LMFDB - Embedded newform 37.3.d.a.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,3,Mod(6,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	37.d (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:	$1.00817697813$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 18 x^{10} + 8 x^{9} + 42 x^{8} - 268 x^{7} + 884 x^{6} + 704 x^{5} + 761 x^{4} + \cdots + 16 $ x^12 - 6x^11 + 18x^10 + 8x^9 + 42x^8 - 268x^7 + 884x^6 + 704x^5 + 761x^4 - 2054x^3 + 3042x^2 + 312*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.2
Root			$-1.15759 - 1.15759i$ of defining polynomial
Character	$\chi$	$=$	37.31
Dual form			37.3.d.a.6.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15759 - 2.15759i) q^{2} +5.58276i q^{3} +5.31039i q^{4} +(-2.97944 + 2.97944i) q^{5} +(12.0453 - 12.0453i) q^{6} +8.27885 q^{7} +(2.82728 - 2.82728i) q^{8} -22.1672 q^{9} +O(q^{10})$	\(q+(-2.15759 - 2.15759i) q^{2} +5.58276i q^{3} +5.31039i q^{4} +(-2.97944 + 2.97944i) q^{5} +(12.0453 - 12.0453i) q^{6} +8.27885 q^{7} +(2.82728 - 2.82728i) q^{8} -22.1672 q^{9} +12.8568 q^{10} +6.70342i q^{11} -29.6466 q^{12} +(4.81406 - 4.81406i) q^{13} +(-17.8624 - 17.8624i) q^{14} +(-16.6335 - 16.6335i) q^{15} +9.04132 q^{16} +(8.97570 - 8.97570i) q^{17} +(47.8277 + 47.8277i) q^{18} +(-2.58831 + 2.58831i) q^{19} +(-15.8220 - 15.8220i) q^{20} +46.2188i q^{21} +(14.4632 - 14.4632i) q^{22} +(22.5883 - 22.5883i) q^{23} +(15.7840 + 15.7840i) q^{24} +7.24587i q^{25} -20.7735 q^{26} -73.5094i q^{27} +43.9639i q^{28} +(22.9788 + 22.9788i) q^{29} +71.7765i q^{30} +(-7.78397 - 7.78397i) q^{31} +(-30.8166 - 30.8166i) q^{32} -37.4236 q^{33} -38.7317 q^{34} +(-24.6663 + 24.6663i) q^{35} -117.717i q^{36} +(6.96809 + 36.3379i) q^{37} +11.1690 q^{38} +(26.8757 + 26.8757i) q^{39} +16.8474i q^{40} +2.70784i q^{41} +(99.7213 - 99.7213i) q^{42} +(-0.467035 + 0.467035i) q^{43} -35.5978 q^{44} +(66.0459 - 66.0459i) q^{45} -97.4727 q^{46} -4.93710 q^{47} +50.4755i q^{48} +19.5394 q^{49} +(15.6336 - 15.6336i) q^{50} +(50.1092 + 50.1092i) q^{51} +(25.5645 + 25.5645i) q^{52} +21.4230 q^{53} +(-158.603 + 158.603i) q^{54} +(-19.9725 - 19.9725i) q^{55} +(23.4066 - 23.4066i) q^{56} +(-14.4499 - 14.4499i) q^{57} -99.1577i q^{58} +(15.2646 - 15.2646i) q^{59} +(88.3303 - 88.3303i) q^{60} +(-53.6065 - 53.6065i) q^{61} +33.5892i q^{62} -183.519 q^{63} +96.8139i q^{64} +28.6864i q^{65} +(80.7448 + 80.7448i) q^{66} -64.0688i q^{67} +(47.6644 + 47.6644i) q^{68} +(126.105 + 126.105i) q^{69} +106.440 q^{70} -79.3933 q^{71} +(-62.6730 + 62.6730i) q^{72} -80.3695i q^{73} +(63.3681 - 93.4367i) q^{74} -40.4520 q^{75} +(-13.7449 - 13.7449i) q^{76} +55.4967i q^{77} -115.974i q^{78} +(30.6038 - 30.6038i) q^{79} +(-26.9381 + 26.9381i) q^{80} +210.880 q^{81} +(5.84240 - 5.84240i) q^{82} +144.407 q^{83} -245.440 q^{84} +53.4851i q^{85} +2.01534 q^{86} +(-128.285 + 128.285i) q^{87} +(18.9525 + 18.9525i) q^{88} +(-105.839 - 105.839i) q^{89} -285.000 q^{90} +(39.8549 - 39.8549i) q^{91} +(119.953 + 119.953i) q^{92} +(43.4560 - 43.4560i) q^{93} +(10.6522 + 10.6522i) q^{94} -15.4234i q^{95} +(172.042 - 172.042i) q^{96} +(-57.6988 + 57.6988i) q^{97} +(-42.1580 - 42.1580i) q^{98} -148.596i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9	$ 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9} - 16 q^{10} + 64 q^{12} + 14 q^{13} - 70 q^{14} - 2 q^{15} - 96 q^{16} + 2 q^{17} + 132 q^{18} + 14 q^{19} - 24 q^{20} + 22 q^{22} + 56 q^{23} - 84 q^{24} - 48 q^{26} + 60 q^{29} + 72 q^{31} + 208 q^{32} + 56 q^{33} + 112 q^{34} - 154 q^{35} - 66 q^{37} - 336 q^{38} - 46 q^{39} + 90 q^{42} + 70 q^{43} + 80 q^{44} + 232 q^{45} - 424 q^{46} - 384 q^{47} + 144 q^{49} - 34 q^{50} - 126 q^{51} + 328 q^{52} - 56 q^{53} - 194 q^{54} + 70 q^{55} + 16 q^{56} - 94 q^{57} + 184 q^{59} + 276 q^{60} + 132 q^{61} - 400 q^{63} + 614 q^{66} + 116 q^{68} + 368 q^{69} + 556 q^{70} + 68 q^{71} - 692 q^{72} - 382 q^{74} + 116 q^{75} + 12 q^{76} - 2 q^{79} + 4 q^{80} - 76 q^{81} + 374 q^{82} + 108 q^{83} - 1436 q^{84} + 140 q^{86} - 420 q^{87} - 788 q^{88} + 278 q^{89} - 664 q^{90} - 450 q^{91} + 652 q^{92} + 584 q^{93} + 118 q^{94} + 1584 q^{96} - 244 q^{97} + 416 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9 - 16 * q^10 + 64 * q^12 + 14 * q^13 - 70 * q^14 - 2 * q^15 - 96 * q^16 + 2 * q^17 + 132 * q^18 + 14 * q^19 - 24 * q^20 + 22 * q^22 + 56 * q^23 - 84 * q^24 - 48 * q^26 + 60 * q^29 + 72 * q^31 + 208 * q^32 + 56 * q^33 + 112 * q^34 - 154 * q^35 - 66 * q^37 - 336 * q^38 - 46 * q^39 + 90 * q^42 + 70 * q^43 + 80 * q^44 + 232 * q^45 - 424 * q^46 - 384 * q^47 + 144 * q^49 - 34 * q^50 - 126 * q^51 + 328 * q^52 - 56 * q^53 - 194 * q^54 + 70 * q^55 + 16 * q^56 - 94 * q^57 + 184 * q^59 + 276 * q^60 + 132 * q^61 - 400 * q^63 + 614 * q^66 + 116 * q^68 + 368 * q^69 + 556 * q^70 + 68 * q^71 - 692 * q^72 - 382 * q^74 + 116 * q^75 + 12 * q^76 - 2 * q^79 + 4 * q^80 - 76 * q^81 + 374 * q^82 + 108 * q^83 - 1436 * q^84 + 140 * q^86 - 420 * q^87 - 788 * q^88 + 278 * q^89 - 664 * q^90 - 450 * q^91 + 652 * q^92 + 584 * q^93 + 118 * q^94 + 1584 * q^96 - 244 * q^97 + 416 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.15759	−	2.15759i	−1.07879	−	1.07879i	−0.996618	−	0.0821773i	$-0.973813\pi$
$2$	−2.15759	−	2.15759i	−1.07879	−	1.07879i	−0.0821773	−	0.996618i	$-0.526187\pi$
$3$			5.58276i			1.86092i	0.366393	+	0.930460i	$0.380592\pi$
$3$			5.58276i			1.86092i	−0.366393	+	0.930460i	$0.619408\pi$
$4$			5.31039i			1.32760i
$5$	−2.97944	+	2.97944i	−0.595888	+	0.595888i	−0.939216	−	0.343328i	$-0.888446\pi$
$5$	−2.97944	+	2.97944i	−0.595888	+	0.595888i	0.343328	+	0.939216i	$0.388446\pi$
$6$	12.0453	−	12.0453i	2.00755	−	2.00755i
$7$	8.27885			1.18269			0.591347	−	0.806418i	$-0.298597\pi$
$7$	8.27885			1.18269			0.591347	+	0.806418i	$0.298597\pi$
$8$	2.82728	−	2.82728i	0.353410	−	0.353410i
$9$	−22.1672			−2.46302
$10$	12.8568			1.28568
$11$			6.70342i			0.609402i	0.952448	+	0.304701i	$0.0985566\pi$
$11$			6.70342i			0.609402i	−0.952448	+	0.304701i	$0.901443\pi$
$12$	−29.6466			−2.47055
$13$	4.81406	−	4.81406i	0.370312	−	0.370312i	−0.497279	−	0.867591i	$-0.665667\pi$
$13$	4.81406	−	4.81406i	0.370312	−	0.370312i	0.867591	+	0.497279i	$0.165667\pi$
$14$	−17.8624	−	17.8624i	−1.27588	−	1.27588i
$15$	−16.6335	−	16.6335i	−1.10890	−	1.10890i
$16$	9.04132			0.565083
$17$	8.97570	−	8.97570i	0.527982	−	0.527982i	−0.391988	−	0.919970i	$-0.628213\pi$
$17$	8.97570	−	8.97570i	0.527982	−	0.527982i	0.919970	+	0.391988i	$0.128213\pi$
$18$	47.8277	+	47.8277i	2.65710	+	2.65710i
$19$	−2.58831	+	2.58831i	−0.136227	+	0.136227i	−0.771932	−	0.635705i	$-0.780709\pi$
$19$	−2.58831	+	2.58831i	−0.136227	+	0.136227i	0.635705	+	0.771932i	$0.280709\pi$
$20$	−15.8220	−	15.8220i	−0.791099	−	0.791099i
$21$			46.2188i			2.20090i
$22$	14.4632	−	14.4632i	0.657420	−	0.657420i
$23$	22.5883	−	22.5883i	0.982101	−	0.982101i	−0.0177414	−	0.999843i	$-0.505648\pi$
$23$	22.5883	−	22.5883i	0.982101	−	0.982101i	0.999843	+	0.0177414i	$0.00564756\pi$
$24$	15.7840	+	15.7840i	0.657668	+	0.657668i
$25$			7.24587i			0.289835i
$26$	−20.7735			−0.798981
$27$		−	73.5094i		−	2.72257i
$28$			43.9639i			1.57014i
$29$	22.9788	+	22.9788i	0.792373	+	0.792373i	0.981879	−	0.189506i	$-0.0606888\pi$
$29$	22.9788	+	22.9788i	0.792373	+	0.792373i	−0.189506	+	0.981879i	$0.560689\pi$
$30$			71.7765i			2.39255i
$31$	−7.78397	−	7.78397i	−0.251096	−	0.251096i	0.570324	−	0.821420i	$-0.306818\pi$
$31$	−7.78397	−	7.78397i	−0.251096	−	0.251096i	−0.821420	+	0.570324i	$0.806818\pi$
$32$	−30.8166	−	30.8166i	−0.963019	−	0.963019i
$33$	−37.4236			−1.13405
$34$	−38.7317			−1.13917
$35$	−24.6663	+	24.6663i	−0.704753	+	0.704753i
$36$		−	117.717i		−	3.26990i
$37$	6.96809	+	36.3379i	0.188327	+	0.982106i
$37$	6.96809	+	36.3379i	0.188327	+	0.982106i
$38$	11.1690			0.293921
$39$	26.8757	+	26.8757i	0.689121	+	0.689121i
$40$			16.8474i			0.421186i
$41$			2.70784i			0.0660448i	0.999455	+	0.0330224i	$0.0105133\pi$
$41$			2.70784i			0.0660448i	−0.999455	+	0.0330224i	$0.989487\pi$
$42$	99.7213	−	99.7213i	2.37432	−	2.37432i
$43$	−0.467035	+	0.467035i	−0.0108613	+	0.0108613i	−0.712517	−	0.701655i	$-0.752445\pi$
$43$	−0.467035	+	0.467035i	−0.0108613	+	0.0108613i	0.701655	+	0.712517i	$0.252445\pi$
$44$	−35.5978			−0.809041
$45$	66.0459	−	66.0459i	1.46769	−	1.46769i
$46$	−97.4727			−2.11897
$47$	−4.93710			−0.105045			−0.0525223	−	0.998620i	$-0.516726\pi$
$47$	−4.93710			−0.105045			−0.0525223	+	0.998620i	$0.516726\pi$
$48$			50.4755i			1.05157i
$49$	19.5394			0.398763
$50$	15.6336	−	15.6336i	0.312672	−	0.312672i
$51$	50.1092	+	50.1092i	0.982533	+	0.982533i
$52$	25.5645	+	25.5645i	0.491625	+	0.491625i
$53$	21.4230			0.404208			0.202104	−	0.979364i	$-0.435222\pi$
$53$	21.4230			0.404208			0.202104	+	0.979364i	$0.435222\pi$
$54$	−158.603	+	158.603i	−2.93709	+	2.93709i
$55$	−19.9725	−	19.9725i	−0.363135	−	0.363135i
$56$	23.4066	−	23.4066i	0.417976	−	0.417976i
$57$	−14.4499	−	14.4499i	−0.253507	−	0.253507i
$58$		−	99.1577i		−	1.70962i
$59$	15.2646	−	15.2646i	0.258722	−	0.258722i	−0.565812	−	0.824534i	$-0.691437\pi$
$59$	15.2646	−	15.2646i	0.258722	−	0.258722i	0.824534	+	0.565812i	$0.191437\pi$
$60$	88.3303	−	88.3303i	1.47217	−	1.47217i
$61$	−53.6065	−	53.6065i	−0.878795	−	0.878795i	0.114615	−	0.993410i	$-0.463436\pi$
$61$	−53.6065	−	53.6065i	−0.878795	−	0.878795i	−0.993410	+	0.114615i	$0.963436\pi$
$62$			33.5892i			0.541762i
$63$	−183.519			−2.91300
$64$			96.8139i			1.51272i
$65$			28.6864i			0.441329i
$66$	80.7448	+	80.7448i	1.22341	+	1.22341i
$67$		−	64.0688i		−	0.956250i	−0.878292	−	0.478125i	$-0.841317\pi$
$67$		−	64.0688i		−	0.956250i	0.878292	−	0.478125i	$-0.158683\pi$
$68$	47.6644	+	47.6644i	0.700948	+	0.700948i
$69$	126.105	+	126.105i	1.82761	+	1.82761i
$70$	106.440			1.52057
$71$	−79.3933			−1.11822			−0.559108	−	0.829095i	$-0.688856\pi$
$71$	−79.3933			−1.11822			−0.559108	+	0.829095i	$0.688856\pi$
$72$	−62.6730	+	62.6730i	−0.870458	+	0.870458i
$73$		−	80.3695i		−	1.10095i	−0.834851	−	0.550476i	$-0.814446\pi$
$73$		−	80.3695i		−	1.10095i	0.834851	−	0.550476i	$-0.185554\pi$
$74$	63.3681	−	93.4367i	0.856325	−	1.26266i
$75$	−40.4520			−0.539360
$76$	−13.7449	−	13.7449i	−0.180854	−	0.180854i
$77$			55.4967i			0.720736i
$78$		−	115.974i		−	1.48684i
$79$	30.6038	−	30.6038i	0.387389	−	0.387389i	−0.486366	−	0.873755i	$-0.661678\pi$
$79$	30.6038	−	30.6038i	0.387389	−	0.387389i	0.873755	+	0.486366i	$0.161678\pi$
$80$	−26.9381	+	26.9381i	−0.336726	+	0.336726i
$81$	210.880			2.60346
$82$	5.84240	−	5.84240i	0.0712488	−	0.0712488i
$83$	144.407			1.73984			0.869921	−	0.493191i	$-0.164170\pi$
$83$	144.407			1.73984			0.869921	+	0.493191i	$0.164170\pi$
$84$	−245.440			−2.92190
$85$			53.4851i			0.629237i
$86$	2.01534			0.0234342
$87$	−128.285	+	128.285i	−1.47454	+	1.47454i
$88$	18.9525	+	18.9525i	0.215369	+	0.215369i
$89$	−105.839	−	105.839i	−1.18921	−	1.18921i	−0.977287	−	0.211918i	$-0.932029\pi$
$89$	−105.839	−	105.839i	−1.18921	−	1.18921i	−0.211918	−	0.977287i	$-0.567971\pi$
$90$	−285.000			−3.16666
$91$	39.8549	−	39.8549i	0.437965	−	0.437965i
$92$	119.953	+	119.953i	1.30383	+	1.30383i
$93$	43.4560	−	43.4560i	0.467269	−	0.467269i
$94$	10.6522	+	10.6522i	0.113322	+	0.113322i
$95$		−	15.4234i		−	0.162352i
$96$	172.042	−	172.042i	1.79210	−	1.79210i
$97$	−57.6988	+	57.6988i	−0.594833	+	0.594833i	−0.938933	−	0.344100i	$-0.888184\pi$
$97$	−57.6988	+	57.6988i	−0.594833	+	0.594833i	0.344100	+	0.938933i	$0.388184\pi$
$98$	−42.1580	−	42.1580i	−0.430183	−	0.430183i
$99$		−	148.596i		−	1.50097i
$100$	−38.4784			−0.384784
$101$			118.946i			1.17768i	0.808250	+	0.588840i	$0.200415\pi$
$101$			118.946i			1.17768i	−0.808250	+	0.588840i	$0.799585\pi$
$102$		−	216.230i		−	2.11990i
$103$	32.0639	+	32.0639i	0.311300	+	0.311300i	0.845413	−	0.534113i	$-0.179354\pi$
$103$	32.0639	+	32.0639i	0.311300	+	0.311300i	−0.534113	+	0.845413i	$0.679354\pi$
$104$		−	27.2214i		−	0.261744i
$105$	−137.706	−	137.706i	−1.31149	−	1.31149i
$106$	−46.2221	−	46.2221i	−0.436058	−	0.436058i
$107$	85.4810			0.798888			0.399444	−	0.916758i	$-0.369203\pi$
$107$	85.4810			0.798888			0.399444	+	0.916758i	$0.369203\pi$
$108$	390.363			3.61448
$109$	−101.148	+	101.148i	−0.927966	+	0.927966i	−0.997574	−	0.0696087i	$-0.977825\pi$
$109$	−101.148	+	101.148i	−0.927966	+	0.927966i	0.0696087	+	0.997574i	$0.477825\pi$
$110$			86.1847i			0.783498i
$111$	−202.866	+	38.9012i	−1.82762	+	0.350461i
$112$	74.8518			0.668319
$113$	−47.3027	−	47.3027i	−0.418608	−	0.418608i	0.466116	−	0.884724i	$-0.345653\pi$
$113$	−47.3027	−	47.3027i	−0.418608	−	0.418608i	−0.884724	+	0.466116i	$0.845653\pi$
$114$			62.3539i			0.546964i
$115$			134.601i			1.17044i
$116$	−122.026	+	122.026i	−1.05195	+	1.05195i
$117$	−106.714	+	106.714i	−0.912087	+	0.912087i
$118$	−65.8695			−0.558216
$119$	74.3085	−	74.3085i	0.624441	−	0.624441i
$120$	−94.0552			−0.783793
$121$	76.0641			0.628629
$122$			231.322i			1.89608i
$123$	−15.1172			−0.122904
$124$	41.3359	−	41.3359i	0.333354	−	0.333354i
$125$	−96.0746	−	96.0746i	−0.768597	−	0.768597i
$126$	395.959	+	395.959i	3.14253	+	3.14253i
$127$	158.723			1.24979			0.624893	−	0.780711i	$-0.285143\pi$
$127$	158.723			1.24979			0.624893	+	0.780711i	$0.285143\pi$
$128$	85.6182	−	85.6182i	0.668893	−	0.668893i
$129$	−2.60734	−	2.60734i	−0.0202120	−	0.0202120i
$130$	61.8934	−	61.8934i	0.476103	−	0.476103i
$131$	−25.8295	−	25.8295i	−0.197172	−	0.197172i	0.601614	−	0.798787i	$-0.294524\pi$
$131$	−25.8295	−	25.8295i	−0.197172	−	0.197172i	−0.798787	+	0.601614i	$0.794524\pi$
$132$		−	198.734i		−	1.50556i
$133$	−21.4282	+	21.4282i	−0.161114	+	0.161114i
$134$	−138.234	+	138.234i	−1.03160	+	1.03160i
$135$	219.017	+	219.017i	1.62235	+	1.62235i
$136$		−	50.7537i		−	0.373189i
$137$	183.723			1.34104			0.670522	−	0.741889i	$-0.266070\pi$
$137$	183.723			1.34104			0.670522	+	0.741889i	$0.266070\pi$
$138$		−	544.167i		−	3.94324i
$139$		−	217.572i		−	1.56526i	−0.622484	−	0.782632i	$-0.713876\pi$
$139$		−	217.572i		−	1.56526i	0.622484	−	0.782632i	$-0.286124\pi$
$140$	−130.988	−	130.988i	−0.935628	−	0.935628i
$141$		−	27.5626i		−	0.195480i
$142$	171.298	+	171.298i	1.20633	+	1.20633i
$143$	32.2707	+	32.2707i	0.225669	+	0.225669i
$144$	−200.421			−1.39181
$145$	−136.928			−0.944331
$146$	−173.405	+	173.405i	−1.18770	+	1.18770i
$147$			109.084i			0.742066i
$148$	−192.969	+	37.0033i	−1.30384	+	0.250022i
$149$	−58.5579			−0.393006			−0.196503	−	0.980503i	$-0.562959\pi$
$149$	−58.5579			−0.393006			−0.196503	+	0.980503i	$0.562959\pi$
$150$	87.2788	+	87.2788i	0.581858	+	0.581858i
$151$		−	120.877i		−	0.800508i	−0.916404	−	0.400254i	$-0.868922\pi$
$151$		−	120.877i		−	0.800508i	0.916404	−	0.400254i	$-0.131078\pi$
$152$			14.6357i			0.0962878i
$153$	−198.966	+	198.966i	−1.30043	+	1.30043i
$154$	119.739	−	119.739i	0.777526	−	0.777526i
$155$	46.3837			0.299250
$156$	−142.721	+	142.721i	−0.914875	+	0.914875i
$157$	−145.458			−0.926484			−0.463242	−	0.886232i	$-0.653314\pi$
$157$	−145.458			−0.926484			−0.463242	+	0.886232i	$0.653314\pi$
$158$	−132.061			−0.835827
$159$			119.600i			0.752199i
$160$	183.632			1.14770
$161$	187.005	−	187.005i	1.16152	−	1.16152i
$162$	−454.993	−	454.993i	−2.80860	−	2.80860i
$163$	−72.1320	−	72.1320i	−0.442527	−	0.442527i	0.450333	−	0.892861i	$-0.351305\pi$
$163$	−72.1320	−	72.1320i	−0.442527	−	0.442527i	−0.892861	+	0.450333i	$0.851305\pi$
$164$	−14.3797			−0.0876809
$165$	111.501	−	111.501i	0.675766	−	0.675766i
$166$	−311.571	−	311.571i	−1.87693	−	1.87693i
$167$	−27.1830	+	27.1830i	−0.162772	+	0.162772i	−0.783794	−	0.621021i	$-0.786718\pi$
$167$	−27.1830	+	27.1830i	−0.162772	+	0.162772i	0.621021	+	0.783794i	$0.286718\pi$
$168$	130.674	+	130.674i	0.777820	+	0.777820i
$169$			122.650i			0.725738i
$170$	115.399	−	115.399i	0.678817	−	0.678817i
$171$	57.3755	−	57.3755i	0.335529	−	0.335529i
$172$	−2.48014	−	2.48014i	−0.0144194	−	0.0144194i
$173$			14.8149i			0.0856350i	0.999083	+	0.0428175i	$0.0136334\pi$
$173$			14.8149i			0.0856350i	−0.999083	+	0.0428175i	$0.986367\pi$
$174$	553.574			3.18146
$175$			59.9875i			0.342786i
$176$			60.6078i			0.344363i
$177$	85.2186	+	85.2186i	0.481461	+	0.481461i
$178$			456.716i			2.56582i
$179$	95.8048	+	95.8048i	0.535222	+	0.535222i	0.922122	−	0.386900i	$-0.126454\pi$
$179$	95.8048	+	95.8048i	0.535222	+	0.535222i	−0.386900	+	0.922122i	$0.626454\pi$
$180$	350.729	+	350.729i	1.94850	+	1.94850i
$181$	250.452			1.38371			0.691857	−	0.722035i	$-0.256793\pi$
$181$	250.452			1.38371			0.691857	+	0.722035i	$0.256793\pi$
$182$	−171.981			−0.944950
$183$	299.272	−	299.272i	1.63537	−	1.63537i
$184$		−	127.727i		−	0.694169i
$185$	−129.028	−	87.5057i	−0.697447	−	0.473004i
$186$	−187.521			−1.00818
$187$	60.1679	+	60.1679i	0.321754	+	0.321754i
$188$		−	26.2179i		−	0.139457i
$189$		−	608.573i		−	3.21996i
$190$	−33.2774	+	33.2774i	−0.175144	+	0.175144i
$191$	159.970	−	159.970i	0.837542	−	0.837542i	−0.150993	−	0.988535i	$-0.548247\pi$
$191$	159.970	−	159.970i	0.837542	−	0.837542i	0.988535	+	0.150993i	$0.0482472\pi$
$192$	−540.489			−2.81504
$193$	−271.421	+	271.421i	−1.40633	+	1.40633i	−0.628586	+	0.777740i	$0.716366\pi$
$193$	−271.421	+	271.421i	−1.40633	+	1.40633i	−0.777740	+	0.628586i	$0.783634\pi$
$194$	248.981			1.28341
$195$	−160.149			−0.821278
$196$			103.762i			0.529396i
$197$	−35.2024			−0.178692			−0.0893462	−	0.996001i	$-0.528478\pi$
$197$	−35.2024			−0.178692			−0.0893462	+	0.996001i	$0.528478\pi$
$198$	−320.610	+	320.610i	−1.61924	+	1.61924i
$199$	35.3409	+	35.3409i	0.177593	+	0.177593i	0.790306	−	0.612713i	$-0.209922\pi$
$199$	35.3409	+	35.3409i	0.177593	+	0.177593i	−0.612713	+	0.790306i	$0.709922\pi$
$200$	20.4861	+	20.4861i	0.102431	+	0.102431i
$201$	357.681			1.77950
$202$	256.636	−	256.636i	1.27048	−	1.27048i
$203$	190.238	+	190.238i	0.937134	+	0.937134i
$204$	−266.099	+	266.099i	−1.30441	+	1.30441i
$205$	−8.06783	−	8.06783i	−0.0393553	−	0.0393553i
$206$		−	138.362i		−	0.671658i
$207$	−500.720	+	500.720i	−2.41894	+	2.41894i
$208$	43.5254	−	43.5254i	0.209257	−	0.209257i
$209$	−17.3505	−	17.3505i	−0.0830168	−	0.0830168i
$210$			594.227i			2.82965i
$211$	−401.649			−1.90355			−0.951775	−	0.306797i	$-0.900743\pi$
$211$	−401.649			−1.90355			−0.951775	+	0.306797i	$0.900743\pi$
$212$			113.765i			0.536625i
$213$		−	443.234i		−	2.08091i
$214$	−184.433	−	184.433i	−0.861837	−	0.861837i
$215$		−	2.78300i		−	0.0129442i
$216$	−207.832	−	207.832i	−0.962184	−	0.962184i
$217$	−64.4423	−	64.4423i	−0.296969	−	0.296969i
$218$	436.473			2.00217
$219$	448.684			2.04878
$220$	106.061	−	106.061i	0.482098	−	0.482098i
$221$		−	86.4190i		−	0.391036i
$222$	521.634	+	353.769i	2.34970	+	1.59355i
$223$	−252.107			−1.13052			−0.565262	−	0.824912i	$-0.691225\pi$
$223$	−252.107			−1.13052			−0.565262	+	0.824912i	$0.691225\pi$
$224$	−255.126	−	255.126i	−1.13896	−	1.13896i
$225$		−	160.621i		−	0.713870i
$226$			204.120i			0.903185i
$227$	−10.6621	+	10.6621i	−0.0469697	+	0.0469697i	−0.730202	−	0.683232i	$-0.760574\pi$
$227$	−10.6621	+	10.6621i	−0.0469697	+	0.0469697i	0.683232	+	0.730202i	$0.260574\pi$
$228$	76.7345	−	76.7345i	0.336555	−	0.336555i
$229$	114.456			0.499807			0.249903	−	0.968271i	$-0.419601\pi$
$229$	114.456			0.499807			0.249903	+	0.968271i	$0.419601\pi$
$230$	290.414	−	290.414i	1.26267	−	1.26267i
$231$	−309.825			−1.34123
$232$	129.935			0.560066
$233$		−	401.344i		−	1.72251i	−0.508175	−	0.861254i	$-0.669680\pi$
$233$		−	401.344i		−	1.72251i	0.508175	−	0.861254i	$-0.330320\pi$
$234$	460.491			1.96791
$235$	14.7098	−	14.7098i	0.0625949	−	0.0625949i
$236$	81.0610	+	81.0610i	0.343479	+	0.343479i
$237$	170.853	+	170.853i	0.720900	+	0.720900i
$238$	−320.654			−1.34729
$239$	−186.151	+	186.151i	−0.778875	+	0.778875i	−0.979639	−	0.200765i	$-0.935657\pi$
$239$	−186.151	+	186.151i	−0.778875	+	0.778875i	0.200765	+	0.979639i	$0.435657\pi$
$240$	−150.389	−	150.389i	−0.626620	−	0.626620i
$241$	154.922	−	154.922i	0.642829	−	0.642829i	−0.308421	−	0.951250i	$-0.599800\pi$
$241$	154.922	−	154.922i	0.642829	−	0.642829i	0.951250	+	0.308421i	$0.0998005\pi$
$242$	−164.115	−	164.115i	−0.678162	−	0.678162i
$243$			515.710i			2.12226i
$244$	284.671	−	284.671i	1.16669	−	1.16669i
$245$	−58.2164	+	58.2164i	−0.237618	+	0.237618i
$246$	32.6167	+	32.6167i	0.132588	+	0.132588i
$247$			24.9205i			0.100893i
$248$	−44.0149			−0.177480
$249$			806.189i			3.23771i
$250$			414.579i			1.65832i
$251$	−123.743	−	123.743i	−0.493002	−	0.493002i	0.416249	−	0.909251i	$-0.363345\pi$
$251$	−123.743	−	123.743i	−0.493002	−	0.493002i	−0.909251	+	0.416249i	$0.863345\pi$
$252$		−	974.557i		−	3.86729i
$253$	151.419	+	151.419i	0.598495	+	0.598495i
$254$	−342.459	−	342.459i	−1.34826	−	1.34826i
$255$	−298.594			−1.17096
$256$	17.7974			0.0695210
$257$	−60.4191	+	60.4191i	−0.235094	+	0.235094i	−0.814815	−	0.579721i	$-0.803162\pi$
$257$	−60.4191	+	60.4191i	−0.235094	+	0.235094i	0.579721	+	0.814815i	$0.303162\pi$
$258$			11.2512i			0.0436091i
$259$	57.6878	+	300.836i	0.222733	+	1.16153i
$260$	−152.336			−0.585907
$261$	−509.376	−	509.376i	−1.95163	−	1.95163i
$262$			111.459i			0.425417i
$263$			140.452i			0.534037i	0.963691	+	0.267018i	$0.0860385\pi$
$263$			140.452i			0.534037i	−0.963691	+	0.267018i	$0.913962\pi$
$264$	−105.807	+	105.807i	−0.400784	+	0.400784i
$265$	−63.8286	+	63.8286i	−0.240863	+	0.240863i
$266$	92.4665			0.347619
$267$	590.875	−	590.875i	2.21302	−	2.21302i
$268$	340.230			1.26952
$269$	−311.772			−1.15900			−0.579501	−	0.814971i	$-0.696753\pi$
$269$	−311.772			−1.15900			−0.579501	+	0.814971i	$0.696753\pi$
$270$		−	945.097i		−	3.50036i
$271$	271.673			1.00248			0.501242	−	0.865307i	$-0.332877\pi$
$271$	271.673			1.00248			0.501242	+	0.865307i	$0.332877\pi$
$272$	81.1522	−	81.1522i	0.298354	−	0.298354i
$273$	222.500	+	222.500i	0.815019	+	0.815019i
$274$	−396.399	−	396.399i	−1.44671	−	1.44671i
$275$	−48.5722			−0.176626
$276$	−669.668	+	669.668i	−2.42633	+	2.42633i
$277$	95.0326	+	95.0326i	0.343078	+	0.343078i	0.857523	−	0.514445i	$-0.172002\pi$
$277$	95.0326	+	95.0326i	0.343078	+	0.343078i	−0.514445	+	0.857523i	$0.672002\pi$
$278$	−469.431	+	469.431i	−1.68860	+	1.68860i
$279$	172.549	+	172.549i	0.618455	+	0.618455i
$280$			139.477i			0.498134i
$281$	−217.927	+	217.927i	−0.775541	+	0.775541i	−0.979069	−	0.203528i	$-0.934759\pi$
$281$	−217.927	+	217.927i	−0.775541	+	0.775541i	0.203528	+	0.979069i	$0.434759\pi$
$282$	−59.4689	+	59.4689i	−0.210883	+	0.210883i
$283$	89.7432	+	89.7432i	0.317114	+	0.317114i	0.847658	−	0.530544i	$-0.178012\pi$
$283$	89.7432	+	89.7432i	0.317114	+	0.317114i	−0.530544	+	0.847658i	$0.678012\pi$
$284$		−	421.609i		−	1.48454i
$285$	86.1052			0.302123
$286$		−	139.254i		−	0.486901i
$287$			22.4178i			0.0781107i
$288$	683.118	+	683.118i	2.37194	+	2.37194i
$289$			127.874i			0.442470i
$290$	295.435	+	295.435i	1.01874	+	1.01874i
$291$	−322.118	−	322.118i	−1.10694	−	1.10694i
$292$	426.794			1.46162
$293$	−384.516			−1.31234			−0.656171	−	0.754612i	$-0.727825\pi$
$293$	−384.516			−1.31234			−0.656171	+	0.754612i	$0.727825\pi$
$294$	235.358	−	235.358i	0.800537	−	0.800537i
$295$			90.9600i			0.308339i
$296$	122.438	+	83.0368i	0.413643	+	0.280530i
$297$	492.765			1.65914
$298$	126.344	+	126.344i	0.423973	+	0.423973i
$299$		−	217.483i		−	0.727368i
$300$		−	214.816i		−	0.716052i
$301$	−3.86651	+	3.86651i	−0.0128455	+	0.0128455i
$302$	−260.802	+	260.802i	−0.863584	+	0.863584i
$303$	−664.045			−2.19157
$304$	−23.4017	+	23.4017i	−0.0769793	+	0.0769793i
$305$	319.435			1.04733
$306$	858.575			2.80580
$307$		−	185.925i		−	0.605618i	−0.953051	−	0.302809i	$-0.902076\pi$
$307$		−	185.925i		−	0.605618i	0.953051	−	0.302809i	$-0.0979244\pi$
$308$	−294.709			−0.956847
$309$	−179.005	+	179.005i	−0.579305	+	0.579305i
$310$	−100.077	−	100.077i	−0.322829	−	0.322829i
$311$	135.365	+	135.365i	0.435258	+	0.435258i	0.890413	−	0.455154i	$-0.150416\pi$
$311$	135.365	+	135.365i	0.435258	+	0.435258i	−0.455154	+	0.890413i	$0.650416\pi$
$312$	151.970			0.487085
$313$	191.396	−	191.396i	0.611490	−	0.611490i	−0.331844	−	0.943334i	$-0.607671\pi$
$313$	191.396	−	191.396i	0.611490	−	0.611490i	0.943334	+	0.331844i	$0.107671\pi$
$314$	313.839	+	313.839i	0.999486	+	0.999486i
$315$	546.784	−	546.784i	1.73582	−	1.73582i
$316$	162.518	+	162.518i	0.514297	+	0.514297i
$317$		−	25.8742i		−	0.0816221i	−0.999167	−	0.0408110i	$-0.987006\pi$
$317$		−	25.8742i		−	0.0816221i	0.999167	−	0.0408110i	$-0.0129942\pi$
$318$	258.047	−	258.047i	0.811468	−	0.811468i
$319$	−154.037	+	154.037i	−0.482874	+	0.482874i
$320$	−288.451	−	288.451i	−0.901410	−	0.901410i
$321$			477.220i			1.48667i
$322$	−806.962			−2.50609
$323$			46.4637i			0.143850i
$324$			1119.86i			3.45635i
$325$	34.8820	+	34.8820i	0.107329	+	0.107329i
$326$			311.262i			0.954793i
$327$	−564.686	−	564.686i	−1.72687	−	1.72687i
$328$	7.65581	+	7.65581i	0.0233409	+	0.0233409i
$329$	−40.8735			−0.124236
$330$	−481.149			−1.45803
$331$	248.351	−	248.351i	0.750304	−	0.750304i	−0.224232	−	0.974536i	$-0.571987\pi$
$331$	248.351	−	248.351i	0.750304	−	0.750304i	0.974536	+	0.224232i	$0.0719872\pi$
$332$			766.857i			2.30981i
$333$	−154.463	−	805.511i	−0.463853	−	2.41895i
$334$	117.299			0.351196
$335$	190.889	+	190.889i	0.569818	+	0.569818i
$336$			417.880i			1.24369i
$337$		−	106.000i		−	0.314539i	−0.987556	−	0.157270i	$-0.949731\pi$
$337$		−	106.000i		−	0.314539i	0.987556	−	0.157270i	$-0.0502692\pi$
$338$	264.628	−	264.628i	0.782923	−	0.782923i
$339$	264.080	−	264.080i	0.778996	−	0.778996i
$340$	−284.027			−0.835373
$341$	52.1792	−	52.1792i	0.153018	−	0.153018i
$342$	−247.586			−0.723935
$343$	−243.900			−0.711079
$344$			2.64088i			0.00767697i
$345$	−751.446			−2.17810
$346$	31.9644	−	31.9644i	0.0923826	−	0.0923826i
$347$	298.217	+	298.217i	0.859415	+	0.859415i	0.991269	−	0.131855i	$-0.0420932\pi$
$347$	298.217	+	298.217i	0.859415	+	0.859415i	−0.131855	+	0.991269i	$0.542093\pi$
$348$	−681.245	−	681.245i	−1.95760	−	1.95760i
$349$	95.7542			0.274367			0.137184	−	0.990546i	$-0.456195\pi$
$349$	95.7542			0.274367			0.137184	+	0.990546i	$0.456195\pi$
$350$	129.428	−	129.428i	0.369796	−	0.369796i
$351$	−353.878	−	353.878i	−1.00820	−	1.00820i
$352$	206.577	−	206.577i	0.586866	−	0.586866i
$353$	−481.345	−	481.345i	−1.36358	−	1.36358i	−0.869301	−	0.494283i	$-0.835431\pi$
$353$	−481.345	−	481.345i	−1.36358	−	1.36358i	−0.494283	−	0.869301i	$-0.664569\pi$
$354$		−	367.734i		−	1.03880i
$355$	236.548	−	236.548i	0.666331	−	0.666331i
$356$	562.048	−	562.048i	1.57879	−	1.57879i
$357$	414.846	+	414.846i	1.16203	+	1.16203i
$358$		−	413.415i		−	1.15479i
$359$	463.253			1.29040			0.645199	−	0.764015i	$-0.276775\pi$
$359$	463.253			1.29040			0.645199	+	0.764015i	$0.276775\pi$
$360$		−	373.461i		−	1.03739i
$361$			347.601i			0.962885i
$362$	−540.373	−	540.373i	−1.49274	−	1.49274i
$363$			424.648i			1.16983i
$364$	211.645	+	211.645i	0.581442	+	0.581442i
$365$	239.456	+	239.456i	0.656045	+	0.656045i
$366$	−1291.41			−3.52845
$367$	472.587			1.28770			0.643852	−	0.765150i	$-0.277335\pi$
$367$	472.587			1.28770			0.643852	+	0.765150i	$0.277335\pi$
$368$	204.228	−	204.228i	0.554969	−	0.554969i
$369$		−	60.0252i		−	0.162670i
$370$	89.5875	+	467.190i	0.242128	+	1.26268i
$371$	177.358			0.478054
$372$	230.768	+	230.768i	0.620345	+	0.620345i
$373$			260.554i			0.698537i	0.937023	+	0.349269i	$0.113570\pi$
$373$			260.554i			0.698537i	−0.937023	+	0.349269i	$0.886430\pi$
$374$		−	259.635i		−	0.694212i
$375$	536.362	−	536.362i	1.43030	−	1.43030i
$376$	−13.9586	+	13.9586i	−0.0371239	+	0.0371239i
$377$	221.243			0.586851
$378$	−1313.05	+	1313.05i	−3.47368	+	3.47368i
$379$	−210.011			−0.554118			−0.277059	−	0.960853i	$-0.589360\pi$
$379$	−210.011			−0.554118			−0.277059	+	0.960853i	$0.589360\pi$
$380$	81.9043			0.215538
$381$			886.111i			2.32575i
$382$	−690.301			−1.80707
$383$	−176.117	+	176.117i	−0.459835	+	0.459835i	−0.898601	−	0.438766i	$-0.855416\pi$
$383$	−176.117	+	176.117i	−0.459835	+	0.459835i	0.438766	+	0.898601i	$0.355416\pi$
$384$	477.986	+	477.986i	1.24476	+	1.24476i
$385$	−165.349	−	165.349i	−0.429478	−	0.429478i
$386$	1171.23			3.03428
$387$	10.3529	−	10.3529i	0.0267516	−	0.0267516i
$388$	−306.403	−	306.403i	−0.789698	−	0.789698i
$389$	57.9731	−	57.9731i	0.149031	−	0.149031i	−0.628654	−	0.777685i	$-0.716394\pi$
$389$	57.9731	−	57.9731i	0.149031	−	0.149031i	0.777685	+	0.628654i	$0.216394\pi$
$390$	345.536	+	345.536i	0.885990	+	0.885990i
$391$		−	405.492i		−	1.03706i
$392$	55.2433	−	55.2433i	0.140927	−	0.140927i
$393$	144.200	−	144.200i	0.366922	−	0.366922i
$394$	75.9523	+	75.9523i	0.192772	+	0.192772i
$395$			182.364i			0.461681i
$396$	789.104			1.99269
$397$		−	395.970i		−	0.997406i	−0.866773	−	0.498703i	$-0.833810\pi$
$397$		−	395.970i		−	0.997406i	0.866773	−	0.498703i	$-0.166190\pi$
$398$		−	152.502i		−	0.383172i
$399$	−119.628	−	119.628i	−0.299821	−	0.299821i
$400$			65.5123i			0.163781i
$401$	191.991	+	191.991i	0.478781	+	0.478781i	0.904742	−	0.425961i	$-0.140064\pi$
$401$	191.991	+	191.991i	0.478781	+	0.478781i	−0.425961	+	0.904742i	$0.640064\pi$
$402$	−771.728	−	771.728i	−1.91972	−	1.91972i
$403$	−74.9449			−0.185968
$404$	−631.648			−1.56349
$405$	−628.305	+	628.305i	−1.55137	+	1.55137i
$406$		−	820.912i		−	2.02195i
$407$	−243.589	+	46.7101i	−0.598498	+	0.114767i
$408$	283.345			0.694474
$409$	−2.92669	−	2.92669i	−0.00715572	−	0.00715572i	0.703520	−	0.710676i	$-0.251611\pi$
$409$	−2.92669	−	2.92669i	−0.00715572	−	0.00715572i	−0.710676	+	0.703520i	$0.751611\pi$
$410$			34.8142i			0.0849126i
$411$			1025.68i			2.49558i
$412$	−170.272	+	170.272i	−0.413281	+	0.413281i
$413$	126.373	−	126.373i	0.305989	−	0.305989i
$414$	2160.70			5.21908
$415$	−430.252	+	430.252i	−1.03675	+	1.03675i
$416$	−296.706			−0.713235
$417$	1214.65			2.91283
$418$			74.8706i			0.179116i
$419$	−604.559			−1.44286			−0.721431	−	0.692486i	$-0.756515\pi$
$419$	−604.559			−1.44286			−0.721431	+	0.692486i	$0.756515\pi$
$420$	731.274	−	731.274i	1.74113	−	1.74113i
$421$	50.7472	+	50.7472i	0.120540	+	0.120540i	0.764803	−	0.644264i	$-0.222836\pi$
$421$	50.7472	+	50.7472i	0.120540	+	0.120540i	−0.644264	+	0.764803i	$0.722836\pi$
$422$	866.594	+	866.594i	2.05354	+	2.05354i
$423$	109.442			0.258727
$424$	60.5689	−	60.5689i	0.142851	−	0.142851i
$425$	65.0368	+	65.0368i	0.153028	+	0.153028i
$426$	−956.317	+	956.317i	−2.24487	+	2.24487i
$427$	−443.800	−	443.800i	−1.03934	−	1.03934i
$428$			453.938i			1.06060i
$429$	−180.159	+	180.159i	−0.419952	+	0.419952i
$430$	−6.00458	+	6.00458i	−0.0139641	+	0.0139641i
$431$	84.1744	+	84.1744i	0.195300	+	0.195300i	0.797982	−	0.602682i	$-0.205901\pi$
$431$	84.1744	+	84.1744i	0.195300	+	0.195300i	−0.602682	+	0.797982i	$0.705901\pi$
$432$		−	664.622i		−	1.53848i
$433$	−321.681			−0.742912			−0.371456	−	0.928451i	$-0.621141\pi$
$433$	−321.681			−0.742912			−0.371456	+	0.928451i	$0.621141\pi$
$434$			278.080i			0.640738i
$435$		−	764.436i		−	1.75733i
$436$	−537.137	−	537.137i	−1.23196	−	1.23196i
$437$			116.931i			0.267577i
$438$	−968.076	−	968.076i	−2.21022	−	2.21022i
$439$	143.870	+	143.870i	0.327722	+	0.327722i	0.851720	−	0.523998i	$-0.175560\pi$
$439$	143.870	+	143.870i	0.327722	+	0.327722i	−0.523998	+	0.851720i	$0.675560\pi$
$440$	−112.936			−0.256672
$441$	−433.133			−0.982162
$442$	−186.457	+	186.457i	−0.421848	+	0.421848i
$443$			57.0834i			0.128856i	0.997922	+	0.0644282i	$0.0205223\pi$
$443$			57.0834i			0.128856i	−0.997922	+	0.0644282i	$0.979478\pi$
$444$	−206.580	−	1077.30i	−0.465271	−	2.42635i
$445$	630.684			1.41727
$446$	543.943	+	543.943i	1.21960	+	1.21960i
$447$		−	326.915i		−	0.731352i
$448$			801.508i			1.78908i
$449$	−266.470	+	266.470i	−0.593474	+	0.593474i	−0.938568	−	0.345094i	$-0.887847\pi$
$449$	−266.470	+	266.470i	−0.593474	+	0.593474i	0.345094	+	0.938568i	$0.387847\pi$
$450$	−346.554	+	346.554i	−0.770120	+	0.770120i
$451$	−18.1518			−0.0402478
$452$	251.196	−	251.196i	0.555743	−	0.555743i
$453$	674.826			1.48968
$454$	46.0090			0.101341
$455$			237.490i			0.521957i
$456$	−81.7078			−0.179184
$457$	536.625	−	536.625i	1.17423	−	1.17423i	0.193045	−	0.981190i	$-0.438164\pi$
$457$	536.625	−	536.625i	1.17423	−	1.17423i	0.981190	−	0.193045i	$-0.0618363\pi$
$458$	−246.949	−	246.949i	−0.539189	−	0.539189i
$459$	−659.798	−	659.798i	−1.43747	−	1.43747i
$460$	−714.784			−1.55388
$461$	−320.902	+	320.902i	−0.696099	+	0.696099i	−0.963567	−	0.267468i	$-0.913813\pi$
$461$	−320.902	+	320.902i	−0.696099	+	0.696099i	0.267468	+	0.963567i	$0.413813\pi$
$462$	668.474	+	668.474i	1.44691	+	1.44691i
$463$	545.451	−	545.451i	1.17808	−	1.17808i	0.197848	−	0.980233i	$-0.436605\pi$
$463$	545.451	−	545.451i	1.17808	−	1.17808i	0.980233	−	0.197848i	$-0.0633953\pi$
$464$	207.759	+	207.759i	0.447756	+	0.447756i
$465$			258.949i			0.556880i
$466$	−865.937	+	865.937i	−1.85823	+	1.85823i
$467$	−421.742	+	421.742i	−0.903088	+	0.903088i	−0.995702	−	0.0926138i	$-0.970478\pi$
$467$	−421.742	+	421.742i	−0.903088	+	0.903088i	0.0926138	+	0.995702i	$0.470478\pi$
$468$	−566.694	−	566.694i	−1.21088	−	1.21088i
$469$		−	530.416i		−	1.13095i
$470$	−63.4754			−0.135054
$471$		−	812.057i		−	1.72411i
$472$		−	86.3147i		−	0.182870i
$473$	−3.13073	−	3.13073i	−0.00661888	−	0.00661888i
$474$		−	737.263i		−	1.55541i
$475$	−18.7545	−	18.7545i	−0.0394832	−	0.0394832i
$476$	394.607	+	394.607i	0.829006	+	0.829006i
$477$	−474.889			−0.995574
$478$	803.275			1.68049
$479$	−199.659	+	199.659i	−0.416825	+	0.416825i	−0.884108	−	0.467283i	$-0.845233\pi$
$479$	−199.659	+	199.659i	−0.416825	+	0.416825i	0.467283	+	0.884108i	$0.345233\pi$
$480$			1025.18i			2.13578i
$481$	208.478	+	141.388i	0.433425	+	0.293946i
$482$	−668.516			−1.38696
$483$	1044.01	+	1044.01i	2.16150	+	2.16150i
$484$			403.930i			0.834566i
$485$		−	343.820i		−	0.708907i
$486$	1112.69	−	1112.69i	2.28949	−	2.28949i
$487$	−389.704	+	389.704i	−0.800214	+	0.800214i	−0.983129	−	0.182915i	$-0.941447\pi$
$487$	−389.704	+	389.704i	−0.800214	+	0.800214i	0.182915	+	0.983129i	$0.441447\pi$
$488$	−303.121			−0.621150
$489$	402.695	−	402.695i	0.823508	−	0.823508i
$490$	251.214			0.512682
$491$	−611.754			−1.24594			−0.622968	−	0.782248i	$-0.714073\pi$
$491$	−611.754			−1.24594			−0.622968	+	0.782248i	$0.714073\pi$
$492$		−	80.2782i		−	0.163167i
$493$	412.502			0.836718
$494$	53.7682	−	53.7682i	0.108843	−	0.108843i
$495$	442.734	+	442.734i	0.894411	+	0.894411i
$496$	−70.3774	−	70.3774i	−0.141890	−	0.141890i
$497$	−657.285			−1.32251
$498$	1739.43	−	1739.43i	3.49282	−	3.49282i
$499$	−460.731	−	460.731i	−0.923309	−	0.923309i	0.0739526	−	0.997262i	$-0.476439\pi$
$499$	−460.731	−	460.731i	−0.923309	−	0.923309i	−0.997262	+	0.0739526i	$0.976439\pi$
$500$	510.194	−	510.194i	1.02039	−	1.02039i
$501$	−151.756	−	151.756i	−0.302906	−	0.302906i
$502$			533.975i			1.06370i
$503$	445.737	−	445.737i	0.886157	−	0.886157i	−0.107994	−	0.994152i	$-0.534443\pi$
$503$	445.737	−	445.737i	0.886157	−	0.886157i	0.994152	+	0.107994i	$0.0344428\pi$
$504$	−518.860	+	518.860i	−1.02948	+	1.02948i
$505$	−354.392	−	354.392i	−0.701766	−	0.701766i
$506$		−	653.401i		−	1.29131i
$507$	−684.724			−1.35054
$508$			842.880i			1.65921i
$509$			321.417i			0.631468i	0.948848	+	0.315734i	$0.102251\pi$
$509$			321.417i			0.631468i	−0.948848	+	0.315734i	$0.897749\pi$
$510$	644.244	+	644.244i	1.26322	+	1.26322i
$511$		−	665.368i		−	1.30209i
$512$	−380.872	−	380.872i	−0.743891	−	0.743891i
$513$	190.265	+	190.265i	0.370886	+	0.370886i
$514$	260.719			0.507236
$515$	−191.065			−0.371000
$516$	13.8460	−	13.8460i	0.0268333	−	0.0268333i
$517$		−	33.0955i		−	0.0640145i
$518$	524.615	−	773.548i	1.01277	−	1.49334i
$519$	−82.7078			−0.159360
$520$	81.1045	+	81.1045i	0.155970	+	0.155970i
$521$		−	897.758i		−	1.72314i	−0.507635	−	0.861572i	$-0.669480\pi$
$521$		−	897.758i		−	1.72314i	0.507635	−	0.861572i	$-0.330520\pi$
$522$			2198.05i			4.21082i
$523$	−476.682	+	476.682i	−0.911439	+	0.911439i	−0.996385	−	0.0849469i	$-0.972928\pi$
$523$	−476.682	+	476.682i	−0.911439	+	0.911439i	0.0849469	+	0.996385i	$0.472928\pi$
$524$	137.165	−	137.165i	0.261765	−	0.261765i
$525$	−334.896			−0.637897
$526$	303.037	−	303.037i	0.576116	−	0.576116i
$527$	−139.733			−0.265148
$528$	−338.359			−0.640831
$529$		−	491.465i		−	0.929046i
$530$	275.432			0.519683
$531$	−338.374	+	338.374i	−0.637239	+	0.637239i
$532$	−113.792	−	113.792i	−0.213895	−	0.213895i
$533$	13.0357	+	13.0357i	0.0244572	+	0.0244572i
$534$	−2549.73			−4.77478
$535$	−254.686	+	254.686i	−0.476048	+	0.476048i
$536$	−181.140	−	181.140i	−0.337949	−	0.337949i
$537$	−534.855	+	534.855i	−0.996006	+	0.996006i
$538$	672.675	+	672.675i	1.25033	+	1.25033i
$539$			130.981i			0.243007i
$540$	−1163.06	+	1163.06i	−2.15382	+	2.15382i
$541$	−329.518	+	329.518i	−0.609090	+	0.609090i	−0.942708	−	0.333619i	$-0.891730\pi$
$541$	−329.518	+	329.518i	−0.609090	+	0.609090i	0.333619	+	0.942708i	$0.391730\pi$
$542$	−586.160	−	586.160i	−1.08148	−	1.08148i
$543$			1398.21i			2.57498i
$544$	−553.201			−1.01691
$545$		−	602.730i		−	1.10593i
$546$		−	960.128i		−	1.75848i
$547$	363.991	+	363.991i	0.665432	+	0.665432i	0.956655	−	0.291223i	$-0.0940622\pi$
$547$	363.991	+	363.991i	0.665432	+	0.665432i	−0.291223	+	0.956655i	$0.594062\pi$
$548$			975.641i			1.78037i
$549$	1188.31	+	1188.31i	2.16449	+	2.16449i
$550$	104.799	+	104.799i	0.190543	+	0.190543i
$551$	−118.952			−0.215885
$552$	713.070			1.29179
$553$	253.364	−	253.364i	0.458163	−	0.458163i
$554$		−	410.083i		−	0.740221i
$555$	488.523	−	720.331i	0.880222	−	1.29789i
$556$	1155.39			2.07804
$557$	−53.0738	−	53.0738i	−0.0952850	−	0.0952850i	0.657857	−	0.753142i	$-0.271463\pi$
$557$	−53.0738	−	53.0738i	−0.0952850	−	0.0952850i	−0.753142	+	0.657857i	$0.771463\pi$
$558$		−	744.579i		−	1.33437i
$559$			4.49666i			0.00804412i
$560$	−223.016	+	223.016i	−0.398244	+	0.398244i
$561$	−335.903	+	335.903i	−0.598758	+	0.598758i
$562$	940.394			1.67330
$563$	71.8932	−	71.8932i	0.127697	−	0.127697i	−0.640370	−	0.768067i	$-0.721219\pi$
$563$	71.8932	−	71.8932i	0.127697	−	0.127697i	0.768067	+	0.640370i	$0.221219\pi$
$564$	146.368			0.259518
$565$	281.871			0.498887
$566$		−	387.258i		−	0.684201i
$567$	1745.85			3.07909
$568$	−224.467	+	224.467i	−0.395189	+	0.395189i
$569$	70.8300	+	70.8300i	0.124481	+	0.124481i	0.766603	−	0.642121i	$-0.221946\pi$
$569$	70.8300	+	70.8300i	0.124481	+	0.124481i	−0.642121	+	0.766603i	$0.721946\pi$
$570$	−185.780	−	185.780i	−0.325929	−	0.325929i
$571$	712.573			1.24794			0.623969	−	0.781449i	$-0.285519\pi$
$571$	712.573			1.24794			0.623969	+	0.781449i	$0.285519\pi$
$572$	−171.370	+	171.370i	−0.299597	+	0.299597i
$573$	893.077	+	893.077i	1.55860	+	1.55860i
$574$	48.3683	−	48.3683i	0.0842654	−	0.0842654i
$575$	163.672	+	163.672i	0.284647	+	0.284647i
$576$		−	2146.09i		−	3.72586i
$577$	45.4440	−	45.4440i	0.0787591	−	0.0787591i	−0.666630	−	0.745389i	$-0.732264\pi$
$577$	45.4440	−	45.4440i	0.0787591	−	0.0787591i	0.745389	+	0.666630i	$0.232264\pi$
$578$	275.899	−	275.899i	0.477334	−	0.477334i
$579$	−1515.28	−	1515.28i	−2.61706	−	2.61706i
$580$		−	727.141i		−	1.25369i
$581$	1195.52			2.05770
$582$			1390.00i			2.38831i
$583$			143.608i			0.246325i
$584$	−227.227	−	227.227i	−0.389088	−	0.389088i
$585$		−	635.897i		−	1.08700i
$586$	829.629	+	829.629i	1.41575	+	1.41575i
$587$	52.3572	+	52.3572i	0.0891945	+	0.0891945i	0.750296	−	0.661102i	$-0.229911\pi$
$587$	52.3572	+	52.3572i	0.0891945	+	0.0891945i	−0.661102	+	0.750296i	$0.729911\pi$
$588$	−579.277			−0.985164
$589$	40.2946			0.0684119
$590$	196.254	−	196.254i	0.332634	−	0.332634i
$591$		−	196.526i		−	0.332532i
$592$	63.0008	+	328.543i	0.106420	+	0.554971i
$593$	−208.668			−0.351885			−0.175942	−	0.984400i	$-0.556297\pi$
$593$	−208.668			−0.351885			−0.175942	+	0.984400i	$0.556297\pi$
$594$	−1063.18	−	1063.18i	−1.78987	−	1.78987i
$595$			442.795i			0.744194i
$596$		−	310.965i		−	0.521753i
$597$	−197.300	+	197.300i	−0.330485	+	0.330485i
$598$	−469.239	+	469.239i	−0.784681	+	0.784681i
$599$	368.353			0.614947			0.307473	−	0.951557i	$-0.400516\pi$
$599$	368.353			0.614947			0.307473	+	0.951557i	$0.400516\pi$
$600$	−114.369	+	114.369i	−0.190615	+	0.190615i
$601$	−1069.14			−1.77894			−0.889469	−	0.456995i	$-0.848926\pi$
$601$	−1069.14			−1.77894			−0.889469	+	0.456995i	$0.848926\pi$
$602$	16.6847			0.0277154
$603$			1420.23i			2.35527i
$604$	641.903			1.06275
$605$	−226.628	+	226.628i	−0.374592	+	0.374592i
$606$	1432.74	+	1432.74i	2.36425	+	2.36425i
$607$	105.027	+	105.027i	0.173026	+	0.173026i	0.788308	−	0.615281i	$-0.210958\pi$
$607$	105.027	+	105.027i	0.173026	+	0.173026i	−0.615281	+	0.788308i	$0.710958\pi$
$608$	159.526			0.262378
$609$	−1062.05	+	1062.05i	−1.74393	+	1.74393i
$610$	−689.209	−	689.209i	−1.12985	−	1.12985i
$611$	−23.7675	+	23.7675i	−0.0388993	+	0.0388993i
$612$	−1056.59	−	1056.59i	−1.72645	−	1.72645i
$613$			578.300i			0.943394i	0.881761	+	0.471697i	$0.156358\pi$
$613$			578.300i			0.943394i	−0.881761	+	0.471697i	$0.843642\pi$
$614$	−401.149	+	401.149i	−0.653338	+	0.653338i
$615$	45.0408	−	45.0408i	0.0732370	−	0.0732370i
$616$	156.905	+	156.905i	0.254715	+	0.254715i
$617$		−	225.939i		−	0.366189i	−0.983095	−	0.183094i	$-0.941389\pi$
$617$		−	225.939i		−	0.366189i	0.983095	−	0.183094i	$-0.0586114\pi$
$618$	772.440			1.24990
$619$			144.395i			0.233271i	0.993175	+	0.116635i	$0.0372109\pi$
$619$			144.395i			0.233271i	−0.993175	+	0.116635i	$0.962789\pi$
$620$			246.316i			0.397283i
$621$	−1660.45	−	1660.45i	−2.67384	−	2.67384i
$622$		−	584.126i		−	0.939109i
$623$	−876.228	−	876.228i	−1.40646	−	1.40646i
$624$	242.992	+	242.992i	0.389410	+	0.389410i
$625$	391.350			0.626161
$626$	−825.910			−1.31934
$627$	96.8638	−	96.8638i	0.154488	−	0.154488i
$628$		−	772.438i		−	1.23000i
$629$	388.702	+	263.615i	0.617968	+	0.419101i
$630$	−2359.47			−3.74519
$631$	−589.625	−	589.625i	−0.934430	−	0.934430i	0.0635491	−	0.997979i	$-0.479758\pi$
$631$	−589.625	−	589.625i	−0.934430	−	0.934430i	−0.997979	+	0.0635491i	$0.979758\pi$
$632$		−	173.051i		−	0.273815i
$633$		−	2242.31i		−	3.54235i
$634$	−55.8259	+	55.8259i	−0.0880535	+	0.0880535i
$635$	−472.905	+	472.905i	−0.744732	+	0.744732i
$636$	−635.120			−0.998617
$637$	94.0636	−	94.0636i	0.147667	−	0.147667i
$638$	664.696			1.04184
$639$	1759.93			2.75419
$640$			510.189i			0.797170i
$641$	−274.312			−0.427944			−0.213972	−	0.976840i	$-0.568640\pi$
$641$	−274.312			−0.427944			−0.213972	+	0.976840i	$0.568640\pi$
$642$	1029.65	−	1029.65i	1.60381	−	1.60381i
$643$	−416.820	−	416.820i	−0.648243	−	0.648243i	0.304325	−	0.952568i	$-0.401569\pi$
$643$	−416.820	−	416.820i	−0.648243	−	0.648243i	−0.952568	+	0.304325i	$0.901569\pi$
$644$	993.071	+	993.071i	1.54204	+	1.54204i
$645$	15.5368			0.0240881
$646$	100.250	−	100.250i	0.155185	−	0.155185i
$647$	−726.809	−	726.809i	−1.12335	−	1.12335i	−0.991234	−	0.132118i	$-0.957822\pi$
$647$	−726.809	−	726.809i	−1.12335	−	1.12335i	−0.132118	−	0.991234i	$-0.542178\pi$
$648$	596.218	−	596.218i	0.920090	−	0.920090i
$649$	102.325	+	102.325i	0.157666	+	0.157666i
$650$		−	150.522i		−	0.231573i
$651$	359.766	−	359.766i	0.552636	−	0.552636i
$652$	383.049	−	383.049i	0.587498	−	0.587498i
$653$	−526.231	−	526.231i	−0.805867	−	0.805867i	0.178139	−	0.984005i	$-0.442992\pi$
$653$	−526.231	−	526.231i	−0.805867	−	0.805867i	−0.984005	+	0.178139i	$0.942992\pi$
$654$			2436.72i			3.72588i
$655$	153.915			0.234985
$656$			24.4824i			0.0373208i
$657$			1781.57i			2.71167i
$658$	88.1883	+	88.1883i	0.134025	+	0.134025i
$659$			915.086i			1.38860i	0.719686	+	0.694299i	$0.244286\pi$
$659$			915.086i			1.38860i	−0.719686	+	0.694299i	$0.755714\pi$
$660$	592.116	+	592.116i	0.897145	+	0.897145i
$661$	730.389	+	730.389i	1.10498	+	1.10498i	0.993801	+	0.111175i	$0.0354614\pi$
$661$	730.389	+	730.389i	1.10498	+	1.10498i	0.111175	+	0.993801i	$0.464539\pi$
$662$	−1071.68			−1.61885
$663$	482.457			0.727687
$664$	408.279	−	408.279i	0.614878	−	0.614878i
$665$		−	127.688i		−	0.192012i
$666$	−1404.69	+	2071.23i	−2.10915	+	3.10995i
$667$	1038.11			1.55638
$668$	−144.352	−	144.352i	−0.216096	−	0.216096i
$669$		−	1407.45i		−	2.10381i
$670$		−	823.720i		−	1.22943i
$671$	359.347	−	359.347i	0.535539	−	0.535539i
$672$	1424.31	−	1424.31i	2.11951	−	2.11951i
$673$	234.003			0.347701			0.173851	−	0.984772i	$-0.444379\pi$
$673$	234.003			0.347701			0.173851	+	0.984772i	$0.444379\pi$
$674$	−228.704	+	228.704i	−0.339323	+	0.339323i
$675$	532.640			0.789096
$676$	−651.318			−0.963488
$677$		−	237.924i		−	0.351438i	−0.984440	−	0.175719i	$-0.943775\pi$
$677$		−	237.924i		−	0.351438i	0.984440	−	0.175719i	$-0.0562251\pi$
$678$	−1139.55			−1.68075
$679$	−477.680	+	477.680i	−0.703505	+	0.703505i
$680$	151.217	+	151.217i	0.222379	+	0.222379i
$681$	−59.5241	−	59.5241i	−0.0874069	−	0.0874069i
$682$	−225.163			−0.330151
$683$	535.690	−	535.690i	0.784319	−	0.784319i	−0.196238	−	0.980556i	$-0.562872\pi$
$683$	535.690	−	535.690i	0.784319	−	0.784319i	0.980556	+	0.196238i	$0.0628724\pi$
$684$	304.686	+	304.686i	0.445448	+	0.445448i
$685$	−547.392	+	547.392i	−0.799113	+	0.799113i
$686$	526.236	+	526.236i	0.767109	+	0.767109i
$687$			638.979i			0.930101i
$688$	−4.22261	+	4.22261i	−0.00613752	+	0.00613752i
$689$	103.132	−	103.132i	0.149683	−	0.149683i
$690$	1621.31	+	1621.31i	2.34973	+	2.34973i
$691$		−	1074.07i		−	1.55436i	−0.629276	−	0.777182i	$-0.716648\pi$
$691$		−	1074.07i		−	1.55436i	0.629276	−	0.777182i	$-0.283352\pi$
$692$	−78.6726			−0.113689
$693$		−	1230.21i		−	1.77519i
$694$		−	1286.86i		−	1.85426i
$695$	648.242	+	648.242i	0.932723	+	0.932723i
$696$			725.397i			1.04224i
$697$	24.3047	+	24.3047i	0.0348705	+	0.0348705i
$698$	−206.598	−	206.598i	−0.295986	−	0.295986i
$699$	2240.61			3.20545
$700$	−318.557			−0.455081
$701$	592.077	−	592.077i	0.844617	−	0.844617i	−0.144838	−	0.989455i	$-0.546266\pi$
$701$	592.077	−	592.077i	0.844617	−	0.844617i	0.989455	+	0.144838i	$0.0462661\pi$
$702$			1527.05i			2.17528i
$703$	−112.089	−	76.0181i	−0.159444	−	0.108134i
$704$	−648.985			−0.921853
$705$	82.1212	+	82.1212i	0.116484	+	0.116484i
$706$			2077.09i			2.94205i
$707$			984.734i			1.39283i
$708$	−452.544	+	452.544i	−0.639187	+	0.639187i
$709$	−671.392	+	671.392i	−0.946957	+	0.946957i	−0.998662	−	0.0517055i	$-0.983534\pi$
$709$	−671.392	+	671.392i	−0.946957	+	0.946957i	0.0517055	+	0.998662i	$0.483534\pi$
$710$	−1020.75			−1.43767
$711$	−678.400	+	678.400i	−0.954149	+	0.954149i
$712$	−598.475			−0.840555
$713$	−351.654			−0.493203
$714$		−	1790.14i		−	2.50719i
$715$	−192.297			−0.268947
$716$	−508.761	+	508.761i	−0.710559	+	0.710559i
$717$	−1039.24	−	1039.24i	−1.44942	−	1.44942i
$718$	−999.509	−	999.509i	−1.39207	−	1.39207i
$719$	1045.12			1.45358			0.726788	−	0.686862i	$-0.241012\pi$
$719$	1045.12			1.45358			0.726788	+	0.686862i	$0.241012\pi$
$720$	597.142	−	597.142i	0.829364	−	0.829364i
$721$	265.453	+	265.453i	0.368173	+	0.368173i
$722$	749.981	−	749.981i	1.03876	−	1.03876i
$723$	864.891	+	864.891i	1.19625	+	1.19625i
$724$			1330.00i			1.83701i
$725$	−166.502	+	166.502i	−0.229657	+	0.229657i
$726$	916.215	−	916.215i	1.26200	−	1.26200i
$727$	495.763	+	495.763i	0.681929	+	0.681929i	0.960435	−	0.278505i	$-0.0898390\pi$
$727$	495.763	+	495.763i	0.681929	+	0.681929i	−0.278505	+	0.960435i	$0.589839\pi$
$728$		−	225.362i		−	0.309563i
$729$	−981.161			−1.34590
$730$		−	1033.30i		−	1.41548i
$731$			8.38392i			0.0114691i
$732$	1589.25	+	1589.25i	2.17111	+	2.17111i
$733$			446.007i			0.608468i	0.952597	+	0.304234i	$0.0984005\pi$
$733$			446.007i			0.608468i	−0.952597	+	0.304234i	$0.901600\pi$
$734$	−1019.65	−	1019.65i	−1.38917	−	1.38917i
$735$	−325.008	−	325.008i	−0.442188	−	0.442188i
$736$	−1392.19			−1.89156
$737$	429.480			0.582741
$738$	−129.510	+	129.510i	−0.175487	+	0.175487i
$739$		−	682.939i		−	0.924139i	−0.886844	−	0.462070i	$-0.847107\pi$
$739$		−	682.939i		−	0.924139i	0.886844	−	0.462070i	$-0.152893\pi$
$740$	464.689	−	685.187i	0.627958	−	0.925929i
$741$	−139.125			−0.187753
$742$	−382.666	−	382.666i	−0.515722	−	0.515722i
$743$			808.589i			1.08828i	0.838996	+	0.544138i	$0.183143\pi$
$743$			808.589i			1.08828i	−0.838996	+	0.544138i	$0.816857\pi$
$744$		−	245.725i		−	0.330275i
$745$	174.470	−	174.470i	0.234187	−	0.234187i
$746$	562.170	−	562.170i	0.753578	−	0.753578i
$747$	−3201.10			−4.28527
$748$	−319.515	+	319.515i	−0.427159	+	0.427159i
$749$	707.685			0.944840
$750$	−2314.50			−3.08600
$751$			23.7194i			0.0315838i	0.999875	+	0.0157919i	$0.00502693\pi$
$751$			23.7194i			0.0315838i	−0.999875	+	0.0157919i	$0.994973\pi$
$752$	−44.6379			−0.0593589
$753$	690.830	−	690.830i	0.917437	−	0.917437i
$754$	−477.351	−	477.351i	−0.633091	−	0.633091i
$755$	360.145	+	360.145i	0.477013	+	0.477013i
$756$	3231.76			4.27481
$757$	−55.2321	+	55.2321i	−0.0729618	+	0.0729618i	−0.742646	−	0.669684i	$-0.766429\pi$
$757$	−55.2321	+	55.2321i	−0.0729618	+	0.0729618i	0.669684	+	0.742646i	$0.266429\pi$
$758$	453.117	+	453.117i	0.597780	+	0.597780i
$759$	−845.337	+	845.337i	−1.11375	+	1.11375i
$760$	−43.6063	−	43.6063i	−0.0573767	−	0.0573767i
$761$		−	152.056i		−	0.199811i	−0.994997	−	0.0999054i	$-0.968146\pi$
$761$		−	152.056i		−	0.199811i	0.994997	−	0.0999054i	$-0.0318540\pi$
$762$	1911.86	−	1911.86i	2.50901	−	2.50901i
$763$	−837.391	+	837.391i	−1.09750	+	1.09750i
$764$	849.505	+	849.505i	1.11192	+	1.11192i
$765$		−	1185.62i		−	1.54982i
$766$	759.976			0.992136
$767$		−	146.969i		−	0.191616i
$768$			99.3584i			0.129373i
$769$	−30.9951	−	30.9951i	−0.0403057	−	0.0403057i	0.686667	−	0.726972i	$-0.259073\pi$
$769$	−30.9951	−	30.9951i	−0.0403057	−	0.0403057i	−0.726972	+	0.686667i	$0.759073\pi$
$770$			713.511i			0.926637i
$771$	−337.306	−	337.306i	−0.437491	−	0.437491i
$772$	−1441.35	−	1441.35i	−1.86703	−	1.86703i
$773$	−213.197			−0.275804			−0.137902	−	0.990446i	$-0.544036\pi$
$773$	−213.197			−0.275804			−0.137902	+	0.990446i	$0.544036\pi$
$774$	−44.6744			−0.0577189
$775$	56.4016	−	56.4016i	0.0727763	−	0.0727763i
$776$			326.261i			0.420440i
$777$	−1679.50	+	322.057i	−2.16152	+	0.414488i
$778$	−250.164			−0.321548
$779$	−7.00871	−	7.00871i	−0.00899706	−	0.00899706i
$780$		−	850.454i		−	1.09033i
$781$		−	532.207i		−	0.681443i
$782$	−874.885	+	874.885i	−1.11878	+	1.11878i
$783$	1689.16	−	1689.16i	2.15729	−	2.15729i
$784$	176.662			0.225334
$785$	433.383	−	433.383i	0.552081	−	0.552081i
$786$	−622.250			−0.791666
$787$	402.661			0.511640			0.255820	−	0.966724i	$-0.417655\pi$
$787$	402.661			0.511640			0.255820	+	0.966724i	$0.417655\pi$
$788$		−	186.938i		−	0.237231i
$789$	−784.108			−0.993800
$790$	393.467	−	393.467i	0.498059	−	0.498059i
$791$	−391.612	−	391.612i	−0.495085	−	0.495085i
$792$	−420.123	−	420.123i	−0.530459	−	0.530459i
$793$	−516.129			−0.650856
$794$	−854.342	+	854.342i	−1.07600	+	1.07600i
$795$	−356.340	−	356.340i	−0.448226	−	0.448226i
$796$	−187.674	+	187.674i	−0.235771	+	0.235771i
$797$	85.1838	+	85.1838i	0.106881	+	0.106881i	0.758525	−	0.651644i	$-0.225920\pi$
$797$	85.1838	+	85.1838i	0.106881	+	0.106881i	−0.651644	+	0.758525i	$0.725920\pi$
$798$			516.218i			0.646890i
$799$	−44.3139	+	44.3139i	−0.0554617	+	0.0554617i
$800$	223.293	−	223.293i	0.279116	−	0.279116i
$801$	2346.16	+	2346.16i	2.92904	+	2.92904i
$802$		−	828.476i		−	1.03301i
$803$	538.751			0.670923
$804$			1899.42i			2.36247i
$805$			1114.34i			1.38428i
$806$	161.700	+	161.700i	0.200621	+	0.200621i
$807$		−	1740.55i		−	2.15681i
$808$	336.293	+	336.293i	0.416204	+	0.416204i
$809$	−574.354	−	574.354i	−0.709955	−	0.709955i	0.256570	−	0.966526i	$-0.417408\pi$
$809$	−574.354	−	574.354i	−0.709955	−	0.709955i	−0.966526	+	0.256570i	$0.917408\pi$
$810$	2711.25			3.34722
$811$	−152.248			−0.187729			−0.0938645	−	0.995585i	$-0.529922\pi$
$811$	−152.248			−0.187729			−0.0938645	+	0.995585i	$0.529922\pi$
$812$	−1010.24	+	1010.24i	−1.24414	+	1.24414i
$813$			1516.69i			1.86554i
$814$	626.346	+	424.783i	0.769466	+	0.521847i
$815$	429.826			0.527393
$816$	453.053	+	453.053i	0.555212	+	0.555212i
$817$		−	2.41766i		−	0.00295919i
$818$			12.6292i			0.0154391i
$819$	−883.471	+	883.471i	−1.07872	+	1.07872i
$820$	42.8433	−	42.8433i	0.0522480	−	0.0522480i
$821$	252.662			0.307750			0.153875	−	0.988090i	$-0.450825\pi$
$821$	252.662			0.307750			0.153875	+	0.988090i	$0.450825\pi$
$822$	2213.00	−	2213.00i	2.69222	−	2.69222i
$823$	−968.666			−1.17699			−0.588497	−	0.808499i	$-0.700280\pi$
$823$	−968.666			−1.17699			−0.588497	+	0.808499i	$0.700280\pi$
$824$	181.308			0.220033
$825$		−	271.167i		−	0.328687i
$826$	−545.324			−0.660199
$827$	−475.526	+	475.526i	−0.575001	+	0.575001i	−0.933522	−	0.358521i	$-0.883281\pi$
$827$	−475.526	+	475.526i	−0.575001	+	0.575001i	0.358521	+	0.933522i	$0.383281\pi$
$828$	−2659.02	−	2659.02i	−3.21138	−	3.21138i
$829$	279.445	+	279.445i	0.337087	+	0.337087i	0.855270	−	0.518183i	$-0.173391\pi$
$829$	279.445	+	279.445i	0.337087	+	0.337087i	−0.518183	+	0.855270i	$0.673391\pi$
$830$	1856.61			2.23688
$831$	−530.544	+	530.544i	−0.638440	+	0.638440i
$832$	466.067	+	466.067i	0.560177	+	0.560177i
$833$	175.380	−	175.380i	0.210540	−	0.210540i
$834$	−2620.72	−	2620.72i	−3.14235	−	3.14235i
$835$		−	161.980i		−	0.193988i
$836$	92.1380	−	92.1380i	0.110213	−	0.110213i
$837$	−572.195	+	572.195i	−0.683626	+	0.683626i
$838$	1304.39	+	1304.39i	1.55655	+	1.55655i
$839$			1307.99i			1.55898i	0.626413	+	0.779492i	$0.284522\pi$
$839$			1307.99i			1.55898i	−0.626413	+	0.779492i	$0.715478\pi$
$840$	−778.669			−0.926987
$841$			215.052i			0.255710i
$842$		−	218.983i		−	0.260075i
$843$	−1216.63	−	1216.63i	−1.44322	−	1.44322i
$844$		−	2132.91i		−	2.52715i
$845$	−365.428	−	365.428i	−0.432459	−	0.432459i
$846$	−236.130	−	236.130i	−0.279114	−	0.279114i
$847$	629.723			0.743475
$848$	193.693			0.228411
$849$	−501.015	+	501.015i	−0.590123	+	0.590123i
$850$		−	280.645i		−	0.330171i
$851$	978.211	+	663.416i	1.14948	+	0.779572i
$852$	2353.74			2.76261
$853$	461.196	+	461.196i	0.540675	+	0.540675i	0.923727	−	0.383052i	$-0.125127\pi$
$853$	461.196	+	461.196i	0.540675	+	0.540675i	−0.383052	+	0.923727i	$0.625127\pi$
$854$			1915.08i			2.24248i
$855$			341.894i			0.399876i
$856$	241.679	−	241.679i	0.282335	−	0.282335i
$857$	568.968	−	568.968i	0.663907	−	0.663907i	−0.292392	−	0.956299i	$-0.594451\pi$
$857$	568.968	−	568.968i	0.663907	−	0.663907i	0.956299	+	0.292392i	$0.0944512\pi$
$858$	777.420			0.906084
$859$	−975.430	+	975.430i	−1.13554	+	1.13554i	−0.146302	+	0.989240i	$0.546737\pi$
$859$	−975.430	+	975.430i	−1.13554	+	1.13554i	−0.989240	+	0.146302i	$0.953263\pi$
$860$	14.7788			0.0171847
$861$	−125.153			−0.145358
$862$		−	363.228i		−	0.421378i
$863$	244.884			0.283759			0.141879	−	0.989884i	$-0.454686\pi$
$863$	244.884			0.283759			0.141879	+	0.989884i	$0.454686\pi$
$864$	−2265.31	+	2265.31i	−2.62189	+	2.62189i
$865$	−44.1400	−	44.1400i	−0.0510289	−	0.0510289i
$866$	694.056	+	694.056i	0.801450	+	0.801450i
$867$	−713.888			−0.823401
$868$	342.214	−	342.214i	0.394255	−	0.394255i
$869$	205.150	+	205.150i	0.236076	+	0.236076i
$870$	−1649.34	+	1649.34i	−1.89579	+	1.89579i
$871$	−308.431	−	308.431i	−0.354111	−	0.354111i
$872$			571.949i			0.655905i
$873$	1279.02	−	1279.02i	1.46509	−	1.46509i
$874$	252.289	−	252.289i	0.288660	−	0.288660i
$875$	−795.388	−	795.388i	−0.909015	−	0.909015i
$876$			2382.69i			2.71996i
$877$	226.805			0.258614			0.129307	−	0.991605i	$-0.458725\pi$
$877$	226.805			0.258614			0.129307	+	0.991605i	$0.458725\pi$
$878$		−	620.825i		−	0.707090i
$879$		−	2146.66i		−	2.44217i
$880$	−180.577	−	180.577i	−0.205202	−	0.205202i
$881$		−	171.811i		−	0.195018i	−0.995235	−	0.0975090i	$-0.968913\pi$
$881$		−	171.811i		−	0.195018i	0.995235	−	0.0975090i	$-0.0310875\pi$
$882$	934.524	+	934.524i	1.05955	+	1.05955i
$883$	379.489	+	379.489i	0.429772	+	0.429772i	0.888551	−	0.458778i	$-0.151713\pi$
$883$	379.489	+	379.489i	0.429772	+	0.429772i	−0.458778	+	0.888551i	$0.651713\pi$
$884$	458.919			0.519139
$885$	−507.808			−0.573794
$886$	123.163	−	123.163i	0.139010	−	0.139010i
$887$		−	150.231i		−	0.169370i	−0.996408	−	0.0846849i	$-0.973012\pi$
$887$		−	150.231i		−	0.169370i	0.996408	−	0.0846849i	$-0.0269884\pi$
$888$	−463.575	+	683.544i	−0.522044	+	0.769757i
$889$	1314.04			1.47811
$890$	−1360.76	−	1360.76i	−1.52894	−	1.52894i
$891$			1413.62i			1.58655i
$892$		−	1338.78i		−	1.50088i
$893$	12.7787	−	12.7787i	0.0143099	−	0.0143099i
$894$	−705.347	+	705.347i	−0.788979	+	0.788979i
$895$	−570.889			−0.637865
$896$	708.821	−	708.821i	0.791095	−	0.791095i
$897$	1214.16			1.35357
$898$	1149.87			1.28047
$899$		−	357.733i		−	0.397923i
$900$	852.959			0.947732
$901$	192.287	−	192.287i	0.213415	−	0.213415i
$902$	39.1641	+	39.1641i	0.0434192	+	0.0434192i
$903$	−21.5858	−	21.5858i	−0.0239045	−	0.0239045i
$904$	−267.476			−0.295881
$905$	−746.207	+	746.207i	−0.824539	+	0.824539i
$906$	−1456.00	−	1456.00i	−1.60706	−	1.60706i
$907$	−36.0186	+	36.0186i	−0.0397118	+	0.0397118i	−0.726684	−	0.686972i	$-0.758939\pi$
$907$	−36.0186	+	36.0186i	−0.0397118	+	0.0397118i	0.686972	+	0.726684i	$0.258939\pi$
$908$	−56.6200	−	56.6200i	−0.0623569	−	0.0623569i
$909$		−	2636.69i		−	2.90065i
$910$	512.407	−	512.407i	0.563084	−	0.563084i
$911$	525.018	−	525.018i	0.576310	−	0.576310i	−0.357575	−	0.933885i	$-0.616396\pi$
$911$	525.018	−	525.018i	0.576310	−	0.576310i	0.933885	+	0.357575i	$0.116396\pi$
$912$	−130.646	−	130.646i	−0.143252	−	0.143252i
$913$			968.021i			1.06026i
$914$	−2315.63			−2.53352
$915$			1783.33i			1.94899i
$916$			607.805i			0.663542i
$917$	−213.839	−	213.839i	−0.233194	−	0.233194i
$918$			2847.15i			3.10147i
$919$	−30.0980	−	30.0980i	−0.0327508	−	0.0327508i	0.690542	−	0.723293i	$-0.257372\pi$
$919$	−30.0980	−	30.0980i	−0.0327508	−	0.0327508i	−0.723293	+	0.690542i	$0.757372\pi$
$920$	380.555	+	380.555i	0.413647	+	0.413647i
$921$	1037.97			1.12701
$922$	1384.75			1.50190
$923$	−382.204	+	382.204i	−0.414089	+	0.414089i
$924$		−	1645.29i		−	1.78062i
$925$	−263.300	+	50.4899i	−0.284649	+	0.0545837i
$926$	−2353.72			−2.54182
$927$	−710.768	−	710.768i	−0.766740	−	0.766740i
$928$		−	1416.26i		−	1.52614i
$929$			396.939i			0.427275i	0.976913	+	0.213638i	$0.0685312\pi$
$929$			396.939i			0.427275i	−0.976913	+	0.213638i	$0.931469\pi$
$930$	558.706	−	558.706i	0.600759	−	0.600759i
$931$	−50.5739	+	50.5739i	−0.0543221	+	0.0543221i
$932$	2131.29			2.28680
$933$	−755.712	+	755.712i	−0.809981	+	0.809981i
$934$	1819.89			1.94849
$935$	−358.533			−0.383458
$936$			603.422i			0.644682i
$937$	−447.685			−0.477785			−0.238893	−	0.971046i	$-0.576784\pi$
$937$	−447.685			−0.477785			−0.238893	+	0.971046i	$0.576784\pi$
$938$	−1144.42	+	1144.42i	−1.22006	+	1.22006i
$939$	1068.52	+	1068.52i	1.13793	+	1.13793i
$940$	78.1147	+	78.1147i	0.0831008	+	0.0831008i
$941$	−8.43604			−0.00896497			−0.00448249	−	0.999990i	$-0.501427\pi$
$941$	−8.43604			−0.00896497			−0.00448249	+	0.999990i	$0.501427\pi$
$942$	−1752.09	+	1752.09i	−1.85996	+	1.85996i
$943$	61.1655	+	61.1655i	0.0648626	+	0.0648626i
$944$	138.012	−	138.012i	0.146199	−	0.146199i
$945$	1813.21	+	1813.21i	1.91874	+	1.91874i
$946$			13.5097i			0.0142808i
$947$	952.707	−	952.707i	1.00603	−	1.00603i	0.00604504	−	0.999982i	$-0.498076\pi$
$947$	952.707	−	952.707i	1.00603	−	1.00603i	0.999982	−	0.00604504i	$-0.00192421\pi$
$948$	−907.298	+	907.298i	−0.957065	+	0.957065i
$949$	−386.903	−	386.903i	−0.407696	−	0.407696i
$950$			80.9292i			0.0851886i
$951$	144.449			0.151892
$952$		−	420.182i		−	0.441368i
$953$		−	353.331i		−	0.370757i	−0.982667	−	0.185378i	$-0.940649\pi$
$953$		−	353.331i		−	0.370757i	0.982667	−	0.185378i	$-0.0593511\pi$
$954$	1024.61	+	1024.61i	1.07402	+	1.07402i
$955$			953.245i			0.998162i
$956$	−988.535	−	988.535i	−1.03403	−	1.03403i
$957$	−859.950	−	859.950i	−0.898590	−	0.898590i
$958$	861.564			0.899337
$959$	1521.02			1.58604
$960$	1610.35	−	1610.35i	1.67745	−	1.67745i
$961$		−	839.820i		−	0.873902i
$962$	−144.752	−	754.867i	−0.150470	−	0.784685i
$963$	−1894.88			−1.96768
$964$	822.695	+	822.695i	0.853418	+	0.853418i
$965$		−	1617.36i		−	1.67603i
$966$		−	4505.07i		−	4.66364i
$967$	888.539	−	888.539i	0.918861	−	0.918861i	−0.0780852	−	0.996947i	$-0.524881\pi$
$967$	888.539	−	888.539i	0.918861	−	0.918861i	0.996947	+	0.0780852i	$0.0248806\pi$
$968$	215.055	−	215.055i	0.222164	−	0.222164i
$969$	−259.396			−0.267694
$970$	−741.823	+	741.823i	−0.764766	+	0.764766i
$971$	−1524.17			−1.56969			−0.784845	−	0.619692i	$-0.787257\pi$
$971$	−1524.17			−1.56969			−0.784845	+	0.619692i	$0.787257\pi$
$972$	−2738.62			−2.81751
$973$		−	1801.24i		−	1.85123i
$974$	1681.64			1.72653
$975$	−194.738	+	194.738i	−0.199731	+	0.199731i
$976$	−484.674	−	484.674i	−0.496592	−	0.496592i
$977$	−420.804	−	420.804i	−0.430710	−	0.430710i	0.458160	−	0.888870i	$-0.348509\pi$
$977$	−420.804	−	420.804i	−0.430710	−	0.430710i	−0.888870	+	0.458160i	$0.848509\pi$
$978$	−1737.70			−1.77679
$979$	709.486	−	709.486i	0.724704	−	0.724704i
$980$	−309.152	−	309.152i	−0.315461	−	0.315461i
$981$	2242.17	−	2242.17i	2.28560	−	2.28560i
$982$	1319.91	+	1319.91i	1.34411	+	1.34411i
$983$			595.449i			0.605747i	0.953031	+	0.302873i	$0.0979459\pi$
$983$			595.449i			0.605747i	−0.953031	+	0.302873i	$0.902054\pi$
$984$	−42.7406	+	42.7406i	−0.0434355	+	0.0434355i
$985$	104.883	−	104.883i	0.106481	−	0.106481i
$986$	−890.010	−	890.010i	−0.902647	−	0.902647i
$987$		−	228.187i		−	0.231193i
$988$	−132.338			−0.133945
$989$			21.0991i			0.0213337i
$990$		−	1910.47i		−	1.92977i
$991$	530.742	+	530.742i	0.535562	+	0.535562i	0.922222	−	0.386660i	$-0.126371\pi$
$991$	530.742	+	530.742i	0.535562	+	0.535562i	−0.386660	+	0.922222i	$0.626371\pi$
$992$			479.751i			0.483620i
$993$	1386.48	+	1386.48i	1.39626	+	1.39626i
$994$	1418.15	+	1418.15i	1.42671	+	1.42671i
$995$	−210.592			−0.211651
$996$	−4281.18			−4.29837
$997$	−428.736	+	428.736i	−0.430026	+	0.430026i	−0.888637	−	0.458611i	$-0.848347\pi$
$997$	−428.736	+	428.736i	−0.430026	+	0.430026i	0.458611	+	0.888637i	$0.348347\pi$
$998$			1988.14i			1.99212i
$999$	2671.18	−	512.220i	2.67385	−	0.512733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.3.d.a.31.2	yes	12
3.2	odd	2		333.3.i.a.253.5		12
4.3	odd	2		592.3.k.e.401.1		12
37.6	odd	4	inner	37.3.d.a.6.2	✓	12
111.80	even	4		333.3.i.a.154.5		12
148.43	even	4		592.3.k.e.561.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.3.d.a.6.2	✓	12	37.6	odd	4	inner
37.3.d.a.31.2	yes	12	1.1	even	1	trivial
333.3.i.a.154.5		12	111.80	even	4
333.3.i.a.253.5		12	3.2	odd	2
592.3.k.e.401.1		12	4.3	odd	2
592.3.k.e.561.6		12	148.43	even	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15759 - 2.15759i) q^{2} +5.58276i q^{3} +5.31039i q^{4} +(-2.97944 + 2.97944i) q^{5} +(12.0453 - 12.0453i) q^{6} +8.27885 q^{7} +(2.82728 - 2.82728i) q^{8} -22.1672 q^{9} +O(q^{10})\)	\(q+(-2.15759 - 2.15759i) q^{2} +5.58276i q^{3} +5.31039i q^{4} +(-2.97944 + 2.97944i) q^{5} +(12.0453 - 12.0453i) q^{6} +8.27885 q^{7} +(2.82728 - 2.82728i) q^{8} -22.1672 q^{9} +12.8568 q^{10} +6.70342i q^{11} -29.6466 q^{12} +(4.81406 - 4.81406i) q^{13} +(-17.8624 - 17.8624i) q^{14} +(-16.6335 - 16.6335i) q^{15} +9.04132 q^{16} +(8.97570 - 8.97570i) q^{17} +(47.8277 + 47.8277i) q^{18} +(-2.58831 + 2.58831i) q^{19} +(-15.8220 - 15.8220i) q^{20} +46.2188i q^{21} +(14.4632 - 14.4632i) q^{22} +(22.5883 - 22.5883i) q^{23} +(15.7840 + 15.7840i) q^{24} +7.24587i q^{25} -20.7735 q^{26} -73.5094i q^{27} +43.9639i q^{28} +(22.9788 + 22.9788i) q^{29} +71.7765i q^{30} +(-7.78397 - 7.78397i) q^{31} +(-30.8166 - 30.8166i) q^{32} -37.4236 q^{33} -38.7317 q^{34} +(-24.6663 + 24.6663i) q^{35} -117.717i q^{36} +(6.96809 + 36.3379i) q^{37} +11.1690 q^{38} +(26.8757 + 26.8757i) q^{39} +16.8474i q^{40} +2.70784i q^{41} +(99.7213 - 99.7213i) q^{42} +(-0.467035 + 0.467035i) q^{43} -35.5978 q^{44} +(66.0459 - 66.0459i) q^{45} -97.4727 q^{46} -4.93710 q^{47} +50.4755i q^{48} +19.5394 q^{49} +(15.6336 - 15.6336i) q^{50} +(50.1092 + 50.1092i) q^{51} +(25.5645 + 25.5645i) q^{52} +21.4230 q^{53} +(-158.603 + 158.603i) q^{54} +(-19.9725 - 19.9725i) q^{55} +(23.4066 - 23.4066i) q^{56} +(-14.4499 - 14.4499i) q^{57} -99.1577i q^{58} +(15.2646 - 15.2646i) q^{59} +(88.3303 - 88.3303i) q^{60} +(-53.6065 - 53.6065i) q^{61} +33.5892i q^{62} -183.519 q^{63} +96.8139i q^{64} +28.6864i q^{65} +(80.7448 + 80.7448i) q^{66} -64.0688i q^{67} +(47.6644 + 47.6644i) q^{68} +(126.105 + 126.105i) q^{69} +106.440 q^{70} -79.3933 q^{71} +(-62.6730 + 62.6730i) q^{72} -80.3695i q^{73} +(63.3681 - 93.4367i) q^{74} -40.4520 q^{75} +(-13.7449 - 13.7449i) q^{76} +55.4967i q^{77} -115.974i q^{78} +(30.6038 - 30.6038i) q^{79} +(-26.9381 + 26.9381i) q^{80} +210.880 q^{81} +(5.84240 - 5.84240i) q^{82} +144.407 q^{83} -245.440 q^{84} +53.4851i q^{85} +2.01534 q^{86} +(-128.285 + 128.285i) q^{87} +(18.9525 + 18.9525i) q^{88} +(-105.839 - 105.839i) q^{89} -285.000 q^{90} +(39.8549 - 39.8549i) q^{91} +(119.953 + 119.953i) q^{92} +(43.4560 - 43.4560i) q^{93} +(10.6522 + 10.6522i) q^{94} -15.4234i q^{95} +(172.042 - 172.042i) q^{96} +(-57.6988 + 57.6988i) q^{97} +(-42.1580 - 42.1580i) q^{98} -148.596i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9	\( 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9} - 16 q^{10} + 64 q^{12} + 14 q^{13} - 70 q^{14} - 2 q^{15} - 96 q^{16} + 2 q^{17} + 132 q^{18} + 14 q^{19} - 24 q^{20} + 22 q^{22} + 56 q^{23} - 84 q^{24} - 48 q^{26} + 60 q^{29} + 72 q^{31} + 208 q^{32} + 56 q^{33} + 112 q^{34} - 154 q^{35} - 66 q^{37} - 336 q^{38} - 46 q^{39} + 90 q^{42} + 70 q^{43} + 80 q^{44} + 232 q^{45} - 424 q^{46} - 384 q^{47} + 144 q^{49} - 34 q^{50} - 126 q^{51} + 328 q^{52} - 56 q^{53} - 194 q^{54} + 70 q^{55} + 16 q^{56} - 94 q^{57} + 184 q^{59} + 276 q^{60} + 132 q^{61} - 400 q^{63} + 614 q^{66} + 116 q^{68} + 368 q^{69} + 556 q^{70} + 68 q^{71} - 692 q^{72} - 382 q^{74} + 116 q^{75} + 12 q^{76} - 2 q^{79} + 4 q^{80} - 76 q^{81} + 374 q^{82} + 108 q^{83} - 1436 q^{84} + 140 q^{86} - 420 q^{87} - 788 q^{88} + 278 q^{89} - 664 q^{90} - 450 q^{91} + 652 q^{92} + 584 q^{93} + 118 q^{94} + 1584 q^{96} - 244 q^{97} + 416 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9 - 16 * q^10 + 64 * q^12 + 14 * q^13 - 70 * q^14 - 2 * q^15 - 96 * q^16 + 2 * q^17 + 132 * q^18 + 14 * q^19 - 24 * q^20 + 22 * q^22 + 56 * q^23 - 84 * q^24 - 48 * q^26 + 60 * q^29 + 72 * q^31 + 208 * q^32 + 56 * q^33 + 112 * q^34 - 154 * q^35 - 66 * q^37 - 336 * q^38 - 46 * q^39 + 90 * q^42 + 70 * q^43 + 80 * q^44 + 232 * q^45 - 424 * q^46 - 384 * q^47 + 144 * q^49 - 34 * q^50 - 126 * q^51 + 328 * q^52 - 56 * q^53 - 194 * q^54 + 70 * q^55 + 16 * q^56 - 94 * q^57 + 184 * q^59 + 276 * q^60 + 132 * q^61 - 400 * q^63 + 614 * q^66 + 116 * q^68 + 368 * q^69 + 556 * q^70 + 68 * q^71 - 692 * q^72 - 382 * q^74 + 116 * q^75 + 12 * q^76 - 2 * q^79 + 4 * q^80 - 76 * q^81 + 374 * q^82 + 108 * q^83 - 1436 * q^84 + 140 * q^86 - 420 * q^87 - 788 * q^88 + 278 * q^89 - 664 * q^90 - 450 * q^91 + 652 * q^92 + 584 * q^93 + 118 * q^94 + 1584 * q^96 - 244 * q^97 + 416 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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