LMFDB - Embedded newform 65.4.e.a.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,4,Mod(16,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, 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("65.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	65.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:	$3.83512415037$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 45 x^{12} - 52 x^{11} + 1311 x^{10} - 1336 x^{9} + 20343 x^{8} - 11166 x^{7} + \cdots + 1157776 $ x^14 - 2x^13 + 45x^12 - 52x^11 + 1311x^10 - 1336x^9 + 20343x^8 - 11166x^7 + 216447x^6 - 107836x^5 + 1201133x^4 + 4392x^3 + 3890980x^2 - 1936800*x + 1157776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			61.4
Root			$0.272699 - 0.472328i$ of defining polynomial
Character	$\chi$	$=$	65.61
Dual form			65.4.e.a.16.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.272699 + 0.472328i) q^{2} +(-3.51122 + 6.08161i) q^{3} +(3.85127 + 6.67060i) q^{4} -5.00000 q^{5} +(-1.91501 - 3.31689i) q^{6} +(-11.4358 - 19.8074i) q^{7} -8.56412 q^{8} +(-11.1573 - 19.3250i) q^{9} +O(q^{10})$	\(q+(-0.272699 + 0.472328i) q^{2} +(-3.51122 + 6.08161i) q^{3} +(3.85127 + 6.67060i) q^{4} -5.00000 q^{5} +(-1.91501 - 3.31689i) q^{6} +(-11.4358 - 19.8074i) q^{7} -8.56412 q^{8} +(-11.1573 - 19.3250i) q^{9} +(1.36349 - 2.36164i) q^{10} +(-4.27808 + 7.40986i) q^{11} -54.0906 q^{12} +(-15.2746 + 44.3135i) q^{13} +12.4741 q^{14} +(17.5561 - 30.4080i) q^{15} +(-28.4747 + 49.3197i) q^{16} +(-16.3447 - 28.3099i) q^{17} +12.1703 q^{18} +(43.5823 + 75.4868i) q^{19} +(-19.2564 - 33.3530i) q^{20} +160.615 q^{21} +(-2.33325 - 4.04131i) q^{22} +(4.11990 - 7.13588i) q^{23} +(30.0705 - 52.0836i) q^{24} +25.0000 q^{25} +(-16.7651 - 19.2988i) q^{26} -32.9030 q^{27} +(88.0849 - 152.568i) q^{28} +(-107.073 + 185.456i) q^{29} +(9.57504 + 16.5844i) q^{30} +279.366 q^{31} +(-49.7865 - 86.2328i) q^{32} +(-30.0426 - 52.0352i) q^{33} +17.8287 q^{34} +(57.1791 + 99.0371i) q^{35} +(85.9395 - 148.852i) q^{36} +(-136.972 + 237.242i) q^{37} -47.5394 q^{38} +(-215.865 - 248.489i) q^{39} +42.8206 q^{40} +(42.9160 - 74.3326i) q^{41} +(-43.7994 + 75.8627i) q^{42} +(190.396 + 329.776i) q^{43} -65.9042 q^{44} +(55.7865 + 96.6250i) q^{45} +(2.24698 + 3.89189i) q^{46} +435.021 q^{47} +(-199.962 - 346.344i) q^{48} +(-90.0560 + 155.982i) q^{49} +(-6.81746 + 11.8082i) q^{50} +229.560 q^{51} +(-354.424 + 68.7725i) q^{52} -436.042 q^{53} +(8.97261 - 15.5410i) q^{54} +(21.3904 - 37.0493i) q^{55} +(97.9377 + 169.633i) q^{56} -612.108 q^{57} +(-58.3974 - 101.147i) q^{58} +(-374.566 - 648.767i) q^{59} +270.453 q^{60} +(35.3340 + 61.2003i) q^{61} +(-76.1826 + 131.952i) q^{62} +(-255.186 + 441.994i) q^{63} -401.289 q^{64} +(76.3731 - 221.567i) q^{65} +32.7702 q^{66} +(-103.058 + 178.502i) q^{67} +(125.896 - 218.058i) q^{68} +(28.9317 + 50.1112i) q^{69} -62.3706 q^{70} +(-91.2401 - 158.033i) q^{71} +(95.5524 + 165.502i) q^{72} +188.587 q^{73} +(-74.7041 - 129.391i) q^{74} +(-87.7804 + 152.040i) q^{75} +(-335.695 + 581.440i) q^{76} +195.694 q^{77} +(176.234 - 34.1965i) q^{78} +923.280 q^{79} +(142.374 - 246.599i) q^{80} +(416.777 - 721.878i) q^{81} +(23.4062 + 40.5408i) q^{82} +1215.55 q^{83} +(618.570 + 1071.40i) q^{84} +(81.7237 + 141.550i) q^{85} -207.683 q^{86} +(-751.914 - 1302.35i) q^{87} +(36.6380 - 63.4589i) q^{88} +(9.88021 - 17.1130i) q^{89} -60.8515 q^{90} +(1052.41 - 204.210i) q^{91} +63.4674 q^{92} +(-980.913 + 1698.99i) q^{93} +(-118.630 + 205.472i) q^{94} +(-217.912 - 377.434i) q^{95} +699.245 q^{96} +(-270.951 - 469.300i) q^{97} +(-49.1163 - 85.0719i) q^{98} +190.927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9} + 10 q^{10} - 87 q^{11} - 158 q^{12} + 123 q^{13} + 132 q^{14} - 20 q^{15} + 134 q^{16} + 114 q^{17} + 414 q^{18} - 245 q^{19} + 150 q^{20} - 76 q^{21} - 338 q^{22} + 74 q^{23} - 334 q^{24} + 350 q^{25} + 243 q^{26} - 884 q^{27} - 230 q^{28} + 88 q^{29} + 115 q^{30} + 1000 q^{31} - 80 q^{32} + 194 q^{33} + 854 q^{34} + 35 q^{35} - 425 q^{36} - 633 q^{37} - 596 q^{38} + 970 q^{39} - 210 q^{40} - 162 q^{41} + 1439 q^{42} + 280 q^{43} + 440 q^{44} + 435 q^{45} + 11 q^{46} + 950 q^{47} - 2281 q^{48} - 1694 q^{49} - 50 q^{50} - 860 q^{51} - 956 q^{52} - 1206 q^{53} - 51 q^{54} + 435 q^{55} + 1277 q^{56} + 916 q^{57} + 1213 q^{58} - 1410 q^{59} + 790 q^{60} - 412 q^{61} + 56 q^{62} - 1241 q^{63} - 2358 q^{64} - 615 q^{65} + 4346 q^{66} - 1398 q^{67} + 493 q^{68} - 1080 q^{69} - 660 q^{70} + 584 q^{71} - 1545 q^{72} + 5076 q^{73} - 3840 q^{74} + 100 q^{75} - 3292 q^{76} - 5506 q^{77} + 1179 q^{78} + 928 q^{79} - 670 q^{80} + 473 q^{81} + 1583 q^{82} + 932 q^{83} + 3081 q^{84} - 570 q^{85} + 9858 q^{86} + 282 q^{87} - 3389 q^{88} - 443 q^{89} - 2070 q^{90} + 487 q^{91} + 6182 q^{92} + 2116 q^{93} - 2017 q^{94} + 1225 q^{95} + 954 q^{96} + 1870 q^{97} - 1364 q^{98} + 11378 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9 + 10 * q^10 - 87 * q^11 - 158 * q^12 + 123 * q^13 + 132 * q^14 - 20 * q^15 + 134 * q^16 + 114 * q^17 + 414 * q^18 - 245 * q^19 + 150 * q^20 - 76 * q^21 - 338 * q^22 + 74 * q^23 - 334 * q^24 + 350 * q^25 + 243 * q^26 - 884 * q^27 - 230 * q^28 + 88 * q^29 + 115 * q^30 + 1000 * q^31 - 80 * q^32 + 194 * q^33 + 854 * q^34 + 35 * q^35 - 425 * q^36 - 633 * q^37 - 596 * q^38 + 970 * q^39 - 210 * q^40 - 162 * q^41 + 1439 * q^42 + 280 * q^43 + 440 * q^44 + 435 * q^45 + 11 * q^46 + 950 * q^47 - 2281 * q^48 - 1694 * q^49 - 50 * q^50 - 860 * q^51 - 956 * q^52 - 1206 * q^53 - 51 * q^54 + 435 * q^55 + 1277 * q^56 + 916 * q^57 + 1213 * q^58 - 1410 * q^59 + 790 * q^60 - 412 * q^61 + 56 * q^62 - 1241 * q^63 - 2358 * q^64 - 615 * q^65 + 4346 * q^66 - 1398 * q^67 + 493 * q^68 - 1080 * q^69 - 660 * q^70 + 584 * q^71 - 1545 * q^72 + 5076 * q^73 - 3840 * q^74 + 100 * q^75 - 3292 * q^76 - 5506 * q^77 + 1179 * q^78 + 928 * q^79 - 670 * q^80 + 473 * q^81 + 1583 * q^82 + 932 * q^83 + 3081 * q^84 - 570 * q^85 + 9858 * q^86 + 282 * q^87 - 3389 * q^88 - 443 * q^89 - 2070 * q^90 + 487 * q^91 + 6182 * q^92 + 2116 * q^93 - 2017 * q^94 + 1225 * q^95 + 954 * q^96 + 1870 * q^97 - 1364 * q^98 + 11378 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.272699	+	0.472328i	−0.0964135	+	0.166993i	−0.910198	−	0.414174i	$-0.864070\pi$
$2$	−0.272699	+	0.472328i	−0.0964135	+	0.166993i	0.813784	+	0.581167i	$0.197404\pi$
$3$	−3.51122	+	6.08161i	−0.675734	+	1.17041i	0.300520	+	0.953776i	$0.402840\pi$
$3$	−3.51122	+	6.08161i	−0.675734	+	1.17041i	−0.976254	+	0.216630i	$0.930493\pi$
$4$	3.85127	+	6.67060i	0.481409	+	0.833825i
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	−1.91501	−	3.31689i	−0.130300	−	0.225686i
$7$	−11.4358	−	19.8074i	−0.617476	−	1.06950i	−0.989945	−	0.141455i	$-0.954822\pi$
$7$	−11.4358	−	19.8074i	−0.617476	−	1.06950i	0.372468	−	0.928045i	$-0.378512\pi$
$8$	−8.56412			−0.378484
$9$	−11.1573	−	19.3250i	−0.413233	−	0.715741i
$10$	1.36349	−	2.36164i	0.0431174	−	0.0746816i
$11$	−4.27808	+	7.40986i	−0.117263	+	0.203105i	−0.918682	−	0.394998i	$-0.870745\pi$
$11$	−4.27808	+	7.40986i	−0.117263	+	0.203105i	0.801419	+	0.598103i	$0.204079\pi$
$12$	−54.0906			−1.30122
$13$	−15.2746	+	44.3135i	−0.325878	+	0.945412i
$13$	−15.2746	+	44.3135i	−0.325878	+	0.945412i
$14$	12.4741			0.238132
$15$	17.5561	−	30.4080i	0.302197	−	0.523421i
$16$	−28.4747	+	49.3197i	−0.444918	+	0.770620i
$17$	−16.3447	−	28.3099i	−0.233187	−	0.403892i	0.725557	−	0.688162i	$-0.241582\pi$
$17$	−16.3447	−	28.3099i	−0.233187	−	0.403892i	−0.958744	+	0.284270i	$0.908249\pi$
$18$	12.1703			0.159365
$19$	43.5823	+	75.4868i	0.526236	+	0.911467i	0.999533	+	0.0305639i	$0.00973031\pi$
$19$	43.5823	+	75.4868i	0.526236	+	0.911467i	−0.473297	+	0.880903i	$0.656936\pi$
$20$	−19.2564	−	33.3530i	−0.215293	−	0.372898i
$21$	160.615			1.66900
$22$	−2.33325	−	4.04131i	−0.0226114	−	0.0391641i
$23$	4.11990	−	7.13588i	0.0373504	−	0.0646927i	−0.846746	−	0.531997i	$-0.821442\pi$
$23$	4.11990	−	7.13588i	0.0373504	−	0.0646927i	0.884096	+	0.467305i	$0.154775\pi$
$24$	30.0705	−	52.0836i	0.255755	−	0.442980i
$25$	25.0000			0.200000
$26$	−16.7651	−	19.2988i	−0.126458	−	0.145570i
$27$	−32.9030			−0.234526
$28$	88.0849	−	152.568i	0.594517	−	1.02973i
$29$	−107.073	+	185.456i	−0.685620	+	1.18753i	0.287621	+	0.957744i	$0.407136\pi$
$29$	−107.073	+	185.456i	−0.685620	+	1.18753i	−0.973241	+	0.229785i	$0.926198\pi$
$30$	9.57504	+	16.5844i	0.0582718	+	0.100930i
$31$	279.366			1.61857			0.809283	−	0.587419i	$-0.199856\pi$
$31$	279.366			1.61857			0.809283	+	0.587419i	$0.199856\pi$
$32$	−49.7865	−	86.2328i	−0.275034	−	0.476373i
$33$	−30.0426	−	52.0352i	−0.158477	−	0.274490i
$34$	17.8287			0.0899295
$35$	57.1791	+	99.0371i	0.276144	+	0.478295i
$36$	85.9395	−	148.852i	0.397868	−	0.689128i
$37$	−136.972	+	237.242i	−0.608596	+	1.05412i	0.382876	+	0.923800i	$0.374934\pi$
$37$	−136.972	+	237.242i	−0.608596	+	1.05412i	−0.991472	+	0.130319i	$0.958400\pi$
$38$	−47.5394			−0.202945
$39$	−215.865	−	248.489i	−0.886308	−	1.02026i
$40$	42.8206			0.169263
$41$	42.9160	−	74.3326i	0.163472	−	0.283142i	−0.772640	−	0.634845i	$-0.781064\pi$
$41$	42.9160	−	74.3326i	0.163472	−	0.283142i	0.936112	+	0.351703i	$0.114397\pi$
$42$	−43.7994	+	75.8627i	−0.160914	+	0.278711i
$43$	190.396	+	329.776i	0.675237	+	1.16954i	0.976400	+	0.215971i	$0.0692918\pi$
$43$	190.396	+	329.776i	0.675237	+	1.16954i	−0.301163	+	0.953573i	$0.597375\pi$
$44$	−65.9042			−0.225805
$45$	55.7865	+	96.6250i	0.184803	+	0.320089i
$46$	2.24698	+	3.89189i	0.00720216	+	0.0124745i
$47$	435.021			1.35009			0.675046	−	0.737776i	$-0.264124\pi$
$47$	435.021			1.35009			0.675046	+	0.737776i	$0.264124\pi$
$48$	−199.962	−	346.344i	−0.601292	−	1.04147i
$49$	−90.0560	+	155.982i	−0.262554	+	0.454757i
$50$	−6.81746	+	11.8082i	−0.0192827	+	0.0333986i
$51$	229.560			0.630290
$52$	−354.424	+	68.7725i	−0.945188	+	0.183404i
$53$	−436.042			−1.13009			−0.565046	−	0.825059i	$-0.691142\pi$
$53$	−436.042			−1.13009			−0.565046	+	0.825059i	$0.691142\pi$
$54$	8.97261	−	15.5410i	0.0226114	−	0.0391642i
$55$	21.3904	−	37.0493i	0.0524415	−	0.0908314i
$56$	97.9377	+	169.633i	0.233705	+	0.404789i
$57$	−612.108			−1.42238
$58$	−58.3974	−	101.147i	−0.132206	−	0.228988i
$59$	−374.566	−	648.767i	−0.826514	−	1.43156i	−0.900756	−	0.434324i	$-0.856987\pi$
$59$	−374.566	−	648.767i	−0.826514	−	1.43156i	0.0742422	−	0.997240i	$-0.476346\pi$
$60$	270.453			0.581922
$61$	35.3340	+	61.2003i	0.0741649	+	0.128457i	0.900723	−	0.434394i	$-0.143038\pi$
$61$	35.3340	+	61.2003i	0.0741649	+	0.128457i	−0.826558	+	0.562852i	$0.809704\pi$
$62$	−76.1826	+	131.952i	−0.156052	+	0.270289i
$63$	−255.186	+	441.994i	−0.510323	+	0.883906i
$64$	−401.289			−0.783768
$65$	76.3731	−	221.567i	0.145737	−	0.422801i
$66$	32.7702			0.0611172
$67$	−103.058	+	178.502i	−0.187918	+	0.325484i	−0.944556	−	0.328350i	$-0.893507\pi$
$67$	−103.058	+	178.502i	−0.187918	+	0.325484i	0.756638	+	0.653834i	$0.226841\pi$
$68$	125.896	−	218.058i	0.224517	−	0.388874i
$69$	28.9317	+	50.1112i	0.0504778	+	0.0874302i
$70$	−62.3706			−0.106496
$71$	−91.2401	−	158.033i	−0.152510	−	0.264155i	0.779640	−	0.626228i	$-0.215402\pi$
$71$	−91.2401	−	158.033i	−0.152510	−	0.264155i	−0.932150	+	0.362073i	$0.882069\pi$
$72$	95.5524	+	165.502i	0.156402	+	0.270896i
$73$	188.587			0.302363			0.151181	−	0.988506i	$-0.451692\pi$
$73$	188.587			0.302363			0.151181	+	0.988506i	$0.451692\pi$
$74$	−74.7041	−	129.391i	−0.117354	−	0.203263i
$75$	−87.7804	+	152.040i	−0.135147	+	0.234081i
$76$	−335.695	+	581.440i	−0.506669	+	0.877576i
$77$	195.694			0.289628
$78$	176.234	−	34.1965i	0.255828	−	0.0496408i
$79$	923.280			1.31490			0.657450	−	0.753498i	$-0.271635\pi$
$79$	923.280			1.31490			0.657450	+	0.753498i	$0.271635\pi$
$80$	142.374	−	246.599i	0.198973	−	0.344632i
$81$	416.777	−	721.878i	0.571710	−	0.990231i
$82$	23.4062	+	40.5408i	0.0315218	+	0.0545973i
$83$	1215.55			1.60752			0.803759	−	0.594955i	$-0.202830\pi$
$83$	1215.55			1.60752			0.803759	+	0.594955i	$0.202830\pi$
$84$	618.570	+	1071.40i	0.803471	+	1.39165i
$85$	81.7237	+	141.550i	0.104284	+	0.180626i
$86$	−207.683			−0.260408
$87$	−751.914	−	1302.35i	−0.926594	−	1.60491i
$88$	36.6380	−	63.4589i	0.0443821	−	0.0768721i
$89$	9.88021	−	17.1130i	0.0117674	−	0.0203818i	−0.860082	−	0.510156i	$-0.829588\pi$
$89$	9.88021	−	17.1130i	0.0117674	−	0.0203818i	0.871849	+	0.489774i	$0.162921\pi$
$90$	−60.8515			−0.0712702
$91$	1052.41	−	204.210i	1.21234	−	0.235243i
$92$	63.4674			0.0719232
$93$	−980.913	+	1698.99i	−1.09372	+	1.89438i
$94$	−118.630	+	205.472i	−0.130167	+	0.225456i
$95$	−217.912	−	377.434i	−0.235340	−	0.407620i
$96$	699.245			0.743400
$97$	−270.951	−	469.300i	−0.283617	−	0.491239i	0.688656	−	0.725088i	$-0.258201\pi$
$97$	−270.951	−	469.300i	−0.283617	−	0.491239i	−0.972273	+	0.233849i	$0.924868\pi$
$98$	−49.1163	−	85.0719i	−0.0506275	−	0.0876894i
$99$	190.927			0.193827
$100$	96.2818	+	166.765i	0.0962818	+	0.166765i
$101$	−623.022	+	1079.11i	−0.613792	+	1.06312i	0.376803	+	0.926293i	$0.377023\pi$
$101$	−623.022	+	1079.11i	−0.613792	+	1.06312i	−0.990595	+	0.136826i	$0.956310\pi$
$102$	−62.6006	+	108.427i	−0.0607684	+	0.105254i
$103$	439.445			0.420387			0.210193	−	0.977660i	$-0.432591\pi$
$103$	439.445			0.420387			0.210193	+	0.977660i	$0.432591\pi$
$104$	130.814	−	379.506i	0.123340	−	0.357823i
$105$	−803.073			−0.746399
$106$	118.908	−	205.955i	0.108956	−	0.188718i
$107$	609.040	−	1054.89i	0.550263	−	0.953083i	−0.447992	−	0.894037i	$-0.647861\pi$
$107$	609.040	−	1054.89i	0.550263	−	0.953083i	0.998255	−	0.0590458i	$-0.0188058\pi$
$108$	−126.719	−	219.483i	−0.112903	−	0.195553i
$109$	503.852			0.442755			0.221377	−	0.975188i	$-0.428945\pi$
$109$	503.852			0.442755			0.221377	+	0.975188i	$0.428945\pi$
$110$	11.6663	+	20.2066i	0.0101121	+	0.0175147i
$111$	−961.876	−	1666.02i	−0.822498	−	1.42461i
$112$	1302.53			1.09891
$113$	−655.703	−	1135.71i	−0.545870	−	0.945475i	−0.998552	−	0.0538029i	$-0.982866\pi$
$113$	−655.703	−	1135.71i	−0.545870	−	0.945475i	0.452681	−	0.891672i	$-0.350468\pi$
$114$	166.921	−	289.116i	0.137137	−	0.237528i
$115$	−20.5995	+	35.6794i	−0.0167036	+	0.0289315i
$116$	−1649.47			−1.32025
$117$	1026.78	−	199.237i	0.811333	−	0.157431i
$118$	408.574			0.318748
$119$	−373.831	+	647.494i	−0.287975	+	0.498787i
$120$	−150.352	+	260.418i	−0.114377	+	0.198107i
$121$	628.896	+	1089.28i	0.472499	+	0.818392i
$122$	−38.5421			−0.0286020
$123$	301.375	+	521.996i	0.220927	+	0.382657i
$124$	1075.91	+	1863.53i	0.779192	+	1.34960i
$125$	−125.000			−0.0894427
$126$	−139.177	−	241.062i	−0.0984041	−	0.170441i
$127$	−1219.05	+	2111.46i	−0.851760	+	1.47529i	0.0278592	+	0.999612i	$0.491131\pi$
$127$	−1219.05	+	2111.46i	−0.851760	+	1.47529i	−0.879619	+	0.475679i	$0.842202\pi$
$128$	507.723	−	879.402i	0.350600	−	0.607257i
$129$	−2674.09			−1.82512
$130$	83.8256	+	96.4942i	0.0565538	+	0.0651008i
$131$	−1854.96			−1.23716			−0.618582	−	0.785720i	$-0.712293\pi$
$131$	−1854.96			−1.23716			−0.618582	+	0.785720i	$0.712293\pi$
$132$	231.404	−	400.804i	0.152584	−	0.264284i
$133$	996.800	−	1726.51i	0.649876	−	1.12562i
$134$	−56.2075	−	97.3543i	−0.0362357	−	0.0627621i
$135$	164.515			0.104883
$136$	139.978	+	242.449i	0.0882576	+	0.152867i
$137$	1433.84	+	2483.48i	0.894168	+	1.54874i	0.834831	+	0.550506i	$0.185565\pi$
$137$	1433.84	+	2483.48i	0.894168	+	1.54874i	0.0593371	+	0.998238i	$0.481101\pi$
$138$	−31.5586			−0.0194670
$139$	−1002.43	−	1736.27i	−0.611693	−	1.05948i	−0.990955	−	0.134194i	$-0.957156\pi$
$139$	−1002.43	−	1736.27i	−0.611693	−	1.05948i	0.379262	−	0.925289i	$-0.376178\pi$
$140$	−440.424	+	762.838i	−0.265876	+	0.460511i
$141$	−1527.45	+	2645.63i	−0.912303	+	1.58016i
$142$	99.5242			0.0588161
$143$	−263.011	−	302.760i	−0.153805	−	0.177049i
$144$	1270.80			0.735419
$145$	535.366	−	927.281i	0.306619	−	0.531079i
$146$	−51.4275	+	89.0750i	−0.0291518	+	0.0504925i
$147$	−632.413	−	1095.37i	−0.354833	−	0.614590i
$148$	−2110.06			−1.17193
$149$	17.4910	+	30.2953i	0.00961690	+	0.0166570i	0.870794	−	0.491648i	$-0.163605\pi$
$149$	17.4910	+	30.2953i	0.00961690	+	0.0166570i	−0.861177	+	0.508305i	$0.830272\pi$
$150$	−47.8752	−	82.9222i	−0.0260599	−	0.0451372i
$151$	−2486.15			−1.33987			−0.669934	−	0.742421i	$-0.733678\pi$
$151$	−2486.15			−1.33987			−0.669934	+	0.742421i	$0.733678\pi$
$152$	−373.244	−	646.478i	−0.199172	−	0.344976i
$153$	−364.726	+	631.724i	−0.192721	+	0.333803i
$154$	−53.3654	+	92.4315i	−0.0279240	+	0.0483659i
$155$	−1396.83			−0.723844
$156$	826.213	−	2396.94i	0.424038	−	1.23019i
$157$	3322.18			1.68878			0.844391	−	0.535728i	$-0.179963\pi$
$157$	3322.18			1.68878			0.844391	+	0.535728i	$0.179963\pi$
$158$	−251.777	+	436.091i	−0.126774	+	0.219579i
$159$	1531.04	−	2651.83i	0.763642	−	1.32267i
$160$	248.933	+	431.164i	0.122999	+	0.213041i
$161$	−188.458			−0.0922519
$162$	227.309	+	393.710i	0.110241	+	0.190943i
$163$	−312.706	−	541.623i	−0.150264	−	0.260265i	0.781060	−	0.624455i	$-0.214679\pi$
$163$	−312.706	−	541.623i	−0.150264	−	0.260265i	−0.931324	+	0.364191i	$0.881346\pi$
$164$	661.124			0.314787
$165$	150.213	+	260.176i	0.0708730	+	0.122756i
$166$	−331.479	+	574.138i	−0.154986	+	0.268444i
$167$	251.395	−	435.429i	0.116488	−	0.201764i	−0.801885	−	0.597478i	$-0.796170\pi$
$167$	251.395	−	435.429i	0.116488	−	0.201764i	0.918374	+	0.395714i	$0.129503\pi$
$168$	−1375.52			−0.631690
$169$	−1730.37	−	1353.74i	−0.787607	−	0.616178i
$170$	−89.1437			−0.0402177
$171$	972.522	−	1684.46i	0.434916	−	0.753296i
$172$	−1466.54	+	2540.11i	−0.650130	+	1.12606i
$173$	1122.37	+	1944.00i	0.493249	+	0.854333i	0.999970	−	0.00777764i	$-0.00247572\pi$
$173$	1122.37	+	1944.00i	0.493249	+	0.854333i	−0.506721	+	0.862110i	$0.669142\pi$
$174$	820.183			0.357345
$175$	−285.896	−	495.186i	−0.123495	−	0.213900i
$176$	−243.635	−	421.988i	−0.104345	−	0.180730i
$177$	5260.73			2.23402
$178$	5.38864	+	9.33339i	0.00226908	+	0.00393015i
$179$	1550.41	−	2685.39i	0.647392	−	1.12132i	−0.336351	−	0.941737i	$-0.609193\pi$
$179$	1550.41	−	2685.39i	0.647392	−	1.12132i	0.983743	−	0.179580i	$-0.0574737\pi$
$180$	−429.698	+	744.258i	−0.177932	+	0.308187i
$181$	74.4030			0.0305543			0.0152772	−	0.999883i	$-0.495137\pi$
$181$	74.4030			0.0305543			0.0152772	+	0.999883i	$0.495137\pi$
$182$	−190.537	+	552.772i	−0.0776021	+	0.225133i
$183$	−496.262			−0.200463
$184$	−35.2833	+	61.1125i	−0.0141365	+	0.0244852i
$185$	684.859	−	1186.21i	0.272172	−	0.471416i
$186$	−534.987	−	926.625i	−0.210899	−	0.365287i
$187$	279.696			0.109377
$188$	1675.38	+	2901.85i	0.649946	+	1.12574i
$189$	376.273	+	651.724i	0.144814	+	0.250825i
$190$	237.697			0.0907597
$191$	2433.65	+	4215.21i	0.921953	+	1.59687i	0.796390	+	0.604784i	$0.206741\pi$
$191$	2433.65	+	4215.21i	0.921953	+	1.59687i	0.125564	+	0.992086i	$0.459926\pi$
$192$	1409.01	−	2440.48i	0.529619	−	0.917326i
$193$	−123.563	+	214.018i	−0.0460844	+	0.0798205i	−0.888147	−	0.459559i	$-0.848008\pi$
$193$	−123.563	+	214.018i	−0.0460844	+	0.0798205i	0.842063	+	0.539379i	$0.181341\pi$
$194$	295.551			0.109378
$195$	1079.32	+	1242.44i	0.396369	+	0.456273i
$196$	−1387.32			−0.505583
$197$	−1756.89	+	3043.01i	−0.635395	+	1.10054i	0.351036	+	0.936362i	$0.385830\pi$
$197$	−1756.89	+	3043.01i	−0.635395	+	1.10054i	−0.986431	+	0.164175i	$0.947504\pi$
$198$	−52.0656	+	90.1802i	−0.0186876	+	0.0323678i
$199$	1680.50	+	2910.71i	0.598629	+	1.03686i	0.993024	+	0.117915i	$0.0376211\pi$
$199$	1680.50	+	2910.71i	0.598629	+	1.03686i	−0.394394	+	0.918941i	$0.629046\pi$
$200$	−214.103			−0.0756968
$201$	−723.718	−	1253.52i	−0.253966	−	0.439882i
$202$	−339.794	−	588.541i	−0.118356	−	0.204998i
$203$	4897.88			1.69342
$204$	884.096	+	1531.30i	0.303427	+	0.525551i
$205$	−214.580	+	371.663i	−0.0731069	+	0.126625i
$206$	−119.836	+	207.562i	−0.0405310	+	0.0702017i
$207$	−183.868			−0.0617376
$208$	−1750.59	−	2015.16i	−0.583565	−	0.671759i
$209$	−745.796			−0.246831
$210$	218.997	−	379.314i	0.0719629	−	0.124643i
$211$	−794.470	+	1376.06i	−0.259211	+	0.448967i	−0.966031	−	0.258427i	$-0.916796\pi$
$211$	−794.470	+	1376.06i	−0.259211	+	0.448967i	0.706820	+	0.707394i	$0.250129\pi$
$212$	−1679.31	−	2908.66i	−0.544037	−	0.942299i
$213$	1281.46			0.412225
$214$	332.169	+	575.333i	0.106106	+	0.183780i
$215$	−951.982	−	1648.88i	−0.301975	−	0.523036i
$216$	281.786			0.0887643
$217$	−3194.77	−	5533.51i	−0.999426	−	1.73106i
$218$	−137.400	+	237.983i	−0.0426875	+	0.0739369i
$219$	−662.171	+	1146.91i	−0.204317	+	0.353887i
$220$	329.521			0.100983
$221$	1504.17	−	291.869i	0.457835	−	0.0888383i
$222$	1049.21			0.317199
$223$	1425.09	−	2468.34i	0.427944	−	0.741220i	−0.568747	−	0.822513i	$-0.692572\pi$
$223$	1425.09	−	2468.34i	0.427944	−	0.741220i	0.996690	+	0.0812928i	$0.0259049\pi$
$224$	−1138.70	+	1972.29i	−0.339654	+	0.588299i
$225$	−278.932	−	483.125i	−0.0826466	−	0.143148i
$226$	715.237			0.210517
$227$	−1881.42	−	3258.71i	−0.550106	−	0.952811i	−0.998266	−	0.0588582i	$-0.981254\pi$
$227$	−1881.42	−	3258.71i	−0.550106	−	0.952811i	0.448160	−	0.893953i	$-0.352079\pi$
$228$	−2357.39	−	4083.13i	−0.684747	−	1.18602i
$229$	−2209.34			−0.637543			−0.318772	−	0.947832i	$-0.603270\pi$
$229$	−2209.34			−0.637543			−0.318772	+	0.947832i	$0.603270\pi$
$230$	−11.2349	−	19.4594i	−0.00322090	−	0.00557877i
$231$	−687.123	+	1190.13i	−0.195711	+	0.338982i
$232$	916.987	−	1588.27i	0.259496	−	0.449461i
$233$	−1399.97			−0.393627			−0.196813	−	0.980441i	$-0.563059\pi$
$233$	−1399.97			−0.393627			−0.196813	+	0.980441i	$0.563059\pi$
$234$	−185.897	+	539.309i	−0.0519335	+	0.150665i
$235$	−2175.10			−0.603779
$236$	2885.11	−	4997.16i	0.795783	−	1.37834i
$237$	−3241.84	+	5615.03i	−0.888523	+	1.53897i
$238$	−203.886	−	353.141i	−0.0555293	−	0.0961796i
$239$	−158.031			−0.0427706			−0.0213853	−	0.999771i	$-0.506808\pi$
$239$	−158.031			−0.0427706			−0.0213853	+	0.999771i	$0.506808\pi$
$240$	999.810	+	1731.72i	0.268906	+	0.465759i
$241$	−1334.82	−	2311.98i	−0.356778	−	0.617957i	0.630643	−	0.776073i	$-0.282791\pi$
$241$	−1334.82	−	2311.98i	−0.356778	−	0.617957i	−0.987421	+	0.158116i	$0.949458\pi$
$242$	−685.996			−0.182221
$243$	2482.60	+	4299.98i	0.655385	+	1.13516i
$244$	−272.162	+	471.398i	−0.0714073	+	0.123681i
$245$	450.280	−	779.908i	0.117418	−	0.203373i
$246$	−328.738			−0.0852014
$247$	−4010.79	+	778.254i	−1.03320	+	0.200482i
$248$	−2392.52			−0.612601
$249$	−4268.06	+	7392.50i	−1.08625	+	1.88145i
$250$	34.0873	−	59.0410i	0.00862348	−	0.0149363i
$251$	3413.28	+	5911.97i	0.858343	+	1.48669i	0.873509	+	0.486809i	$0.161839\pi$
$251$	3413.28	+	5911.97i	0.858343	+	1.48669i	−0.0151655	+	0.999885i	$0.504828\pi$
$252$	−3931.16			−0.982696
$253$	35.2505	+	61.0557i	0.00875962	+	0.0151721i
$254$	−664.868	−	1151.59i	−0.164242	−	0.284476i
$255$	−1147.80			−0.281874
$256$	−1328.25	−	2300.59i	−0.324279	−	0.561667i
$257$	−1376.10	+	2383.47i	−0.334002	+	0.578509i	−0.983293	−	0.182032i	$-0.941733\pi$
$257$	−1376.10	+	2383.47i	−0.334002	+	0.578509i	0.649290	+	0.760541i	$0.275066\pi$
$258$	729.221	−	1263.05i	0.175966	−	0.304783i
$259$	6265.54			1.50317
$260$	1772.12	−	343.862i	0.422701	−	0.0820209i
$261$	4778.58			1.13328
$262$	505.845	−	876.149i	0.119279	−	0.206598i
$263$	−1367.09	+	2367.86i	−0.320525	+	0.555166i	−0.980597	−	0.196037i	$-0.937193\pi$
$263$	−1367.09	+	2367.86i	−0.320525	+	0.555166i	0.660071	+	0.751203i	$0.270526\pi$
$264$	257.288	+	445.636i	0.0599810	+	0.103890i
$265$	2180.21			0.505393
$266$	543.652	+	941.632i	0.125314	+	0.217050i
$267$	69.3831	+	120.175i	0.0159033	+	0.0275453i
$268$	−1587.62			−0.361862
$269$	−2857.91	−	4950.05i	−0.647770	−	1.12197i	−0.983654	−	0.180067i	$-0.942368\pi$
$269$	−2857.91	−	4950.05i	−0.647770	−	1.12197i	0.335884	−	0.941903i	$-0.390965\pi$
$270$	−44.8630	+	77.7051i	−0.0101121	+	0.0175147i
$271$	657.270	−	1138.43i	0.147330	−	0.255182i	−0.782910	−	0.622135i	$-0.786266\pi$
$271$	657.270	−	1138.43i	0.147330	−	0.255182i	0.930240	+	0.366953i	$0.119599\pi$
$272$	1861.65			0.414996
$273$	−2453.33	+	7117.40i	−0.543890	+	1.57789i
$274$	−1564.02			−0.344839
$275$	−106.952	+	185.246i	−0.0234526	+	0.0406210i
$276$	−222.848	+	385.984i	−0.0486010	+	0.0841793i
$277$	1016.94	+	1761.38i	0.220584	+	0.382063i	0.954985	−	0.296653i	$-0.0958704\pi$
$277$	1016.94	+	1761.38i	0.220584	+	0.382063i	−0.734402	+	0.678715i	$0.762537\pi$
$278$	1093.45			0.235902
$279$	−3116.96	−	5398.74i	−0.668845	−	1.15847i
$280$	−489.689	−	848.166i	−0.104516	−	0.181027i
$281$	−3958.11			−0.840289			−0.420144	−	0.907457i	$-0.638021\pi$
$281$	−3958.11			−0.840289			−0.420144	+	0.907457i	$0.638021\pi$
$282$	−833.068	−	1442.92i	−0.175917	−	0.304697i
$283$	3047.83	−	5278.99i	0.640193	−	1.10885i	−0.345197	−	0.938530i	$-0.612188\pi$
$283$	3047.83	−	5278.99i	0.640193	−	1.10885i	0.985390	−	0.170316i	$-0.0544788\pi$
$284$	702.781	−	1217.25i	0.146839	−	0.254333i
$285$	3060.54			0.636108
$286$	214.724	−	41.6651i	0.0443948	−	0.00861437i
$287$	−1963.12			−0.403760
$288$	−1110.97	+	1924.25i	−0.227306	+	0.393706i
$289$	1922.20	−	3329.35i	0.391248	−	0.677661i
$290$	291.987	+	505.736i	0.0591243	+	0.102406i
$291$	3805.46			0.766599
$292$	726.301	+	1257.99i	0.145560	+	0.252117i
$293$	1792.39	+	3104.51i	0.357381	+	0.619002i	0.987522	−	0.157478i	$-0.0503364\pi$
$293$	1792.39	+	3104.51i	0.357381	+	0.619002i	−0.630141	+	0.776480i	$0.717003\pi$
$294$	689.832			0.136843
$295$	1872.83	+	3243.84i	0.369628	+	0.640215i
$296$	1173.04	−	2031.77i	0.230344	−	0.398967i
$297$	140.762	−	243.807i	0.0275011	−	0.0476334i
$298$	−19.0791			−0.00370880
$299$	253.286	+	291.565i	0.0489896	+	0.0563934i
$300$	−1352.26			−0.260243
$301$	4354.68	−	7542.52i	0.833885	−	1.44433i
$302$	677.970	−	1174.28i	0.129181	−	0.223749i
$303$	−4375.13	−	7577.95i	−0.829520	−	1.43677i
$304$	−4963.98			−0.936526
$305$	−176.670	−	306.002i	−0.0331675	−	0.0574479i
$306$	−198.920	−	344.540i	−0.0371618	−	0.0643662i
$307$	−2943.87			−0.547283			−0.273641	−	0.961832i	$-0.588228\pi$
$307$	−2943.87			−0.547283			−0.273641	+	0.961832i	$0.588228\pi$
$308$	753.669	+	1305.39i	0.139429	+	0.241499i
$309$	−1542.99	+	2672.53i	−0.284070	+	0.492023i
$310$	380.913	−	659.760i	0.0697884	−	0.120877i
$311$	8067.29			1.47091			0.735457	−	0.677571i	$-0.236967\pi$
$311$	8067.29			1.47091			0.735457	+	0.677571i	$0.236967\pi$
$312$	1848.69	+	2128.09i	0.335454	+	0.386151i
$313$	−6091.78			−1.10009			−0.550044	−	0.835135i	$-0.685389\pi$
$313$	−6091.78			−1.10009			−0.550044	+	0.835135i	$0.685389\pi$
$314$	−905.953	+	1569.16i	−0.162821	+	0.282015i
$315$	1275.93	−	2209.97i	0.228223	−	0.395295i
$316$	3555.80	+	6158.83i	0.633005	+	1.09640i
$317$	2247.21			0.398157			0.199079	−	0.979984i	$-0.436205\pi$
$317$	2247.21			0.398157			0.199079	+	0.979984i	$0.436205\pi$
$318$	835.023	+	1446.30i	0.147251	+	0.255046i
$319$	−916.136	−	1586.79i	−0.160795	−	0.278506i
$320$	2006.45			0.350512
$321$	4276.94	+	7407.88i	0.743663	+	1.28806i
$322$	51.3922	−	89.0138i	0.00889432	−	0.0154054i
$323$	1424.68	−	2467.62i	0.245423	−	0.425084i
$324$	6420.48			1.10091
$325$	−381.865	+	1107.84i	−0.0651756	+	0.189082i
$326$	341.098			0.0579499
$327$	−1769.13	+	3064.23i	−0.299184	+	0.518203i
$328$	−367.537	+	636.594i	−0.0618715	+	0.107165i
$329$	−4974.82	−	8616.64i	−0.833650	−	1.44392i
$330$	−163.851			−0.0273325
$331$	−4683.92	−	8112.79i	−0.777799	−	1.34719i	−0.933208	−	0.359337i	$-0.883003\pi$
$331$	−4683.92	−	8112.79i	−0.777799	−	1.34719i	0.155409	−	0.987850i	$-0.450331\pi$
$332$	4681.41	+	8108.45i	0.773873	+	1.34039i
$333$	6112.94			1.00597
$334$	137.110	+	237.482i	0.0224621	+	0.0389055i
$335$	515.290	−	892.508i	0.0840397	−	0.145561i
$336$	−4573.46	+	7921.47i	−0.742568	+	1.28616i
$337$	2123.63			0.343269			0.171635	−	0.985161i	$-0.445095\pi$
$337$	2123.63			0.343269			0.171635	+	0.985161i	$0.445095\pi$
$338$	1111.28	−	448.139i	0.178833	−	0.0721170i
$339$	9209.26			1.47545
$340$	−629.480	+	1090.29i	−0.100407	+	0.173910i
$341$	−1195.15	+	2070.06i	−0.189797	+	0.328739i
$342$	530.410	+	918.698i	0.0838635	+	0.145256i
$343$	−3725.51			−0.586469
$344$	−1630.58	−	2824.24i	−0.255566	−	0.442654i
$345$	−144.659	−	250.556i	−0.0225744	−	0.0391000i
$346$	−1224.27			−0.190224
$347$	3974.42	+	6883.91i	0.614865	+	1.06498i	0.990408	+	0.138173i	$0.0441230\pi$
$347$	3974.42	+	6883.91i	0.614865	+	1.06498i	−0.375543	+	0.926805i	$0.622544\pi$
$348$	5791.65	−	10031.4i	0.892141	−	1.54523i
$349$	1202.06	−	2082.02i	0.184369	−	0.319336i	−0.758995	−	0.651096i	$-0.774309\pi$
$349$	1202.06	−	2082.02i	0.184369	−	0.319336i	0.943364	+	0.331761i	$0.107643\pi$
$350$	311.853			0.0476264
$351$	502.581	−	1458.05i	0.0764268	−	0.221723i
$352$	851.964			0.129005
$353$	−1055.90	+	1828.86i	−0.159206	+	0.275753i	−0.934583	−	0.355746i	$-0.884227\pi$
$353$	−1055.90	+	1828.86i	−0.159206	+	0.275753i	0.775377	+	0.631499i	$0.217560\pi$
$354$	−1434.59	+	2484.79i	−0.215389	+	0.373065i
$355$	456.201	+	790.163i	0.0682045	+	0.118134i
$356$	152.205			0.0226598
$357$	−2625.20	−	4546.98i	−0.389189	−	0.674095i
$358$	845.590	+	1464.60i	0.124835	+	0.216220i
$359$	−9615.51			−1.41361			−0.706807	−	0.707407i	$-0.749865\pi$
$359$	−9615.51			−1.41361			−0.706807	+	0.707407i	$0.749865\pi$
$360$	−477.762	−	827.508i	−0.0699452	−	0.121149i
$361$	−369.341	+	639.718i	−0.0538477	+	0.0932669i
$362$	−20.2896	+	35.1426i	−0.00294585	+	0.00510236i
$363$	−8832.76			−1.27713
$364$	5415.34	+	6233.76i	0.779782	+	0.897631i
$365$	−942.936			−0.135221
$366$	135.330	−	234.398i	0.0193273	−	0.0334759i
$367$	1868.05	−	3235.57i	0.265699	−	0.460205i	−0.702047	−	0.712130i	$-0.747730\pi$
$367$	1868.05	−	3235.57i	0.265699	−	0.460205i	0.967747	+	0.251926i	$0.0810638\pi$
$368$	234.626	+	406.385i	0.0332357	+	0.0575659i
$369$	−1915.30			−0.270208
$370$	373.520	+	646.956i	0.0524822	+	0.0909018i
$371$	4986.49	+	8636.86i	0.697806	+	1.20863i
$372$	−15111.0			−2.10611
$373$	−242.801	−	420.544i	−0.0337044	−	0.0583778i	0.848681	−	0.528905i	$-0.177397\pi$
$373$	−242.801	−	420.544i	−0.0337044	−	0.0583778i	−0.882386	+	0.470527i	$0.844064\pi$
$374$	−76.2728	+	132.108i	−0.0105454	+	0.0182651i
$375$	438.902	−	760.201i	0.0604395	−	0.104684i
$376$	−3725.57			−0.510988
$377$	−6582.71	−	7577.56i	−0.899275	−	1.03518i
$378$	−410.437			−0.0558481
$379$	1690.84	−	2928.63i	0.229163	−	0.396922i	−0.728397	−	0.685155i	$-0.759734\pi$
$379$	1690.84	−	2928.63i	0.229163	−	0.396922i	0.957560	+	0.288233i	$0.0930678\pi$
$380$	1678.47	−	2907.20i	0.226589	−	0.392464i
$381$	−8560.72	−	14827.6i	−1.15113	−	1.99381i
$382$	−2654.62			−0.355555
$383$	4879.50	+	8451.54i	0.650994	+	1.12756i	0.982882	+	0.184236i	$0.0589811\pi$
$383$	4879.50	+	8451.54i	0.650994	+	1.12756i	−0.331888	+	0.943319i	$0.607686\pi$
$384$	3565.45	+	6175.54i	0.473825	+	0.820689i
$385$	−978.468			−0.129526
$386$	−67.3911	−	116.725i	−0.00888631	−	0.0153915i
$387$	4248.61	−	7358.82i	0.558060	−	0.966588i
$388$	2087.01	−	3614.80i	0.273072	−	0.472974i
$389$	−6561.59			−0.855233			−0.427617	−	0.903960i	$-0.640647\pi$
$389$	−6561.59			−0.855233			−0.427617	+	0.903960i	$0.640647\pi$
$390$	−881.170	+	170.982i	−0.114410	+	0.0222001i
$391$	−269.355			−0.0348385
$392$	771.251	−	1335.85i	0.0993726	−	0.172118i
$393$	6513.17	−	11281.1i	0.835994	−	1.44798i
$394$	−958.200	−	1659.65i	−0.122521	−	0.212213i
$395$	−4616.40			−0.588041
$396$	735.313	+	1273.60i	0.0933102	+	0.161618i
$397$	−906.943	−	1570.87i	−0.114655	−	0.198589i	0.802987	−	0.595997i	$-0.203243\pi$
$397$	−906.943	−	1570.87i	−0.114655	−	0.198589i	−0.917642	+	0.397408i	$0.869910\pi$
$398$	−1833.08			−0.230864
$399$	6999.96	+	12124.3i	0.878287	+	1.52124i
$400$	−711.869	+	1232.99i	−0.0889836	+	0.154124i
$401$	4522.55	−	7833.29i	0.563206	−	0.975501i	−0.434009	−	0.900909i	$-0.642901\pi$
$401$	4522.55	−	7833.29i	0.563206	−	0.975501i	0.997214	−	0.0745919i	$-0.0237654\pi$
$402$	789.427			0.0979429
$403$	−4267.20	+	12379.7i	−0.527455	+	1.53021i
$404$	−9597.71			−1.18194
$405$	−2083.88	+	3609.39i	−0.255676	+	0.442845i
$406$	−1335.64	+	2313.40i	−0.163268	+	0.282789i
$407$	−1171.95	−	2029.88i	−0.142731	−	0.247218i
$408$	−1965.98			−0.238555
$409$	5054.93	+	8755.39i	0.611125	+	1.05850i	0.991051	+	0.133482i	$0.0426160\pi$
$409$	5054.93	+	8755.39i	0.611125	+	1.05850i	−0.379926	+	0.925017i	$0.624051\pi$
$410$	−117.031	−	202.704i	−0.0140970	−	0.0244167i
$411$	−20138.1			−2.41688
$412$	1692.42	+	2931.36i	0.202378	+	0.350529i
$413$	−8566.94	+	14838.4i	−1.02071	+	1.76791i
$414$	50.1404	−	86.8458i	0.00595234	−	0.0103098i
$415$	−6077.75			−0.718904
$416$	4581.75	−	889.042i	0.539997	−	0.104781i
$417$	14079.0			1.65337
$418$	203.377	−	352.260i	0.0237979	−	0.0412191i
$419$	−1259.67	+	2181.81i	−0.146871	+	0.254388i	−0.930069	−	0.367384i	$-0.880254\pi$
$419$	−1259.67	+	2181.81i	−0.146871	+	0.254388i	0.783199	+	0.621772i	$0.213587\pi$
$420$	−3092.85	−	5356.98i	−0.359323	−	0.622366i
$421$	−1683.18			−0.194853			−0.0974264	−	0.995243i	$-0.531061\pi$
$421$	−1683.18			−0.194853			−0.0974264	+	0.995243i	$0.531061\pi$
$422$	−433.302	−	750.501i	−0.0499829	−	0.0865730i
$423$	−4853.65	−	8406.78i	−0.557903	−	0.966315i
$424$	3734.31			0.427722
$425$	−408.618	−	707.748i	−0.0466374	−	0.0807784i
$426$	−349.451	+	605.267i	−0.0397440	+	0.0688387i
$427$	808.147	−	1399.75i	0.0915901	−	0.158639i
$428$	9382.31			1.05961
$429$	2764.75	−	536.473i	0.311150	−	0.0603756i
$430$	1038.42			0.116458
$431$	−2024.40	+	3506.37i	−0.226246	+	0.391870i	−0.956693	−	0.291100i	$-0.905979\pi$
$431$	−2024.40	+	3506.37i	−0.226246	+	0.391870i	0.730446	+	0.682970i	$0.239312\pi$
$432$	936.906	−	1622.77i	0.104345	−	0.180730i
$433$	−848.891	−	1470.32i	−0.0942151	−	0.163185i	0.815066	−	0.579369i	$-0.196701\pi$
$433$	−848.891	−	1470.32i	−0.0942151	−	0.163185i	−0.909281	+	0.416183i	$0.863367\pi$
$434$	3484.84			0.385432
$435$	3759.57	+	6511.77i	0.414385	+	0.717736i
$436$	1940.47	+	3360.99i	0.213146	+	0.369180i
$437$	718.220			0.0786204
$438$	−361.146	−	625.523i	−0.0393978	−	0.0682389i
$439$	−3263.78	+	5653.04i	−0.354833	+	0.614590i	−0.987089	−	0.160170i	$-0.948796\pi$
$439$	−3263.78	+	5653.04i	−0.354833	+	0.614590i	0.632256	+	0.774760i	$0.282129\pi$
$440$	−183.190	+	317.295i	−0.0198483	+	0.0343782i
$441$	4019.13			0.433984
$442$	−272.327	+	790.054i	−0.0293061	+	0.0850204i
$443$	−992.738			−0.106470			−0.0532352	−	0.998582i	$-0.516953\pi$
$443$	−992.738			−0.106470			−0.0532352	+	0.998582i	$0.516953\pi$
$444$	7408.89	−	12832.6i	0.791915	−	1.37164i
$445$	−49.4011	+	85.5651i	−0.00526255	+	0.00911500i
$446$	777.242	+	1346.22i	0.0825191	+	0.142927i
$447$	−245.659			−0.0259939
$448$	4589.07	+	7948.50i	0.483958	+	0.838240i
$449$	4398.78	+	7618.91i	0.462341	+	0.800798i	0.999077	−	0.0429520i	$-0.0136762\pi$
$449$	4398.78	+	7618.91i	0.462341	+	0.800798i	−0.536736	+	0.843750i	$0.680343\pi$
$450$	304.258			0.0318730
$451$	367.196	+	636.002i	0.0383383	+	0.0664040i
$452$	5050.58	−	8747.86i	0.525574	−	0.910320i
$453$	8729.42	−	15119.8i	0.905395	−	1.56819i
$454$	2052.24			0.212151
$455$	−5262.07	+	1021.05i	−0.542175	+	0.105204i
$456$	5242.17			0.538349
$457$	3300.80	−	5717.16i	0.337866	−	0.585202i	−0.646165	−	0.763198i	$-0.723628\pi$
$457$	3300.80	−	5717.16i	0.337866	−	0.585202i	0.984031	+	0.177996i	$0.0569614\pi$
$458$	602.484	−	1043.53i	0.0614678	−	0.106465i
$459$	537.791	+	931.482i	0.0546883	+	0.0947230i
$460$	−317.337			−0.0321650
$461$	−8479.37	−	14686.7i	−0.856668	−	1.48379i	−0.875089	−	0.483962i	$-0.839197\pi$
$461$	−8479.37	−	14686.7i	−0.856668	−	1.48379i	0.0184215	−	0.999830i	$-0.494136\pi$
$462$	−374.755	−	649.094i	−0.0377385	−	0.0653649i
$463$	5002.16			0.502095			0.251048	−	0.967975i	$-0.419225\pi$
$463$	5002.16			0.502095			0.251048	+	0.967975i	$0.419225\pi$
$464$	−6097.76	−	10561.6i	−0.610089	−	1.05671i
$465$	4904.56	−	8494.96i	0.489126	−	0.847192i
$466$	381.770	−	661.244i	0.0379509	−	0.0657329i
$467$	896.692			0.0888522			0.0444261	−	0.999013i	$-0.485854\pi$
$467$	896.692			0.0888522			0.0444261	+	0.999013i	$0.485854\pi$
$468$	5283.44	+	6081.93i	0.521853	+	0.600721i
$469$	4714.21			0.464141
$470$	593.148	−	1027.36i	0.0582125	−	0.100827i
$471$	−11664.9	+	20204.2i	−1.14117	+	1.97656i
$472$	3207.83	+	5556.12i	0.312823	+	0.541825i
$473$	−3258.13			−0.316720
$474$	−1768.09	−	3062.42i	−0.171331	−	0.296754i
$475$	1089.56	+	1887.17i	0.105247	+	0.182293i
$476$	−5758.90			−0.554535
$477$	4865.04	+	8426.50i	0.466992	+	0.808853i
$478$	43.0948	−	74.6424i	0.00412367	−	0.00714240i
$479$	7314.88	−	12669.7i	0.697757	−	1.20855i	−0.271486	−	0.962442i	$-0.587515\pi$
$479$	7314.88	−	12669.7i	0.697757	−	1.20855i	0.969243	−	0.246108i	$-0.0791517\pi$
$480$	−3496.23			−0.332459
$481$	−8420.84	−	9693.49i	−0.798248	−	0.918888i
$482$	1456.02			0.137593
$483$	661.716	−	1146.13i	0.0623377	−	0.107972i
$484$	−4844.10	+	8390.22i	−0.454930	+	0.787962i
$485$	1354.75	+	2346.50i	0.126837	+	0.219689i
$486$	−2708.00			−0.252752
$487$	2935.54	+	5084.51i	0.273146	+	0.473103i	0.969666	−	0.244435i	$-0.0786024\pi$
$487$	2935.54	+	5084.51i	0.273146	+	0.473103i	−0.696520	+	0.717538i	$0.745269\pi$
$488$	−302.605	−	524.127i	−0.0280702	−	0.0486191i
$489$	4391.92			0.406154
$490$	245.581	+	425.360i	0.0226413	+	0.0392159i
$491$	−4194.86	+	7265.72i	−0.385563	+	0.667815i	−0.991847	−	0.127433i	$-0.959326\pi$
$491$	−4194.86	+	7265.72i	−0.385563	+	0.667815i	0.606284	+	0.795248i	$0.292659\pi$
$492$	−2321.35	+	4020.70i	−0.212712	+	0.368429i
$493$	7000.33			0.639511
$494$	726.145	−	2106.64i	0.0661353	−	0.191866i
$495$	−954.636			−0.0866823
$496$	−7954.86	+	13778.2i	−0.720129	+	1.24730i
$497$	−2086.81	+	3614.46i	−0.188343	+	0.326219i
$498$	−2327.79	−	4031.85i	−0.209459	−	0.362794i
$499$	12745.1			1.14339			0.571693	−	0.820468i	$-0.306287\pi$
$499$	12745.1			1.14339			0.571693	+	0.820468i	$0.306287\pi$
$500$	−481.409	−	833.825i	−0.0430585	−	0.0745795i
$501$	1765.41	+	3057.77i	0.157430	+	0.272677i
$502$	−3723.18			−0.331023
$503$	7519.42	+	13024.0i	0.666549	+	1.15450i	0.978863	+	0.204518i	$0.0655627\pi$
$503$	7519.42	+	13024.0i	0.666549	+	1.15450i	−0.312314	+	0.949979i	$0.601104\pi$
$504$	2185.44	−	3785.29i	0.193149	−	0.334544i
$505$	3115.11	−	5395.53i	0.274496	−	0.475441i
$506$	−38.4511			−0.00337818
$507$	14308.6	−	5770.16i	1.25339	−	0.505447i
$508$	−18779.6			−1.64018
$509$	9298.83	−	16106.0i	0.809751	−	1.40253i	−0.103285	−	0.994652i	$-0.532935\pi$
$509$	9298.83	−	16106.0i	0.809751	−	1.40253i	0.913036	−	0.407879i	$-0.133731\pi$
$510$	313.003	−	542.137i	0.0271765	−	0.0470710i
$511$	−2156.65	−	3735.43i	−0.186702	−	0.323377i
$512$	9572.41			0.826259
$513$	−1433.99	−	2483.75i	−0.123416	−	0.213762i
$514$	−750.519	−	1299.94i	−0.0644046	−	0.111552i
$515$	−2197.23			−0.188003
$516$	−10298.7	−	17837.8i	−0.878630	−	1.52183i
$517$	−1861.06	+	3223.44i	−0.158316	+	0.274211i
$518$	−1708.60	+	2959.39i	−0.144926	+	0.251020i
$519$	−15763.5			−1.33322
$520$	−654.068	+	1897.53i	−0.0551592	+	0.160023i
$521$	22308.4			1.87591			0.937953	−	0.346761i	$-0.112719\pi$
$521$	22308.4			1.87591			0.937953	+	0.346761i	$0.112719\pi$
$522$	−1303.11	+	2257.06i	−0.109264	+	0.189250i
$523$	2269.30	−	3930.54i	0.189731	−	0.328624i	−0.755429	−	0.655230i	$-0.772572\pi$
$523$	2269.30	−	3930.54i	0.189731	−	0.328624i	0.945161	+	0.326606i	$0.105905\pi$
$524$	−7143.95	−	12373.7i	−0.595582	−	1.03158i
$525$	4015.37			0.333800
$526$	−745.605	−	1291.43i	−0.0618059	−	0.107051i
$527$	−4566.15	−	7908.81i	−0.377428	−	0.653725i
$528$	3421.82			0.282037
$529$	6049.55	+	10478.1i	0.497210	+	0.861193i
$530$	−594.539	+	1029.77i	−0.0487267	+	0.0843971i
$531$	−8358.28	+	14477.0i	−0.683086	+	1.18314i
$532$	15355.8			1.25142
$533$	2638.41	+	3037.16i	0.214414	+	0.246818i
$534$	−75.6827			−0.00613317
$535$	−3045.20	+	5274.44i	−0.246085	+	0.426232i
$536$	882.601	−	1528.71i	0.0711242	−	0.123191i
$537$	10887.7	+	18858.0i	0.874930	+	1.51542i
$538$	3117.40			0.249815
$539$	−770.534	−	1334.60i	−0.0615756	−	0.106652i
$540$	633.593	+	1097.41i	0.0504916	+	0.0874541i
$541$	23005.3			1.82824			0.914118	−	0.405448i	$-0.132884\pi$
$541$	23005.3			1.82824			0.914118	+	0.405448i	$0.132884\pi$
$542$	358.473	+	620.894i	0.0284091	+	0.0492060i
$543$	−261.245	+	452.490i	−0.0206466	+	0.0357610i
$544$	−1627.49	+	2818.90i	−0.128269	+	0.222168i
$545$	−2519.26			−0.198006
$546$	−2692.72	−	3099.68i	−0.211059	−	0.242956i
$547$	−1258.68			−0.0983863			−0.0491932	−	0.998789i	$-0.515665\pi$
$547$	−1258.68			−0.0983863			−0.0491932	+	0.998789i	$0.515665\pi$
$548$	−11044.2	+	19129.1i	−0.860921	+	1.49116i
$549$	788.464	−	1365.66i	0.0612948	−	0.106166i
$550$	−58.3313	−	101.033i	−0.00452229	−	0.00783283i
$551$	−18666.0			−1.44319
$552$	−247.775	−	429.158i	−0.0191051	−	0.0330909i
$553$	−10558.5	−	18287.8i	−0.811920	−	1.40629i
$554$	−1109.27			−0.0850690
$555$	4809.38	+	8330.09i	0.367832	+	0.637104i
$556$	7721.28	−	13373.7i	0.588949	−	1.02009i
$557$	−8531.11	+	14776.3i	−0.648967	+	1.12404i	0.334402	+	0.942430i	$0.391466\pi$
$557$	−8531.11	+	14776.3i	−0.648967	+	1.12404i	−0.983370	+	0.181614i	$0.941868\pi$
$558$	3399.96			0.257943
$559$	−17521.8	+	3399.92i	−1.32575	+	0.257248i
$560$	−6512.64			−0.491445
$561$	−982.075	+	1701.00i	−0.0739095	+	0.128015i
$562$	1079.37	−	1869.53i	0.0810152	−	0.140322i
$563$	−6752.60	−	11695.8i	−0.505485	−	0.875526i	−0.999980	−	0.00634515i	$-0.997980\pi$
$563$	−6752.60	−	11695.8i	−0.505485	−	0.875526i	0.494495	−	0.869181i	$-0.335353\pi$
$564$	−23530.5			−1.75676
$565$	3278.52	+	5678.56i	0.244121	+	0.422829i
$566$	1662.28	+	2879.15i	0.123446	+	0.213815i
$567$	−19064.7			−1.41207
$568$	781.391	+	1353.41i	0.0577226	+	0.0999785i
$569$	−2402.33	+	4160.96i	−0.176997	+	0.306567i	−0.940850	−	0.338822i	$-0.889971\pi$
$569$	−2402.33	+	4160.96i	−0.176997	+	0.306567i	0.763854	+	0.645389i	$0.223305\pi$
$570$	−834.605	+	1445.58i	−0.0613294	+	0.106226i
$571$	18967.1			1.39010			0.695051	−	0.718961i	$-0.255382\pi$
$571$	18967.1			1.39010			0.695051	+	0.718961i	$0.255382\pi$
$572$	1006.66	−	2920.45i	0.0735850	−	0.213479i
$573$	−34180.4			−2.49198
$574$	535.339	−	927.235i	0.0389279	−	0.0674251i
$575$	102.997	−	178.397i	0.00747007	−	0.0129385i
$576$	4477.30	+	7754.91i	0.323879	+	0.560974i
$577$	6023.19			0.434573			0.217286	−	0.976108i	$-0.430279\pi$
$577$	6023.19			0.434573			0.217286	+	0.976108i	$0.430279\pi$
$578$	1048.36	+	1815.82i	0.0754431	+	0.130671i
$579$	−867.716	−	1502.93i	−0.0622816	−	0.107875i
$580$	8247.35			0.590436
$581$	−13900.8	−	24076.9i	−0.992604	−	1.71924i
$582$	−1037.74	+	1797.43i	−0.0739105	+	0.128017i
$583$	1865.42	−	3231.01i	0.132518	−	0.229528i
$584$	−1615.08			−0.114439
$585$	−5133.91	+	996.184i	−0.362839	+	0.0704053i
$586$	−1955.13			−0.137825
$587$	7119.83	−	12331.9i	0.500625	−	0.867108i	−0.499375	−	0.866386i	$-0.666437\pi$
$587$	7119.83	−	12331.9i	0.500625	−	0.867108i	1.00000		0.000722020i	$-0.000229826\pi$
$588$	4871.18	−	8437.14i	0.341640	−	0.591738i
$589$	12175.4	+	21088.4i	0.851747	+	1.47527i
$590$	−2042.87			−0.142549
$591$	−12337.6	−	21369.4i	−0.858717	−	1.48734i
$592$	−7800.48	−	13510.8i	−0.541550	−	0.937993i
$593$	27625.9			1.91309			0.956544	−	0.291587i	$-0.0941833\pi$
$593$	27625.9			1.91309			0.956544	+	0.291587i	$0.0941833\pi$
$594$	76.7711	+	132.972i	0.00530296	+	0.00918500i
$595$	1869.15	−	3237.47i	0.128786	−	0.223064i
$596$	−134.725	+	233.351i	−0.00925932	+	0.0160376i
$597$	−23602.4			−1.61806
$598$	−206.785	+	40.1245i	−0.0141406	+	0.00274384i
$599$	4314.14			0.294276			0.147138	−	0.989116i	$-0.452994\pi$
$599$	4314.14			0.294276			0.147138	+	0.989116i	$0.452994\pi$
$600$	751.762	−	1302.09i	0.0511509	−	0.0885960i
$601$	−5652.41	+	9790.26i	−0.383638	+	0.664481i	−0.991579	−	0.129501i	$-0.958662\pi$
$601$	−5652.41	+	9790.26i	−0.383638	+	0.664481i	0.607941	+	0.793982i	$0.291996\pi$
$602$	2375.03	+	4113.67i	0.160796	+	0.278506i
$603$	4599.39			0.310616
$604$	−9574.84	−	16584.1i	−0.645024	−	1.11722i
$605$	−3144.48	−	5446.40i	−0.211308	−	0.365996i
$606$	4772.37			0.319908
$607$	1272.12	+	2203.37i	0.0850636	+	0.147335i	0.905418	−	0.424520i	$-0.139557\pi$
$607$	1272.12	+	2203.37i	0.0850636	+	0.147335i	−0.820355	+	0.571855i	$0.806224\pi$
$608$	4339.63	−	7516.45i	0.289466	−	0.501369i
$609$	−17197.5	+	29787.0i	−1.14430	+	1.98198i
$610$	192.711			0.0127912
$611$	−6644.78	+	19277.3i	−0.439965	+	1.27639i
$612$	−5618.63			−0.371111
$613$	619.913	−	1073.72i	0.0408451	−	0.0707458i	−0.844880	−	0.534956i	$-0.820328\pi$
$613$	619.913	−	1073.72i	0.0408451	−	0.0707458i	0.885725	+	0.464210i	$0.153662\pi$
$614$	802.790	−	1390.47i	0.0527654	−	0.0913924i
$615$	−1506.87	−	2609.98i	−0.0988016	−	0.171129i
$616$	−1675.94			−0.109620
$617$	−4668.33	−	8085.79i	−0.304603	−	0.527588i	0.672570	−	0.740034i	$-0.265190\pi$
$617$	−4668.33	−	8085.79i	−0.304603	−	0.527588i	−0.977173	+	0.212446i	$0.931857\pi$
$618$	−841.541	−	1457.59i	−0.0547763	−	0.0948753i
$619$	10049.7			0.652553			0.326276	−	0.945274i	$-0.394206\pi$
$619$	10049.7			0.652553			0.326276	+	0.945274i	$0.394206\pi$
$620$	−5379.56	−	9317.67i	−0.348465	−	0.603559i
$621$	−135.557	+	234.792i	−0.00875962	+	0.0151721i
$622$	−2199.94	+	3810.41i	−0.141816	+	0.245632i
$623$	−451.953			−0.0290644
$624$	18402.1	−	3570.74i	1.18056	−	0.229077i
$625$	625.000			0.0400000
$626$	1661.22	−	2877.32i	0.106063	−	0.183707i
$627$	2618.65	−	4535.64i	0.166792	−	0.288893i
$628$	12794.6	+	22160.9i	0.812994	+	1.40815i
$629$	8955.07			0.567666
$630$	695.887	+	1205.31i	0.0440076	+	0.0762235i
$631$	7130.56	+	12350.5i	0.449862	+	0.779184i	0.998377	−	0.0569568i	$-0.0181397\pi$
$631$	7130.56	+	12350.5i	0.449862	+	0.779184i	−0.548514	+	0.836141i	$0.684806\pi$
$632$	−7907.08			−0.497669
$633$	−5579.11	−	9663.31i	−0.350316	−	0.606765i
$634$	−612.810	+	1061.42i	−0.0383877	+	0.0664895i
$635$	6095.27	−	10557.3i	0.380918	−	0.659770i
$636$	23585.8			1.47050
$637$	−5536.52	−	6373.26i	−0.344372	−	0.396417i
$638$	999.315			0.0620114
$639$	−2035.98	+	3526.43i	−0.126044	+	0.218315i
$640$	−2538.62	+	4397.01i	−0.156793	+	0.271574i
$641$	11239.3	+	19467.1i	0.692553	+	1.19954i	0.970999	+	0.239085i	$0.0768475\pi$
$641$	11239.3	+	19467.1i	0.692553	+	1.19954i	−0.278445	+	0.960452i	$0.589819\pi$
$642$	−4665.26			−0.286796
$643$	−573.151	−	992.726i	−0.0351522	−	0.0608854i	0.847914	−	0.530134i	$-0.177858\pi$
$643$	−573.151	−	992.726i	−0.0351522	−	0.0608854i	−0.883066	+	0.469248i	$0.844525\pi$
$644$	−725.802	−	1257.13i	−0.0444109	−	0.0769219i
$645$	13370.5			0.816219
$646$	777.018	+	1345.83i	0.0473241	+	0.0819677i
$647$	−5917.19	+	10248.9i	−0.359550	+	0.622758i	−0.987886	−	0.155184i	$-0.950403\pi$
$647$	−5917.19	+	10248.9i	−0.359550	+	0.622758i	0.628336	+	0.777942i	$0.283736\pi$
$648$	−3569.32	+	6182.25i	−0.216383	+	0.374787i
$649$	6409.70			0.387677
$650$	−419.128	−	482.471i	−0.0252916	−	0.0291140i
$651$	44870.2			2.70138
$652$	2408.63	−	4171.87i	0.144677	−	0.250588i
$653$	13269.3	−	22983.0i	0.795201	−	1.37733i	−0.127511	−	0.991837i	$-0.540699\pi$
$653$	13269.3	−	22983.0i	0.795201	−	1.37733i	0.922712	−	0.385491i	$-0.125968\pi$
$654$	−964.880	−	1671.22i	−0.0576908	−	0.0999234i
$655$	9274.80			0.553277
$656$	2444.04	+	4233.21i	0.145463	+	0.251950i
$657$	−2104.12	−	3644.45i	−0.124946	−	0.216413i
$658$	5426.51			0.321500
$659$	3289.66	+	5697.86i	0.194457	+	0.336809i	0.946722	−	0.322051i	$-0.104372\pi$
$659$	3289.66	+	5697.86i	0.194457	+	0.336809i	−0.752266	+	0.658860i	$0.771039\pi$
$660$	−1157.02	+	2004.02i	−0.0682378	+	0.118191i
$661$	1737.97	−	3010.25i	0.102268	−	0.177133i	−0.810351	−	0.585945i	$-0.800723\pi$
$661$	1737.97	−	3010.25i	0.102268	−	0.177133i	0.912619	+	0.408812i	$0.134057\pi$
$662$	5109.19			0.299961
$663$	−3506.43	+	10172.6i	−0.205398	+	0.595883i
$664$	−10410.1			−0.608420
$665$	−4984.00	+	8632.54i	−0.290633	+	0.503392i
$666$	−1666.99	+	2887.31i	−0.0969888	+	0.167990i
$667$	882.261	+	1528.12i	0.0512163	+	0.0887093i
$668$	3872.76			0.224314
$669$	10007.6	+	17333.7i	0.578352	+	1.00174i
$670$	281.038	+	486.771i	0.0162051	+	0.0280681i
$671$	−604.648			−0.0347871
$672$	−7996.44	−	13850.2i	−0.459032	−	0.795067i
$673$	−4136.59	+	7164.79i	−0.236930	+	0.410375i	−0.959832	−	0.280576i	$-0.909475\pi$
$673$	−4136.59	+	7164.79i	−0.236930	+	0.410375i	0.722902	+	0.690951i	$0.242808\pi$
$674$	−579.112	+	1003.05i	−0.0330958	+	0.0573236i
$675$	−822.576			−0.0469051
$676$	2366.14	−	16756.2i	0.134624	−	0.953360i
$677$	−24565.9			−1.39460			−0.697299	−	0.716781i	$-0.745615\pi$
$677$	−24565.9			−1.39460			−0.697299	+	0.716781i	$0.745615\pi$
$678$	−2511.35	+	4349.79i	−0.142254	+	0.246390i
$679$	−6197.08	+	10733.7i	−0.350254	+	0.606657i
$680$	−699.891	−	1212.25i	−0.0394700	−	0.0683640i
$681$	26424.3			1.48690
$682$	−651.831	−	1129.00i	−0.0365981	−	0.0633897i
$683$	324.205	+	561.540i	0.0181631	+	0.0314593i	0.874964	−	0.484188i	$-0.160885\pi$
$683$	324.205	+	561.540i	0.0181631	+	0.0314593i	−0.856801	+	0.515647i	$0.827552\pi$
$684$	14981.8			0.837489
$685$	−7169.19	−	12417.4i	−0.399884	−	0.692620i
$686$	1015.94	−	1759.66i	0.0565435	−	0.0979363i
$687$	7757.48	−	13436.4i	0.430810	−	0.746185i
$688$	−21685.9			−1.20170
$689$	6660.37	−	19322.5i	0.368273	−	1.06840i
$690$	157.793			0.00870590
$691$	−6039.24	+	10460.3i	−0.332480	+	0.575872i	−0.982997	−	0.183619i	$-0.941219\pi$
$691$	−6039.24	+	10460.3i	−0.332480	+	0.575872i	0.650518	+	0.759491i	$0.274552\pi$
$692$	−8645.09	+	14973.7i	−0.474909	+	0.822567i
$693$	−2183.41	−	3781.78i	−0.119684	−	0.207298i
$694$	−4335.28			−0.237125
$695$	5012.17	+	8681.33i	0.273557	+	0.473815i
$696$	6439.48	+	11153.5i	0.350701	+	0.607432i
$697$	−2805.80			−0.152478
$698$	655.598	+	1135.53i	0.0355512	+	0.0615765i
$699$	4915.60	−	8514.06i	0.265987	−	0.460703i
$700$	2202.12	−	3814.19i	0.118903	−	0.205947i
$701$	−30979.5			−1.66916			−0.834579	−	0.550888i	$-0.814289\pi$
$701$	−30979.5			−1.66916			−0.834579	+	0.550888i	$0.814289\pi$
$702$	551.624	+	634.991i	0.0296577	+	0.0341399i
$703$	−23878.2			−1.28106
$704$	1716.75	−	2973.50i	0.0919068	−	0.159187i
$705$	7637.26	−	13228.1i	0.407994	−	0.706667i
$706$	−575.882	−	997.458i	−0.0306992	−	0.0531725i
$707$	28499.1			1.51601
$708$	20260.5	+	35092.2i	1.07547	+	1.86278i
$709$	−15841.6	−	27438.5i	−0.839131	−	1.45342i	−0.890622	−	0.454744i	$-0.849731\pi$
$709$	−15841.6	−	27438.5i	−0.839131	−	1.45342i	0.0514911	−	0.998673i	$-0.483603\pi$
$710$	−497.621			−0.0263033
$711$	−10301.3	−	17842.4i	−0.543360	−	0.941128i
$712$	−84.6153	+	146.558i	−0.00445378	+	0.00771418i
$713$	1150.96	−	1993.52i	0.0604540	−	0.104709i
$714$	2863.56			0.150092
$715$	1315.05	+	1513.80i	0.0687835	+	0.0791788i
$716$	23884.2			1.24664
$717$	554.881	−	961.083i	0.0289016	−	0.0500590i
$718$	2622.14	−	4541.67i	0.136291	−	0.236064i
$719$	−4.38641	−	7.59748i	−0.000227518	−	0.000394073i	0.865912	−	0.500197i	$-0.166739\pi$
$719$	−4.38641	−	7.59748i	−0.000227518	−	0.000394073i	−0.866139	+	0.499803i	$0.833406\pi$
$720$	−6354.02			−0.328889
$721$	−5025.42	−	8704.28i	−0.259579	−	0.449604i
$722$	−201.438	−	348.900i	−0.0103833	−	0.0179844i
$723$	18747.4			0.964348
$724$	286.546	+	496.313i	0.0147091	+	0.0254769i
$725$	−2676.83	+	4636.40i	−0.137124	+	0.237506i
$726$	2408.68	−	4171.96i	0.123133	−	0.213273i
$727$	−19474.1			−0.993470			−0.496735	−	0.867902i	$-0.665468\pi$
$727$	−19474.1			−0.993470			−0.496735	+	0.867902i	$0.665468\pi$
$728$	−9013.00	+	1748.88i	−0.458852	+	0.0890356i
$729$	−12361.8			−0.628044
$730$	257.137	−	445.375i	0.0130371	−	0.0225809i
$731$	6223.95	−	10780.2i	0.314913	−	0.545445i
$732$	−1911.24	−	3310.36i	−0.0965047	−	0.167151i
$733$	9433.64			0.475361			0.237680	−	0.971343i	$-0.423613\pi$
$733$	9433.64			0.475361			0.237680	+	0.971343i	$0.423613\pi$
$734$	1018.83	+	1764.67i	0.0512340	+	0.0887399i
$735$	3162.06	+	5476.85i	0.158686	+	0.274853i
$736$	−820.462			−0.0410905
$737$	−881.781	−	1527.29i	−0.0440717	−	0.0763344i
$738$	522.300	−	904.651i	0.0260517	−	0.0451228i
$739$	−3515.45	+	6088.94i	−0.174990	+	0.303092i	−0.940158	−	0.340739i	$-0.889323\pi$
$739$	−3515.45	+	6088.94i	−0.174990	+	0.303092i	0.765168	+	0.643831i	$0.222656\pi$
$740$	10550.3			0.524105
$741$	9349.72	−	27124.7i	0.463523	−	1.34474i
$742$	−5439.24			−0.269111
$743$	2389.26	−	4138.32i	0.117972	−	0.204334i	−0.800992	−	0.598675i	$-0.795694\pi$
$743$	2389.26	−	4138.32i	0.117972	−	0.204334i	0.918964	+	0.394341i	$0.129027\pi$
$744$	8400.66	−	14550.4i	0.413956	−	0.716992i
$745$	−87.4550	−	151.476i	−0.00430081	−	0.00744922i
$746$	264.846			0.0129983
$747$	−13562.2	−	23490.5i	−0.664279	−	1.15057i
$748$	1077.19	+	1865.74i	0.0526549	+	0.0912009i
$749$	−27859.5			−1.35910
$750$	239.376	+	414.611i	0.0116544	+	0.0201859i
$751$	1363.29	−	2361.29i	0.0662412	−	0.114733i	−0.831003	−	0.556268i	$-0.812233\pi$
$751$	1363.29	−	2361.29i	0.0662412	−	0.114733i	0.897244	+	0.441535i	$0.145566\pi$
$752$	−12387.1	+	21455.1i	−0.600680	+	1.04041i
$753$	−47939.0			−2.32005
$754$	5374.18	−	1042.81i	0.259571	−	0.0503671i
$755$	12430.8			0.599207
$756$	−2898.26	+	5019.94i	−0.139430	+	0.241499i
$757$	−12658.0	+	21924.3i	−0.607744	+	1.05264i	0.383867	+	0.923388i	$0.374592\pi$
$757$	−12658.0	+	21924.3i	−0.607744	+	1.05264i	−0.991611	+	0.129255i	$0.958741\pi$
$758$	922.181	+	1597.26i	0.0441888	+	0.0765373i
$759$	−495.089			−0.0236767
$760$	1866.22	+	3232.39i	0.0890723	+	0.154278i
$761$	13694.0	+	23718.7i	0.652310	+	1.12983i	0.982561	+	0.185941i	$0.0595332\pi$
$761$	13694.0	+	23718.7i	0.652310	+	1.12983i	−0.330251	+	0.943893i	$0.607133\pi$
$762$	9337.98			0.443936
$763$	−5761.96	−	9980.01i	−0.273390	−	0.473526i
$764$	−18745.3	+	32467.9i	−0.887673	+	1.53749i
$765$	1823.63	−	3158.62i	0.0861875	−	0.149281i
$766$	−5322.53			−0.251058
$767$	34470.5	−	6688.66i	1.62276	−	0.314881i
$768$	18655.0			0.876505
$769$	−5391.53	+	9338.41i	−0.252827	+	0.437909i	−0.964303	−	0.264801i	$-0.914694\pi$
$769$	−5391.53	+	9338.41i	−0.252827	+	0.437909i	0.711476	+	0.702710i	$0.248027\pi$
$770$	266.827	−	462.157i	0.0124880	−	0.0216299i
$771$	−9663.55	−	16737.8i	−0.451393	−	0.781836i
$772$	−1903.50			−0.0887417
$773$	12306.9	+	21316.2i	0.572639	+	0.991839i	0.996294	+	0.0860155i	$0.0274135\pi$
$773$	12306.9	+	21316.2i	0.572639	+	0.991839i	−0.423655	+	0.905824i	$0.639253\pi$
$774$	2317.18	+	4013.48i	0.107609	+	0.186384i
$775$	6984.14			0.323713
$776$	2320.45	+	4019.14i	0.107345	+	0.185926i
$777$	−21999.7	+	38104.6i	−1.01575	+	1.75932i
$778$	1789.34	−	3099.22i	0.0824560	−	0.142818i
$779$	7481.51			0.344099
$780$	−4131.07	+	11984.7i	−0.189636	+	0.550156i
$781$	1561.33			0.0715350
$782$	73.4526	−	127.224i	0.00335890	−	0.00581779i
$783$	3523.03	−	6102.07i	0.160796	−	0.278506i
$784$	−5128.65	−	8883.07i	−0.233630	−	0.404659i
$785$	−16610.9			−0.755246
$786$	3552.26	+	6152.70i	0.161202	+	0.279211i
$787$	−1362.66	−	2360.20i	−0.0617200	−	0.106902i	0.833514	−	0.552498i	$-0.186325\pi$
$787$	−1362.66	−	2360.20i	−0.0617200	−	0.106902i	−0.895234	+	0.445596i	$0.852992\pi$
$788$	−27065.0			−1.22354
$789$	−9600.27	−	16628.2i	−0.433180	−	0.750289i
$790$	1258.89	−	2180.45i	0.0566951	−	0.0981988i
$791$	−14997.0	+	25975.6i	−0.674124	+	1.16762i
$792$	−1635.12			−0.0733606
$793$	−3251.71	+	630.963i	−0.145614	+	0.0282549i
$794$	989.288			0.0442173
$795$	−7655.18	+	13259.2i	−0.341511	+	0.591515i
$796$	−12944.1	+	22419.8i	−0.576371	+	0.998304i
$797$	−8343.63	−	14451.6i	−0.370824	−	0.642286i	0.618869	−	0.785494i	$-0.287591\pi$
$797$	−8343.63	−	14451.6i	−0.370824	−	0.642286i	−0.989693	+	0.143209i	$0.954258\pi$
$798$	−7635.52			−0.338715
$799$	−7110.30	−	12315.4i	−0.314824	−	0.545291i
$800$	−1244.66	−	2155.82i	−0.0550069	−	0.0952747i
$801$	−440.946			−0.0194507
$802$	2466.59	+	4272.25i	0.108601	+	0.188103i
$803$	−806.792	+	1397.41i	−0.0354559	+	0.0614114i
$804$	5574.47	−	9655.26i	0.244523	−	0.423526i
$805$	942.289			0.0412563
$806$	−4683.60	−	5391.43i	−0.204681	−	0.235614i
$807$	40139.0			1.75088
$808$	5335.63	−	9241.59i	0.232311	−	0.402374i
$809$	10504.2	−	18193.8i	0.456500	−	0.790681i	−0.542273	−	0.840202i	$-0.682436\pi$
$809$	10504.2	−	18193.8i	0.456500	−	0.790681i	0.998773	+	0.0495212i	$0.0157696\pi$
$810$	−1136.54	−	1968.55i	−0.0493013	−	0.0853924i
$811$	−6817.34			−0.295178			−0.147589	−	0.989049i	$-0.547151\pi$
$811$	−6817.34			−0.295178			−0.147589	+	0.989049i	$0.547151\pi$
$812$	18863.1	+	32671.8i	0.815226	+	1.41201i
$813$	4615.64	+	7994.52i	0.199111	+	0.344871i
$814$	1278.36			0.0550449
$815$	1563.53	+	2708.11i	0.0672001	+	0.116394i
$816$	−6536.65	+	11321.8i	−0.280427	+	0.485714i
$817$	−16595.8	+	28744.8i	−0.710667	+	1.23091i
$818$	−5513.88			−0.235683
$819$	−15688.5	−	18059.5i	−0.669352	−	0.770511i
$820$	−3305.62			−0.140777
$821$	14940.1	−	25877.0i	0.635095	−	1.10002i	−0.351400	−	0.936225i	$-0.614294\pi$
$821$	14940.1	−	25877.0i	0.635095	−	1.10002i	0.986495	−	0.163791i	$-0.0523724\pi$
$822$	5491.62	−	9511.76i	0.233020	−	0.403602i
$823$	−16534.1	−	28637.9i	−0.700294	−	1.21294i	−0.968363	−	0.249545i	$-0.919719\pi$
$823$	−16534.1	−	28637.9i	−0.700294	−	1.21294i	0.268069	−	0.963400i	$-0.413614\pi$
$824$	−3763.46			−0.159110
$825$	−751.064	−	1300.88i	−0.0316954	−	0.0548980i
$826$	−4672.38	−	8092.81i	−0.196820	−	0.340902i
$827$	5187.68			0.218130			0.109065	−	0.994035i	$-0.465214\pi$
$827$	5187.68			0.218130			0.109065	+	0.994035i	$0.465214\pi$
$828$	−708.124	−	1226.51i	−0.0297210	−	0.0514783i
$829$	436.837	−	756.624i	0.0183016	−	0.0316992i	−0.856730	−	0.515766i	$-0.827507\pi$
$829$	436.837	−	756.624i	0.0183016	−	0.0316992i	0.875031	+	0.484067i	$0.160841\pi$
$830$	1657.39	−	2870.69i	0.0693120	−	0.120052i
$831$	−14282.7			−0.596224
$832$	6129.54	−	17782.5i	0.255413	−	0.740983i
$833$	5887.77			0.244897
$834$	−3839.33	+	6649.92i	−0.159407	+	0.276101i
$835$	−1256.98	+	2177.15i	−0.0520951	+	0.0902314i
$836$	−2872.26	−	4974.90i	−0.118827	−	0.205814i
$837$	−9191.97			−0.379595
$838$	−687.020	−	1189.95i	−0.0283207	−	0.0490528i
$839$	−5319.00	−	9212.78i	−0.218871	−	0.379095i	0.735592	−	0.677424i	$-0.236904\pi$
$839$	−5319.00	−	9212.78i	−0.218871	−	0.379095i	−0.954463	+	0.298330i	$0.903571\pi$
$840$	6877.61			0.282500
$841$	−10734.8	−	18593.2i	−0.440150	−	0.762362i
$842$	459.000	−	795.011i	0.0187864	−	0.0325391i
$843$	13897.8	−	24071.7i	0.567812	−	0.983479i
$844$	−12238.9			−0.499146
$845$	8651.86	+	6768.72i	0.352228	+	0.275563i
$846$	5294.34			0.215157
$847$	14383.9	−	24913.6i	0.583514	−	1.01068i
$848$	12416.2	−	21505.4i	0.502799	−	0.870873i
$849$	21403.2	+	37071.4i	0.865200	+	1.49857i
$850$	445.718			0.0179859
$851$	1128.62	+	1954.83i	0.0454625	+	0.0787434i
$852$	4935.23	+	8548.07i	0.198449	+	0.343723i
$853$	36699.3			1.47311			0.736554	−	0.676379i	$-0.236452\pi$
$853$	36699.3			1.47311			0.736554	+	0.676379i	$0.236452\pi$
$854$	440.761	+	763.421i	0.0176610	+	0.0305898i
$855$	−4862.61	+	8422.29i	−0.194500	+	0.336884i
$856$	−5215.89	+	9034.19i	−0.208266	+	0.360727i
$857$	−9154.44			−0.364889			−0.182444	−	0.983216i	$-0.558401\pi$
$857$	−9154.44			−0.364889			−0.182444	+	0.983216i	$0.558401\pi$
$858$	−500.553	+	1452.16i	−0.0199168	+	0.0577810i
$859$	22184.1			0.881156			0.440578	−	0.897714i	$-0.354774\pi$
$859$	22184.1			0.881156			0.440578	+	0.897714i	$0.354774\pi$
$860$	7332.68	−	12700.6i	0.290747	−	0.503588i
$861$	6892.93	−	11938.9i	0.272834	−	0.472563i
$862$	−1104.10	−	1912.36i	−0.0436264	−	0.0755631i
$863$	−44982.7			−1.77431			−0.887155	−	0.461472i	$-0.847321\pi$
$863$	−44982.7			−1.77431			−0.887155	+	0.461472i	$0.847321\pi$
$864$	1638.13	+	2837.32i	0.0645026	+	0.111722i
$865$	−5611.84	−	9720.00i	−0.220588	−	0.382069i
$866$	925.966			0.0363344
$867$	13498.5	+	23380.1i	0.528759	+	0.915837i
$868$	24607.9	−	42622.1i	0.962265	−	1.66669i
$869$	−3949.87	+	6841.38i	−0.154189	+	0.267063i
$870$	−4100.92			−0.159809
$871$	−6335.86	−	7293.40i	−0.246478	−	0.283729i
$872$	−4315.05			−0.167576
$873$	−6046.15	+	10472.2i	−0.234400	+	0.405992i
$874$	−195.857	+	339.235i	−0.00758006	+	0.0131291i
$875$	1429.48	+	2475.93i	0.0552288	+	0.0956590i
$876$	−10200.8			−0.393440
$877$	−8308.49	−	14390.7i	−0.319906	−	0.554094i	0.660562	−	0.750772i	$-0.270318\pi$
$877$	−8308.49	−	14390.7i	−0.319906	−	0.554094i	−0.980468	+	0.196678i	$0.936985\pi$
$878$	−1780.06	−	3083.15i	−0.0684215	−	0.118509i
$879$	−25173.9			−0.965979
$880$	1218.17	+	2109.94i	0.0466643	+	0.0808250i
$881$	−12867.1	+	22286.4i	−0.492058	+	0.852269i	−0.999958	−	0.00914666i	$-0.997088\pi$
$881$	−12867.1	+	22286.4i	−0.492058	+	0.852269i	0.507900	+	0.861416i	$0.330422\pi$
$882$	−1096.01	+	1898.34i	−0.0418419	+	0.0724723i
$883$	18857.6			0.718697			0.359349	−	0.933203i	$-0.382999\pi$
$883$	18857.6			0.718697			0.359349	+	0.933203i	$0.382999\pi$
$884$	7739.91	+	8909.65i	0.294481	+	0.338986i
$885$	−26303.7			−0.999082
$886$	270.718	−	468.897i	0.0102652	−	0.0177798i
$887$	18035.3	−	31238.1i	0.682713	−	1.18249i	−0.291437	−	0.956590i	$-0.594133\pi$
$887$	18035.3	−	31238.1i	0.682713	−	1.18249i	0.974150	−	0.225903i	$-0.0725334\pi$
$888$	8237.62	+	14268.0i	0.311302	+	0.539192i
$889$	55763.5			2.10377
$890$	−26.9432	−	46.6670i	−0.00101476	−	0.00175762i
$891$	3566.01	+	6176.51i	0.134081	+	0.232234i
$892$	21953.7			0.824063
$893$	18959.2	+	32838.3i	0.710466	+	1.23056i
$894$	66.9908	−	116.031i	0.00250616	−	0.00434080i
$895$	−7752.06	+	13427.0i	−0.289523	+	0.501468i
$896$	−23224.9			−0.865949
$897$	−2662.52	+	516.636i	−0.0991071	+	0.0192308i
$898$	−4798.16			−0.178304
$899$	−29912.5	+	51810.0i	−1.10972	+	1.92209i
$900$	2148.49	−	3721.29i	0.0795736	−	0.137826i
$901$	7126.98	+	12344.3i	0.263523	+	0.456435i
$902$	−400.535			−0.0147853
$903$	30580.4	+	52966.9i	1.12697	+	1.95197i
$904$	5615.52	+	9726.37i	0.206603	+	0.357847i
$905$	−372.015			−0.0136643
$906$	4761.00	+	8246.29i	0.174584	+	0.302389i
$907$	14628.8	−	25337.9i	0.535548	−	0.927597i	−0.463589	−	0.886051i	$-0.653438\pi$
$907$	14628.8	−	25337.9i	0.535548	−	0.927597i	0.999137	−	0.0415459i	$-0.0132283\pi$
$908$	14491.7	−	25100.4i	0.529652	−	0.917384i
$909$	27804.9			1.01456
$910$	952.687	−	2763.86i	0.0347047	−	0.100683i
$911$	10407.8			0.378512			0.189256	−	0.981928i	$-0.439392\pi$
$911$	10407.8			0.378512			0.189256	+	0.981928i	$0.439392\pi$
$912$	17429.6	−	30189.0i	0.632843	−	1.09612i
$913$	−5200.23	+	9007.05i	−0.188502	+	0.326495i
$914$	1800.25	+	3118.12i	0.0651498	+	0.112843i
$915$	2481.31			0.0896498
$916$	−8508.78	−	14737.6i	−0.306919	−	0.531599i
$917$	21213.0	+	36742.0i	0.763920	+	1.32315i
$918$	−586.620			−0.0210908
$919$	−6792.91	−	11765.7i	−0.243827	−	0.422321i	0.717974	−	0.696070i	$-0.245070\pi$
$919$	−6792.91	−	11765.7i	−0.243827	−	0.422321i	−0.961801	+	0.273749i	$0.911736\pi$
$920$	176.417	−	305.562i	0.00632205	−	0.0109501i
$921$	10336.6	−	17903.5i	0.369817	−	0.640543i
$922$	9249.25			0.330377
$923$	8396.63	−	1629.28i	0.299435	−	0.0581024i
$924$	−10585.2			−0.376869
$925$	−3424.30	+	5931.06i	−0.121719	+	0.210824i
$926$	−1364.08	+	2362.66i	−0.0484087	+	0.0838464i
$927$	−4903.02	−	8492.28i	−0.173718	−	0.300888i
$928$	21323.2			0.754276
$929$	8073.16	+	13983.1i	0.285115	+	0.493833i	0.972637	−	0.232330i	$-0.0746349\pi$
$929$	8073.16	+	13983.1i	0.285115	+	0.493833i	−0.687522	+	0.726163i	$0.741302\pi$
$930$	2674.93	+	4633.12i	0.0943167	+	0.163361i
$931$	−15699.4			−0.552661
$932$	−5391.66	−	9338.63i	−0.189495	−	0.328216i
$933$	−28326.0	+	49062.1i	−0.993947	+	1.72157i
$934$	−244.527	+	423.533i	−0.00856655	+	0.0148377i
$935$	−1398.48			−0.0489147
$936$	−8793.48	+	1706.29i	−0.307077	+	0.0595852i
$937$	4077.89			0.142176			0.0710880	−	0.997470i	$-0.477353\pi$
$937$	4077.89			0.142176			0.0710880	+	0.997470i	$0.477353\pi$
$938$	−1285.56	+	2226.65i	−0.0447494	+	0.0775083i
$939$	21389.6	−	37047.8i	0.743368	−	1.28755i
$940$	−8376.92	−	14509.2i	−0.290665	−	0.503446i
$941$	−13410.0			−0.464562			−0.232281	−	0.972649i	$-0.574619\pi$
$941$	−13410.0			−0.464562			−0.232281	+	0.972649i	$0.574619\pi$
$942$	−6362.00	−	11019.3i	−0.220048	−	0.381134i
$943$	−353.619	−	612.486i	−0.0122115	−	0.0211509i
$944$	42662.7			1.47092
$945$	−1881.37	−	3258.62i	−0.0647628	−	0.112172i
$946$	888.486	−	1538.90i	0.0305361	−	0.0528901i
$947$	8581.66	−	14863.9i	0.294474	−	0.510043i	−0.680389	−	0.732852i	$-0.738189\pi$
$947$	8581.66	−	14863.9i	0.294474	−	0.510043i	0.974862	+	0.222808i	$0.0715223\pi$
$948$	−49940.8			−1.71097
$949$	−2880.60	+	8356.96i	−0.0985334	+	0.285857i
$950$	−1188.48			−0.0405890
$951$	−7890.44	+	13666.6i	−0.269048	+	0.466005i
$952$	3201.53	−	5545.22i	0.108994	−	0.188783i
$953$	−16308.2	−	28246.7i	−0.554329	−	0.960126i	−0.997955	−	0.0639138i	$-0.979642\pi$
$953$	−16308.2	−	28246.7i	−0.554329	−	0.960126i	0.443627	−	0.896212i	$-0.353692\pi$
$954$	−5306.76			−0.180097
$955$	−12168.3	−	21076.1i	−0.412310	−	0.714142i
$956$	−608.620	−	1054.16i	−0.0205902	−	0.0356632i
$957$	12867.0			0.434620
$958$	3989.51	+	6910.04i	0.134546	+	0.233041i
$959$	32794.2	−	56801.3i	1.10426	−	1.91263i
$960$	−7045.07	+	12202.4i	−0.236853	+	0.410241i
$961$	48254.1			1.61975
$962$	6874.85	−	1334.00i	0.230410	−	0.0447087i
$963$	−27180.9			−0.909547
$964$	10281.5	−	17808.1i	0.343512	−	0.594980i
$965$	617.817	−	1070.09i	0.0206096	−	0.0356968i
$966$	360.898	+	625.094i	0.0120204	+	0.0208199i
$967$	−48167.6			−1.60183			−0.800913	−	0.598781i	$-0.795652\pi$
$967$	−48167.6			−1.60183			−0.800913	+	0.598781i	$0.795652\pi$
$968$	−5385.94	−	9328.72i	−0.178833	−	0.309748i
$969$	10004.7	+	17328.7i	0.331681	+	0.574488i
$970$	−1477.76			−0.0489153
$971$	−9780.88	−	16941.0i	−0.323258	−	0.559899i	0.657900	−	0.753105i	$-0.271445\pi$
$971$	−9780.88	−	16941.0i	−0.323258	−	0.559899i	−0.981158	+	0.193206i	$0.938111\pi$
$972$	−19122.3	+	33120.8i	−0.631016	+	1.09295i
$973$	−22927.3	+	39711.2i	−0.755411	+	1.30841i
$974$	−3202.07			−0.105340
$975$	−5396.62	−	6212.21i	−0.177262	−	0.204051i
$976$	−4024.51			−0.131989
$977$	−12478.4	+	21613.2i	−0.408616	+	0.707744i	−0.994735	−	0.102481i	$-0.967322\pi$
$977$	−12478.4	+	21613.2i	−0.408616	+	0.707744i	0.586119	+	0.810225i	$0.300655\pi$
$978$	−1197.67	+	2074.42i	−0.0391587	+	0.0678249i
$979$	84.5367	+	146.422i	0.00275976	+	0.00478005i
$980$	6936.60			0.226104
$981$	−5621.62	−	9736.93i	−0.182961	−	0.316897i
$982$	−2287.87	−	3962.70i	−0.0743470	−	0.128773i
$983$	5283.69			0.171438			0.0857190	−	0.996319i	$-0.472681\pi$
$983$	5283.69			0.171438			0.0857190	+	0.996319i	$0.472681\pi$
$984$	−2581.01	−	4470.44i	−0.0836174	−	0.144830i
$985$	8784.43	−	15215.1i	0.284157	−	0.492175i
$986$	−1908.98	+	3306.45i	−0.0616575	+	0.106794i
$987$	69870.7			2.25330
$988$	−20638.1	−	23757.1i	−0.664559	−	0.764994i
$989$	3137.66			0.100881
$990$	260.328	−	450.901i	0.00835734	−	0.0144753i
$991$	−25457.4	+	44093.6i	−0.816026	+	1.41340i	0.0925629	+	0.995707i	$0.470494\pi$
$991$	−25457.4	+	44093.6i	−0.816026	+	1.41340i	−0.908589	+	0.417692i	$0.862839\pi$
$992$	−13908.6	−	24090.5i	−0.445161	−	0.771041i
$993$	65785.0			2.10234
$994$	−1138.14	−	1971.32i	−0.0363175	−	0.0629038i
$995$	−8402.48	−	14553.5i	−0.267715	−	0.463696i
$996$	−65749.8			−2.09173
$997$	−17785.3	−	30805.1i	−0.564962	−	0.978542i	−0.997053	−	0.0767126i	$-0.975558\pi$
$997$	−17785.3	−	30805.1i	−0.564962	−	0.978542i	0.432092	−	0.901830i	$-0.357776\pi$
$998$	−3475.57	+	6019.87i	−0.110238	+	0.190937i
$999$	4506.79	−	7805.99i	0.142731	−	0.247218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.4.e.a.61.4	yes	14
13.3	even	3	inner	65.4.e.a.16.4	✓	14
13.4	even	6		845.4.a.h.1.4		7
13.9	even	3		845.4.a.k.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.e.a.16.4	✓	14	13.3	even	3	inner
65.4.e.a.61.4	yes	14	1.1	even	1	trivial
845.4.a.h.1.4		7	13.4	even	6
845.4.a.k.1.4		7	13.9	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	65.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.272699 + 0.472328i) q^{2} +(-3.51122 + 6.08161i) q^{3} +(3.85127 + 6.67060i) q^{4} -5.00000 q^{5} +(-1.91501 - 3.31689i) q^{6} +(-11.4358 - 19.8074i) q^{7} -8.56412 q^{8} +(-11.1573 - 19.3250i) q^{9} +O(q^{10})\)	\(q+(-0.272699 + 0.472328i) q^{2} +(-3.51122 + 6.08161i) q^{3} +(3.85127 + 6.67060i) q^{4} -5.00000 q^{5} +(-1.91501 - 3.31689i) q^{6} +(-11.4358 - 19.8074i) q^{7} -8.56412 q^{8} +(-11.1573 - 19.3250i) q^{9} +(1.36349 - 2.36164i) q^{10} +(-4.27808 + 7.40986i) q^{11} -54.0906 q^{12} +(-15.2746 + 44.3135i) q^{13} +12.4741 q^{14} +(17.5561 - 30.4080i) q^{15} +(-28.4747 + 49.3197i) q^{16} +(-16.3447 - 28.3099i) q^{17} +12.1703 q^{18} +(43.5823 + 75.4868i) q^{19} +(-19.2564 - 33.3530i) q^{20} +160.615 q^{21} +(-2.33325 - 4.04131i) q^{22} +(4.11990 - 7.13588i) q^{23} +(30.0705 - 52.0836i) q^{24} +25.0000 q^{25} +(-16.7651 - 19.2988i) q^{26} -32.9030 q^{27} +(88.0849 - 152.568i) q^{28} +(-107.073 + 185.456i) q^{29} +(9.57504 + 16.5844i) q^{30} +279.366 q^{31} +(-49.7865 - 86.2328i) q^{32} +(-30.0426 - 52.0352i) q^{33} +17.8287 q^{34} +(57.1791 + 99.0371i) q^{35} +(85.9395 - 148.852i) q^{36} +(-136.972 + 237.242i) q^{37} -47.5394 q^{38} +(-215.865 - 248.489i) q^{39} +42.8206 q^{40} +(42.9160 - 74.3326i) q^{41} +(-43.7994 + 75.8627i) q^{42} +(190.396 + 329.776i) q^{43} -65.9042 q^{44} +(55.7865 + 96.6250i) q^{45} +(2.24698 + 3.89189i) q^{46} +435.021 q^{47} +(-199.962 - 346.344i) q^{48} +(-90.0560 + 155.982i) q^{49} +(-6.81746 + 11.8082i) q^{50} +229.560 q^{51} +(-354.424 + 68.7725i) q^{52} -436.042 q^{53} +(8.97261 - 15.5410i) q^{54} +(21.3904 - 37.0493i) q^{55} +(97.9377 + 169.633i) q^{56} -612.108 q^{57} +(-58.3974 - 101.147i) q^{58} +(-374.566 - 648.767i) q^{59} +270.453 q^{60} +(35.3340 + 61.2003i) q^{61} +(-76.1826 + 131.952i) q^{62} +(-255.186 + 441.994i) q^{63} -401.289 q^{64} +(76.3731 - 221.567i) q^{65} +32.7702 q^{66} +(-103.058 + 178.502i) q^{67} +(125.896 - 218.058i) q^{68} +(28.9317 + 50.1112i) q^{69} -62.3706 q^{70} +(-91.2401 - 158.033i) q^{71} +(95.5524 + 165.502i) q^{72} +188.587 q^{73} +(-74.7041 - 129.391i) q^{74} +(-87.7804 + 152.040i) q^{75} +(-335.695 + 581.440i) q^{76} +195.694 q^{77} +(176.234 - 34.1965i) q^{78} +923.280 q^{79} +(142.374 - 246.599i) q^{80} +(416.777 - 721.878i) q^{81} +(23.4062 + 40.5408i) q^{82} +1215.55 q^{83} +(618.570 + 1071.40i) q^{84} +(81.7237 + 141.550i) q^{85} -207.683 q^{86} +(-751.914 - 1302.35i) q^{87} +(36.6380 - 63.4589i) q^{88} +(9.88021 - 17.1130i) q^{89} -60.8515 q^{90} +(1052.41 - 204.210i) q^{91} +63.4674 q^{92} +(-980.913 + 1698.99i) q^{93} +(-118.630 + 205.472i) q^{94} +(-217.912 - 377.434i) q^{95} +699.245 q^{96} +(-270.951 - 469.300i) q^{97} +(-49.1163 - 85.0719i) q^{98} +190.927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9} + 10 q^{10} - 87 q^{11} - 158 q^{12} + 123 q^{13} + 132 q^{14} - 20 q^{15} + 134 q^{16} + 114 q^{17} + 414 q^{18} - 245 q^{19} + 150 q^{20} - 76 q^{21} - 338 q^{22} + 74 q^{23} - 334 q^{24} + 350 q^{25} + 243 q^{26} - 884 q^{27} - 230 q^{28} + 88 q^{29} + 115 q^{30} + 1000 q^{31} - 80 q^{32} + 194 q^{33} + 854 q^{34} + 35 q^{35} - 425 q^{36} - 633 q^{37} - 596 q^{38} + 970 q^{39} - 210 q^{40} - 162 q^{41} + 1439 q^{42} + 280 q^{43} + 440 q^{44} + 435 q^{45} + 11 q^{46} + 950 q^{47} - 2281 q^{48} - 1694 q^{49} - 50 q^{50} - 860 q^{51} - 956 q^{52} - 1206 q^{53} - 51 q^{54} + 435 q^{55} + 1277 q^{56} + 916 q^{57} + 1213 q^{58} - 1410 q^{59} + 790 q^{60} - 412 q^{61} + 56 q^{62} - 1241 q^{63} - 2358 q^{64} - 615 q^{65} + 4346 q^{66} - 1398 q^{67} + 493 q^{68} - 1080 q^{69} - 660 q^{70} + 584 q^{71} - 1545 q^{72} + 5076 q^{73} - 3840 q^{74} + 100 q^{75} - 3292 q^{76} - 5506 q^{77} + 1179 q^{78} + 928 q^{79} - 670 q^{80} + 473 q^{81} + 1583 q^{82} + 932 q^{83} + 3081 q^{84} - 570 q^{85} + 9858 q^{86} + 282 q^{87} - 3389 q^{88} - 443 q^{89} - 2070 q^{90} + 487 q^{91} + 6182 q^{92} + 2116 q^{93} - 2017 q^{94} + 1225 q^{95} + 954 q^{96} + 1870 q^{97} - 1364 q^{98} + 11378 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9 + 10 * q^10 - 87 * q^11 - 158 * q^12 + 123 * q^13 + 132 * q^14 - 20 * q^15 + 134 * q^16 + 114 * q^17 + 414 * q^18 - 245 * q^19 + 150 * q^20 - 76 * q^21 - 338 * q^22 + 74 * q^23 - 334 * q^24 + 350 * q^25 + 243 * q^26 - 884 * q^27 - 230 * q^28 + 88 * q^29 + 115 * q^30 + 1000 * q^31 - 80 * q^32 + 194 * q^33 + 854 * q^34 + 35 * q^35 - 425 * q^36 - 633 * q^37 - 596 * q^38 + 970 * q^39 - 210 * q^40 - 162 * q^41 + 1439 * q^42 + 280 * q^43 + 440 * q^44 + 435 * q^45 + 11 * q^46 + 950 * q^47 - 2281 * q^48 - 1694 * q^49 - 50 * q^50 - 860 * q^51 - 956 * q^52 - 1206 * q^53 - 51 * q^54 + 435 * q^55 + 1277 * q^56 + 916 * q^57 + 1213 * q^58 - 1410 * q^59 + 790 * q^60 - 412 * q^61 + 56 * q^62 - 1241 * q^63 - 2358 * q^64 - 615 * q^65 + 4346 * q^66 - 1398 * q^67 + 493 * q^68 - 1080 * q^69 - 660 * q^70 + 584 * q^71 - 1545 * q^72 + 5076 * q^73 - 3840 * q^74 + 100 * q^75 - 3292 * q^76 - 5506 * q^77 + 1179 * q^78 + 928 * q^79 - 670 * q^80 + 473 * q^81 + 1583 * q^82 + 932 * q^83 + 3081 * q^84 - 570 * q^85 + 9858 * q^86 + 282 * q^87 - 3389 * q^88 - 443 * q^89 - 2070 * q^90 + 487 * q^91 + 6182 * q^92 + 2116 * q^93 - 2017 * q^94 + 1225 * q^95 + 954 * q^96 + 1870 * q^97 - 1364 * q^98 + 11378 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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