701$	−531.128			−0.757671			−0.378836	+	0.925464i	$0.623675\pi$
$702$	512.580			0.730171
$703$	−471.155			−0.670206
$704$	−31.4345	+	31.4345i	−0.0446513	+	0.0446513i
$705$	−238.226	+	342.063i	−0.337909	+	0.485196i
$706$		−	736.703i		−	1.04349i
$707$			9.65130i			0.0136511i
$708$	−818.865			−1.15659
$709$	412.969	+	412.969i	0.582467	+	0.582467i	0.935581	−	0.353113i	$-0.114877\pi$
$709$	412.969	+	412.969i	0.582467	+	0.582467i	−0.353113	+	0.935581i	$0.614877\pi$
$710$	−146.468	−	818.531i	−0.206293	−	1.15286i
$711$	−1188.44	+	1188.44i	−1.67151	+	1.67151i
$712$	116.535	−	116.535i	0.163673	−	0.163673i
$713$	−130.206	+	130.206i	−0.182617	+	0.182617i
$714$	−1.12179	−	6.20873i	−0.00157113	−	0.00869570i
$715$	−290.339	+	51.9534i	−0.406068	+	0.0726621i
$716$			560.141i			0.782319i
$717$	239.145			0.333536
$718$	−84.5859	+	84.5859i	−0.117808	+	0.117808i
$719$	869.306	+	869.306i	1.20905	+	1.20905i	0.971335	+	0.237714i	$0.0763980\pi$
$719$	869.306	+	869.306i	1.20905	+	1.20905i	0.237714	+	0.971335i	$0.423602\pi$
$720$	−312.029	+	55.8346i	−0.433373	+	0.0775480i
$721$	0.234060	+	0.234060i	0.000324632	+	0.000324632i
$722$	−235.084	+	235.084i	−0.325601	+	0.325601i
$723$	−422.601	−	422.601i	−0.584511	−	0.584511i
$724$	398.862	−	398.862i	0.550914	−	0.550914i
$725$	−577.765	−	265.860i	−0.796917	−	0.366704i
$726$	−449.244	+	449.244i	−0.618794	+	0.618794i
$727$	−527.909	−	527.909i	−0.726147	−	0.726147i	0.243703	−	0.969850i	$-0.421638\pi$
$727$	−527.909	−	527.909i	−0.726147	−	0.726147i	−0.969850	+	0.243703i	$0.921638\pi$
$728$		−	1.58070i		−	0.00217130i
$729$	1095.06			1.50213
$730$	414.433	+	288.627i	0.567716	+	0.395379i
$731$	−731.009	+	132.078i	−1.00001	+	0.180681i
$732$	−291.213	−	291.213i	−0.397833	−	0.397833i
$733$	148.772	+	148.772i	0.202964	+	0.202964i	0.801268	−	0.598305i	$-0.204159\pi$
$733$	148.772	+	148.772i	0.202964	+	0.202964i	−0.598305	+	0.801268i	$0.704159\pi$
$734$	175.510	+	175.510i	0.239115	+	0.239115i
$735$	215.111	+	1202.14i	0.292668	+	1.63556i
$736$	48.4153	−	48.4153i	0.0657816	−	0.0657816i
$737$			624.582i			0.847465i
$738$	1721.80			2.33306
$739$	750.610			1.01571			0.507855	−	0.861442i	$-0.330438\pi$
$739$	750.610			1.01571			0.507855	+	0.861442i	$0.330438\pi$
$740$	73.9585	+	413.314i	0.0999440	+	0.558532i
$741$	419.884	+	419.884i	0.566645	+	0.566645i
$742$			7.09581i			0.00956308i
$743$		−	1219.13i		−	1.64082i	−0.571775	−	0.820411i	$-0.693745\pi$
$743$		−	1219.13i		−	1.64082i	0.571775	−	0.820411i	$-0.306255\pi$
$744$			214.498i			0.288304i
$745$	47.3409	+	264.562i	0.0635448	+	0.355117i
$746$			584.805i			0.783921i
$747$	−14.8769	−	14.8769i	−0.0199155	−	0.0199155i
$748$	−33.5925	−	185.924i	−0.0449097	−	0.248561i
$749$		−	2.86202i		−	0.00382112i
$750$	852.897	+	221.599i	1.13720	+	0.295465i
$751$	−106.397	+	106.397i	−0.141674	+	0.141674i	−0.774387	−	0.632712i	$-0.781942\pi$
$751$	−106.397	+	106.397i	−0.141674	+	0.141674i	0.632712	+	0.774387i	$0.281942\pi$
$752$	−47.3033	−	47.3033i	−0.0629033	−	0.0629033i
$753$			1057.62i			1.40455i
$754$	−270.062	+	270.062i	−0.358172	+	0.358172i
$755$	79.1775	+	442.479i	0.104871	+	0.586065i
$756$			3.59490i			0.00475516i
$757$	384.973	−	384.973i	0.508550	−	0.508550i	−0.405531	−	0.914081i	$-0.632913\pi$
$757$	384.973	−	384.973i	0.508550	−	0.508550i	0.914081	+	0.405531i	$0.132913\pi$
$758$	177.280			0.233879
$759$	−237.080	+	237.080i	−0.312359	+	0.312359i
$760$	−130.223	−	90.6924i	−0.171346	−	0.119332i
$761$	722.759			0.949749			0.474874	−	0.880054i	$-0.342493\pi$
$761$	722.759			0.949749			0.474874	+	0.880054i	$0.342493\pi$
$762$	172.312			0.226132
$763$	−0.699006	−	0.699006i	−0.000916129	−	0.000916129i
$764$			551.001i			0.721206i
$765$	561.089	−	1224.78i	0.733450	−	1.60102i
$766$	489.300			0.638772
$767$	616.536	−	616.536i	0.803828	−	0.803828i
$768$		−	79.7584i		−	0.103852i
$769$			384.204i			0.499615i	0.968296	+	0.249807i	$0.0803673\pi$
$769$			384.204i			0.499615i	−0.968296	+	0.249807i	$0.919633\pi$
$770$	−0.364367	−	2.03625i	−0.000473204	−	0.00264447i
$771$	−553.723	−	553.723i	−0.718188	−	0.718188i
$772$		−	325.974i		−	0.422246i
$773$	−617.045	−	617.045i	−0.798247	−	0.798247i	0.184572	−	0.982819i	$-0.440910\pi$
$773$	−617.045	−	617.045i	−0.798247	−	0.798247i	−0.982819	+	0.184572i	$0.940910\pi$
$774$	979.429			1.26541
$775$	158.986	−	345.508i	0.205144	−	0.445816i
$776$	−28.5289	−	28.5289i	−0.0367640	−	0.0367640i
$777$	11.0189			0.0141813
$778$	220.249	−	220.249i	0.283096	−	0.283096i
$779$	609.514	+	609.514i	0.782431	+	0.782431i
$780$	302.427	−	434.247i	0.387726	−	0.556727i
$781$	−653.470			−0.836709
$782$	51.7390	+	286.359i	0.0661624	+	0.366188i
$783$	614.186	−	614.186i	0.784401	−	0.784401i
$784$	−195.989			−0.249986
$785$	−459.466	−	319.990i	−0.585307	−	0.407630i
$786$	1833.63			2.33286
$787$	649.152			0.824843			0.412422	−	0.910993i	$-0.364683\pi$
$787$	649.152			0.824843			0.412422	+	0.910993i	$0.364683\pi$
$788$	334.471			0.424456
$789$	−301.507	+	301.507i	−0.382138	+	0.382138i
$790$	132.079	+	738.117i	0.167189	+	0.934325i
$791$		−	6.56232i		−	0.00829624i
$792$			249.106i			0.314528i
$793$	438.518			0.552986
$794$	−438.414	−	438.414i	−0.552159	−	0.552159i
$795$	−1357.60	+	1949.34i	−1.70767	+	2.45200i
$796$	−291.352	+	291.352i	−0.366020	+	0.366020i
$797$	841.777	−	841.777i	1.05618	−	1.05618i	0.0578567	−	0.998325i	$-0.481573\pi$
$797$	841.777	−	841.777i	1.05618	−	1.05618i	0.998325	−	0.0578567i	$-0.0184266\pi$
$798$	−2.94479	+	2.94479i	−0.00369021	+	0.00369021i
$799$	279.782	−	50.5507i	0.350165	−	0.0632675i
$800$	−59.1170	+	128.472i	−0.0738963	+	0.160591i
$801$		−	923.499i		−	1.15293i
$802$	−720.212			−0.898020
$803$	280.642	−	280.642i	0.349492	−	0.349492i
$804$	−792.372	−	792.372i	−0.985538	−	0.985538i
$805$	0.561196	+	3.13622i	0.000697138	+	0.00389592i
$806$	−161.499	−	161.499i	−0.200371	−	0.200371i
$807$	−551.773	+	551.773i	−0.683733	+	0.683733i
$808$	−366.655	−	366.655i	−0.453781	−	0.453781i
$809$	103.897	−	103.897i	0.128427	−	0.128427i	−0.639972	−	0.768398i	$-0.721054\pi$
$809$	103.897	−	103.897i	0.128427	−	0.128427i	0.768398	+	0.639972i	$0.221054\pi$
$810$	−111.354	+	159.890i	−0.137474	+	0.197395i
$811$	149.981	−	149.981i	0.184933	−	0.184933i	−0.608568	−	0.793501i	$-0.708256\pi$
$811$	149.981	−	149.981i	0.184933	−	0.184933i	0.793501	+	0.608568i	$0.208256\pi$
$812$	−1.89404	−	1.89404i	−0.00233256	−	0.00233256i
$813$			1600.64i			1.96880i
$814$	329.967			0.405364
$815$	76.6603	−	13.7176i	0.0940617	−	0.0168314i
$816$	278.488	+	193.254i	0.341285	+	0.236831i
$817$	346.717	+	346.717i	0.424378	+	0.424378i
$818$	−189.446	−	189.446i	−0.231597	−	0.231597i
$819$	−6.26324	−	6.26324i	−0.00764742	−	0.00764742i
$820$	439.010	−	630.364i	0.535378	−	0.768736i
$821$	518.469	−	518.469i	0.631510	−	0.631510i	−0.316937	−	0.948447i	$-0.602654\pi$
$821$	518.469	−	518.469i	0.631510	−	0.631510i	0.948447	+	0.316937i	$0.102654\pi$
$822$			113.820i			0.138468i
$823$	−543.902			−0.660878			−0.330439	−	0.943827i	$-0.607197\pi$
$823$	−543.902			−0.660878			−0.330439	+	0.943827i	$0.607197\pi$
$824$	−17.7840			−0.0215825
$825$	289.485	−	629.105i	0.350890	−	0.762551i
$826$	4.32398	+	4.32398i	0.00523484	+	0.00523484i
$827$		−	1559.72i		−	1.88600i	−0.332788	−	0.943002i	$-0.607989\pi$
$827$		−	1559.72i		−	1.88600i	0.332788	−	0.943002i	$-0.392011\pi$
$828$		−	383.673i		−	0.463373i
$829$		−	1235.65i		−	1.49053i	−0.666768	−	0.745266i	$-0.732323\pi$
$829$		−	1235.65i		−	1.49053i	0.666768	−	0.745266i	$-0.267677\pi$
$830$	−9.23972	+	1.65336i	−0.0111322	+	0.00199200i
$831$			531.824i			0.639981i
$832$	60.0513	+	60.0513i	0.0721771	+	0.0721771i
$833$	474.880	−	684.324i	0.570084	−	0.821517i
$834$			720.513i			0.863925i
$835$	−1482.41	+	265.263i	−1.77534	+	0.317680i
$836$	−88.1833	+	88.1833i	−0.105482	+	0.105482i
$837$	367.288	+	367.288i	0.438815	+	0.438815i
$838$		−	640.753i		−	0.764622i
$839$	−794.970	+	794.970i	−0.947520	+	0.947520i	−0.998690	−	0.0511697i	$-0.983705\pi$
$839$	−794.970	+	794.970i	−0.947520	+	0.947520i	0.0511697	+	0.998690i	$0.483705\pi$
$840$	3.04553	+	2.12102i	0.00362563	+	0.00252502i
$841$		−	193.810i		−	0.230452i
$842$	−44.7427	+	44.7427i	−0.0531385	+	0.0531385i
$843$	2124.20			2.51981
$844$	329.830	−	329.830i	0.390794	−	0.390794i
$845$	−49.5907	−	277.135i	−0.0586872	−	0.327971i
$846$	−374.861			−0.443098
$847$	4.74443			0.00560145
$848$	−269.571	−	269.571i	−0.317891	−	0.317891i
$849$			153.241i			0.180496i
$850$	−305.340	−	517.704i	−0.359224	−	0.609063i
$851$	−508.213			−0.597195
$852$	829.021	−	829.021i	0.973030	−	0.973030i
$853$			33.4538i			0.0392190i	0.999808	+	0.0196095i	$0.00624230\pi$
$853$			33.4538i			0.0392190i	−0.999808	+	0.0196095i	$0.993758\pi$
$854$			3.07548i			0.00360126i
$855$	−875.336	+	156.633i	−1.02378	+	0.183196i
$856$	108.729	+	108.729i	0.127020	+	0.127020i
$857$			390.612i			0.455790i	0.973686	+	0.227895i	$0.0731843\pi$
$857$			390.612i			0.455790i	−0.973686	+	0.227895i	$0.926816\pi$
$858$	−294.060	−	294.060i	−0.342727	−	0.342727i
$859$	−1424.50			−1.65832			−0.829162	−	0.559008i	$-0.811182\pi$
$859$	−1424.50			−1.65832			−0.829162	+	0.559008i	$0.811182\pi$
$860$	249.727	−	358.577i	0.290380	−	0.416950i
$861$	−14.2547	−	14.2547i	−0.0165560	−	0.0165560i
$862$	356.293			0.413334
$863$	−247.011	+	247.011i	−0.286223	+	0.286223i	−0.835585	−	0.549362i	$-0.814871\pi$
$863$	−247.011	+	247.011i	−0.286223	+	0.286223i	0.549362	+	0.835585i	$0.314871\pi$
$864$	−136.571	−	136.571i	−0.158068	−	0.158068i
$865$	11.4876	+	64.1978i	0.0132804	+	0.0742171i
$866$	299.496			0.345839
$867$	−1349.55	+	504.128i	−1.55658	+	0.581462i
$868$	1.13265	−	1.13265i	0.00130490	−	0.00130490i
$869$	589.271			0.678103
$870$	−157.951	−	882.700i	−0.181553	−	1.01460i
$871$	1193.18			1.36990
$872$	53.1109			0.0609070
$873$	−226.080			−0.258970
$874$	135.820	−	135.820i	0.155400	−	0.155400i
$875$	−3.33354	−	5.67382i	−0.00380976	−	0.00648437i
$876$			712.070i			0.812865i
$877$			293.185i			0.334304i	0.985931	+	0.167152i	$0.0534571\pi$
$877$			293.185i			0.334304i	−0.985931	+	0.167152i	$0.946543\pi$
$878$	−396.996			−0.452159
$879$	−1630.67	−	1630.67i	−1.85515	−	1.85515i
$880$	91.1999	+	63.5151i	0.103636	+	0.0721763i
$881$	168.845	−	168.845i	0.191651	−	0.191651i	−0.604758	−	0.796409i	$-0.706730\pi$
$881$	168.845	−	168.845i	0.191651	−	0.191651i	0.796409	+	0.604758i	$0.206730\pi$
$882$	−776.569	+	776.569i	−0.880463	+	0.880463i
$883$	−516.921	+	516.921i	−0.585415	+	0.585415i	−0.936386	−	0.350971i	$-0.885851\pi$
$883$	−516.921	+	516.921i	−0.585415	+	0.585415i	0.350971	+	0.936386i	$0.385851\pi$
$884$	−355.182	+	64.1739i	−0.401790	+	0.0725949i
$885$	360.593	+	2015.15i	0.407449	+	2.27701i
$886$		−	463.741i		−	0.523410i
$887$	−2.03675			−0.00229623			−0.00114811	−	0.999999i	$-0.500365\pi$
$887$	−2.03675			−0.00229623			−0.00114811	+	0.999999i	$0.500365\pi$
$888$	−418.611	+	418.611i	−0.471408	+	0.471408i
$889$	−0.909888	−	0.909888i	−0.00102350	−	0.00102350i
$890$	−338.101	−	235.466i	−0.379888	−	0.264569i
$891$	108.273	+	108.273i	0.121519	+	0.121519i
$892$	380.608	−	380.608i	0.426690	−	0.426690i
$893$	−132.700	−	132.700i	−0.148601	−	0.148601i
$894$	−267.953	+	267.953i	−0.299723	+	0.299723i
$895$	1378.46	−	246.662i	1.54017	−	0.275600i
$896$	−0.421161	+	0.421161i	−0.000470045	+	0.000470045i
$897$	452.910	+	452.910i	0.504916	+	0.504916i
$898$			1040.38i			1.15855i
$899$	−387.024			−0.430505
$900$	274.808	+	743.288i	0.305342	+	0.825875i
$901$	1594.42	−	288.078i	1.76961	−	0.319731i
$902$	−426.864	−	426.864i	−0.473242	−	0.473242i
$903$	−8.10865	−	8.10865i	−0.00897968	−	0.00897968i
$904$	249.304	+	249.304i	0.275779	+	0.275779i
$905$	−1157.20	−	805.922i	−1.27868	−	0.890522i
$906$	−448.150	+	448.150i	−0.494647	+	0.494647i
$907$			67.3467i			0.0742522i	0.999311	+	0.0371261i	$0.0118203\pi$
$907$			67.3467i			0.0742522i	−0.999311	+	0.0371261i	$0.988180\pi$
$908$	−235.927			−0.259832
$909$	−2905.60			−3.19648
$910$	−3.88997	+	0.696074i	−0.00427469	+	0.000764916i
$911$	280.207	+	280.207i	0.307582	+	0.307582i	0.843971	−	0.536389i	$-0.180212\pi$
$911$	280.207	+	280.207i	0.307582	+	0.307582i	−0.536389	+	0.843971i	$0.680212\pi$
$912$		−	223.747i		−	0.245336i
$913$			7.37648i			0.00807939i
$914$		−	709.536i		−	0.776297i
$915$	−588.413	+	844.888i	−0.643074	+	0.923375i
$916$		−	693.310i		−	0.756889i
$917$	−9.68239	−	9.68239i	−0.0105588	−	0.0105588i
$918$	807.769	−	145.947i	0.879923	−	0.158983i
$919$			699.116i			0.760736i	0.924835	+	0.380368i	$0.124203\pi$
$919$			699.116i			0.760736i	−0.924835	+	0.380368i	$0.875797\pi$
$920$	−140.466	−	97.8257i	−0.152680	−	0.106332i
$921$	−1595.84	+	1595.84i	−1.73273	+	1.73273i
$922$	−433.035	−	433.035i	−0.469669	−	0.469669i
$923$			1248.37i			1.35251i
$924$	2.06234	−	2.06234i	0.00223197	−	0.00223197i
$925$	984.560	−	364.011i	1.06439	−	0.393525i
$926$		−	200.091i		−	0.216081i
$927$	−70.4657	+	70.4657i	−0.0760147	+	0.0760147i
$928$	143.910			0.155075
$929$	−490.100	+	490.100i	−0.527556	+	0.527556i	−0.919843	−	0.392287i	$-0.871684\pi$
$929$	−490.100	+	490.100i	−0.527556	+	0.527556i	0.392287	+	0.919843i	$0.371684\pi$
$930$	527.862	−	94.4559i	0.567593	−	0.101565i
$931$	−549.809			−0.590557
$932$	−678.307			−0.727797
$933$	656.101	+	656.101i	0.703217	+	0.703217i
$934$		−	516.711i		−	0.553224i
$935$	−442.749	+	164.541i	−0.473529	+	0.175980i
$936$	475.884			0.508423
$937$	367.552	−	367.552i	0.392264	−	0.392264i	−0.483229	−	0.875494i	$-0.660536\pi$
$937$	367.552	−	367.552i	0.392264	−	0.392264i	0.875494	+	0.483229i	$0.160536\pi$
$938$			8.36817i			0.00892129i
$939$		−	153.470i		−	0.163440i
$940$	−95.5789	+	137.240i	−0.101680	+	0.146000i
$941$	−786.510	−	786.510i	−0.835823	−	0.835823i	0.152483	−	0.988306i	$-0.451273\pi$
$941$	−786.510	−	786.510i	−0.835823	−	0.835823i	−0.988306	+	0.152483i	$0.951273\pi$
$942$		−	789.445i		−	0.838052i
$943$	657.455	+	657.455i	0.697195	+	0.697195i
$944$	−328.538			−0.348028
$945$	8.84673	−	1.58304i	0.00936162	−	0.00167517i
$946$	−242.818	−	242.818i	−0.256679	−	0.256679i
$947$	364.728			0.385141			0.192570	−	0.981283i	$-0.438318\pi$
$947$	364.728			0.385141			0.192570	+	0.981283i	$0.438318\pi$
$948$	−747.576	+	747.576i	−0.788583	+	0.788583i
$949$	−536.128	−	536.128i	−0.564940	−	0.564940i
$950$	−165.841	+	360.405i	−0.174570	+	0.379373i
$951$	−835.928			−0.878999
$952$	−0.450073	−	2.49101i	−0.000472766	−	0.00261661i
$953$	−678.201	+	678.201i	−0.711648	+	0.711648i	−0.966880	−	0.255232i	$-0.917848\pi$
$953$	−678.201	+	678.201i	−0.711648	+	0.711648i	0.255232	+	0.966880i	$0.417848\pi$
$954$	−2136.25			−2.23926
$955$	1355.97	−	242.637i	1.41986	−	0.254070i
$956$	95.9479			0.100364
$957$	−704.699			−0.736363
$958$	598.872			0.625127
$959$	0.601023	−	0.601023i	0.000626719	−	0.000626719i
$960$	−196.278	+	35.1222i	−0.204457	+	0.0365856i
$961$			729.556i			0.759164i
$962$		−	630.357i		−	0.655256i
$963$	861.635			0.894740
$964$	−169.553	−	169.553i	−0.175884	−	0.175884i
$965$	−802.193	+	143.545i	−0.831288	+	0.148751i
$966$	−3.17641	+	3.17641i	−0.00328821	+	0.00328821i
$967$	341.468	−	341.468i	0.353121	−	0.353121i	−0.508149	−	0.861269i	$-0.669670\pi$
$967$	341.468	−	341.468i	0.353121	−	0.353121i	0.861269	+	0.508149i	$0.169670\pi$
$968$	−180.242	+	180.242i	−0.186200	+	0.186200i
$969$	781.244	+	542.137i	0.806238	+	0.559481i
$970$	−57.6442	+	82.7699i	−0.0594270	+	0.0853298i
$971$		−	1803.50i		−	1.85736i	−0.370882	−	0.928680i	$-0.620945\pi$
$971$		−	1803.50i		−	1.85736i	0.370882	−	0.928680i	$-0.379055\pi$
$972$	339.850			0.349640
$973$	3.80464	−	3.80464i	0.00391021	−	0.00391021i
$974$	430.743	+	430.743i	0.442242	+	0.442242i
$975$	−1201.82	−	553.021i	−1.23264	−	0.567201i
$976$	−116.838	−	116.838i	−0.119711	−	0.119711i
$977$	1261.68	−	1261.68i	1.29138	−	1.29138i	0.357451	−	0.933932i	$-0.383646\pi$
$977$	1261.68	−	1261.68i	1.29138	−	1.29138i	0.933932	−	0.357451i	$-0.116354\pi$
$978$	77.6427	+	77.6427i	0.0793893	+	0.0793893i
$979$	−228.952	+	228.952i	−0.233863	+	0.233863i
$980$	86.3051	+	482.311i	0.0880664	+	0.492154i
$981$	210.442	−	210.442i	0.214518	−	0.214518i
$982$	435.187	+	435.187i	0.443164	+	0.443164i
$983$		−	1296.98i		−	1.31941i	−0.751523	−	0.659707i	$-0.770680\pi$
$983$		−	1296.98i		−	1.31941i	0.751523	−	0.659707i	$-0.229320\pi$
$984$	1083.08			1.10069
$985$	−147.287	−	823.103i	−0.149529	−	0.835638i
$986$	−348.693	+	502.483i	−0.353644	+	0.509617i
$987$	3.10346	+	3.10346i	0.00314433	+	0.00314433i
$988$	168.462	+	168.462i	0.170508	+	0.170508i
$989$	373.987	+	373.987i	0.378147	+	0.378147i
$990$	613.029	−	109.696i	0.619221	−	0.110804i
$991$	−804.924	+	804.924i	−0.812234	+	0.812234i	−0.984968	−	0.172735i	$-0.944740\pi$
$991$	−804.924	+	804.924i	−0.812234	+	0.812234i	0.172735	+	0.984968i	$0.444740\pi$
$992$			86.0593i			0.0867533i
$993$	1354.74			1.36429
$994$	−8.75522			−0.00880806
$995$	845.289	+	588.692i	0.849537	+	0.591650i
$996$	−9.35814	−	9.35814i	−0.00939572	−	0.00939572i
$997$			514.076i			0.515623i	0.966195	+	0.257811i	$0.0830013\pi$
$997$			514.076i			0.515623i	−0.966195	+	0.257811i	$0.916999\pi$
$998$		−	398.147i		−	0.398945i
$999$			1433.58i			1.43502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.3.e.b.157.1	yes	16
5.3	odd	4		170.3.j.b.123.8	yes	16
17.13	even	4		170.3.j.b.47.8	yes	16
85.13	odd	4	inner	170.3.e.b.13.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.3.e.b.13.8	✓	16	85.13	odd	4	inner
170.3.e.b.157.1	yes	16	1.1	even	1	trivial
170.3.j.b.47.8	yes	16	17.13	even	4
170.3.j.b.123.8	yes	16	5.3	odd	4

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	170.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -4.98490i q^{3} -2.00000i q^{4} +(-4.92182 + 0.880714i) q^{5} +(-4.98490 - 4.98490i) q^{6} +0.0526451i q^{7} +(-2.00000 - 2.00000i) q^{8} -15.8492 q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} -4.98490i q^{3} -2.00000i q^{4} +(-4.92182 + 0.880714i) q^{5} +(-4.98490 - 4.98490i) q^{6} +0.0526451i q^{7} +(-2.00000 - 2.00000i) q^{8} -15.8492 q^{9} +(-4.04111 + 5.80254i) q^{10} +(3.92931 + 3.92931i) q^{11} -9.96980 q^{12} +(7.50642 - 7.50642i) q^{13} +(0.0526451 + 0.0526451i) q^{14} +(4.39027 + 24.5348i) q^{15} -4.00000 q^{16} +(9.69198 - 13.9666i) q^{17} +(-15.8492 + 15.8492i) q^{18} -11.2212 q^{19} +(1.76143 + 9.84365i) q^{20} +0.262430 q^{21} +7.85862 q^{22} -12.1038 q^{23} +(-9.96980 + 9.96980i) q^{24} +(23.4487 - 8.66943i) q^{25} -15.0128i q^{26} +34.1428i q^{27} +0.105290 q^{28} +(-17.9887 - 17.9887i) q^{29} +(28.9251 + 20.1445i) q^{30} +(10.7574 - 10.7574i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(19.5872 - 19.5872i) q^{33} +(-4.27460 - 23.6586i) q^{34} +(-0.0463652 - 0.259110i) q^{35} +31.6985i q^{36} +41.9878 q^{37} +(-11.2212 + 11.2212i) q^{38} +(-37.4187 - 37.4187i) q^{39} +(11.6051 + 8.08222i) q^{40} +(-54.3180 - 54.3180i) q^{41} +(0.262430 - 0.262430i) q^{42} +(-30.8983 - 30.8983i) q^{43} +(7.85862 - 7.85862i) q^{44} +(78.0072 - 13.9586i) q^{45} +(-12.1038 + 12.1038i) q^{46} +(11.8258 + 11.8258i) q^{47} +19.9396i q^{48} +48.9972 q^{49} +(14.7793 - 32.1181i) q^{50} +(-69.6220 - 48.3136i) q^{51} +(-15.0128 - 15.0128i) q^{52} +(67.3929 + 67.3929i) q^{53} +(34.1428 + 34.1428i) q^{54} +(-22.8000 - 15.8788i) q^{55} +(0.105290 - 0.105290i) q^{56} +55.9367i q^{57} -35.9775 q^{58} +82.1345 q^{59} +(49.0696 - 8.78054i) q^{60} +(29.2095 + 29.2095i) q^{61} -21.5148i q^{62} -0.834384i q^{63} +8.00000i q^{64} +(-30.3343 + 43.5563i) q^{65} -39.1745i q^{66} +(79.4772 + 79.4772i) q^{67} +(-27.9332 - 19.3840i) q^{68} +60.3363i q^{69} +(-0.305475 - 0.212745i) q^{70} +(-83.1532 + 83.1532i) q^{71} +(31.6985 + 31.6985i) q^{72} -71.4227i q^{73} +(41.9878 - 41.9878i) q^{74} +(-43.2163 - 116.889i) q^{75} +22.4424i q^{76} +(-0.206859 + 0.206859i) q^{77} -74.8375 q^{78} +(74.9841 - 74.9841i) q^{79} +(19.6873 - 3.52285i) q^{80} +27.5552 q^{81} -108.636 q^{82} +(0.938649 + 0.938649i) q^{83} -0.524861i q^{84} +(-35.4017 + 77.2769i) q^{85} -61.7966 q^{86} +(-89.6721 + 89.6721i) q^{87} -15.7172i q^{88} +58.2677i q^{89} +(64.0485 - 91.9658i) q^{90} +(0.395176 + 0.395176i) q^{91} +24.2076i q^{92} +(-53.6246 - 53.6246i) q^{93} +23.6517 q^{94} +(55.2289 - 9.88268i) q^{95} +(19.9396 + 19.9396i) q^{96} +14.2644 q^{97} +(48.9972 - 48.9972i) q^{98} +(-62.2766 - 62.2766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9	\( 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9} - 4 q^{10} + 20 q^{11} + 4 q^{13} - 12 q^{14} + 12 q^{15} - 64 q^{16} + 36 q^{17} - 16 q^{18} - 16 q^{19} - 4 q^{20} + 40 q^{22} + 16 q^{23} + 44 q^{25} - 24 q^{28} - 20 q^{29} + 12 q^{30} + 92 q^{31} - 64 q^{32} - 60 q^{33} + 24 q^{34} - 124 q^{35} + 32 q^{37} - 16 q^{38} - 140 q^{39} - 60 q^{41} + 52 q^{43} + 40 q^{44} + 198 q^{45} + 16 q^{46} + 112 q^{47} + 136 q^{49} - 4 q^{50} - 140 q^{51} - 8 q^{52} + 48 q^{53} + 108 q^{54} + 40 q^{55} - 24 q^{56} - 40 q^{58} + 76 q^{61} - 40 q^{65} + 116 q^{67} - 24 q^{68} - 124 q^{70} - 268 q^{71} + 32 q^{72} + 32 q^{74} + 136 q^{75} - 116 q^{77} - 280 q^{78} - 88 q^{79} + 8 q^{80} - 352 q^{81} - 120 q^{82} - 160 q^{83} + 310 q^{85} + 104 q^{86} + 236 q^{87} + 260 q^{90} - 168 q^{91} + 48 q^{93} + 224 q^{94} + 264 q^{95} - 256 q^{97} + 136 q^{98} - 348 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9 - 4 * q^10 + 20 * q^11 + 4 * q^13 - 12 * q^14 + 12 * q^15 - 64 * q^16 + 36 * q^17 - 16 * q^18 - 16 * q^19 - 4 * q^20 + 40 * q^22 + 16 * q^23 + 44 * q^25 - 24 * q^28 - 20 * q^29 + 12 * q^30 + 92 * q^31 - 64 * q^32 - 60 * q^33 + 24 * q^34 - 124 * q^35 + 32 * q^37 - 16 * q^38 - 140 * q^39 - 60 * q^41 + 52 * q^43 + 40 * q^44 + 198 * q^45 + 16 * q^46 + 112 * q^47 + 136 * q^49 - 4 * q^50 - 140 * q^51 - 8 * q^52 + 48 * q^53 + 108 * q^54 + 40 * q^55 - 24 * q^56 - 40 * q^58 + 76 * q^61 - 40 * q^65 + 116 * q^67 - 24 * q^68 - 124 * q^70 - 268 * q^71 + 32 * q^72 + 32 * q^74 + 136 * q^75 - 116 * q^77 - 280 * q^78 - 88 * q^79 + 8 * q^80 - 352 * q^81 - 120 * q^82 - 160 * q^83 + 310 * q^85 + 104 * q^86 + 236 * q^87 + 260 * q^90 - 168 * q^91 + 48 * q^93 + 224 * q^94 + 264 * q^95 - 256 * q^97 + 136 * q^98 - 348 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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