LMFDB - Embedded newform 390.2.bn.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(67,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("390.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.1
Root			$0.339278 + 0.0446668i$ of defining polynomial
Character	$\chi$	$=$	390.97
Dual form			390.2.bn.b.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.66815 - 1.48905i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-0.568824 + 0.328411i) q^{7} -1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.66815 - 1.48905i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-0.568824 + 0.328411i) q^{7} -1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +(-2.12363 + 0.700141i) q^{10} +(-1.26026 + 0.337686i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(0.656060 - 3.54536i) q^{13} +0.656821i q^{14} +(-1.00656 + 1.99671i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.49364 - 1.47202i) q^{17} +1.00000i q^{18} +(-0.425167 + 1.58674i) q^{19} +(-0.455475 + 2.18919i) q^{20} +(0.464443 + 0.464443i) q^{21} +(-0.337686 + 1.26026i) q^{22} +(-0.208047 + 0.0557460i) q^{23} +(0.258819 + 0.965926i) q^{24} +(0.565478 + 4.96792i) q^{25} +(-2.74234 - 2.34084i) q^{26} +(0.707107 + 0.707107i) q^{27} +(0.568824 + 0.328411i) q^{28} +(-0.0656377 - 0.0378960i) q^{29} +(1.22592 + 1.87006i) q^{30} +(5.13765 - 5.13765i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.652360 + 1.12992i) q^{33} +(-4.02163 + 4.02163i) q^{34} +(1.43790 + 0.299166i) q^{35} +(0.866025 + 0.500000i) q^{36} +(0.800508 + 0.462173i) q^{37} +(1.16158 + 1.16158i) q^{38} +(-3.59436 + 0.283902i) q^{39} +(1.66815 + 1.48905i) q^{40} +(-2.01318 - 7.51330i) q^{41} +(0.634441 - 0.169998i) q^{42} +(2.45871 - 9.17603i) q^{43} +(0.922576 + 0.922576i) q^{44} +(2.18919 + 0.455475i) q^{45} +(-0.0557460 + 0.208047i) q^{46} -7.92499i q^{47} +(0.965926 + 0.258819i) q^{48} +(-3.28429 + 5.68856i) q^{49} +(4.58508 + 1.99424i) q^{50} +5.68744i q^{51} +(-3.39840 + 1.20452i) q^{52} +(2.58944 - 2.58944i) q^{53} +(0.965926 - 0.258819i) q^{54} +(2.60514 + 1.31328i) q^{55} +(0.568824 - 0.328411i) q^{56} +1.64272 q^{57} +(-0.0656377 + 0.0378960i) q^{58} +(4.72918 + 1.26718i) q^{59} +(2.23248 - 0.126648i) q^{60} +(1.60754 + 2.78433i) q^{61} +(-1.88051 - 7.01816i) q^{62} +(0.328411 - 0.568824i) q^{63} +1.00000 q^{64} +(-6.37362 + 4.93731i) q^{65} +1.30472 q^{66} +(6.64195 - 11.5042i) q^{67} +(1.47202 + 5.49364i) q^{68} +(0.107693 + 0.186530i) q^{69} +(0.978038 - 1.09568i) q^{70} +(-3.94410 - 1.05682i) q^{71} +(0.866025 - 0.500000i) q^{72} +3.44819 q^{73} +(0.800508 - 0.462173i) q^{74} +(4.65229 - 1.83200i) q^{75} +(1.58674 - 0.425167i) q^{76} +(0.605967 - 0.605967i) q^{77} +(-1.55131 + 3.25476i) q^{78} +11.0648i q^{79} +(2.12363 - 0.700141i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-7.51330 - 2.01318i) q^{82} -2.20398i q^{83} +(0.169998 - 0.634441i) q^{84} +(6.97234 + 10.6358i) q^{85} +(-6.71732 - 6.71732i) q^{86} +(-0.0196164 + 0.0732094i) q^{87} +(1.26026 - 0.337686i) q^{88} +(-1.59876 - 5.96664i) q^{89} +(1.48905 - 1.66815i) q^{90} +(0.791152 + 2.23214i) q^{91} +(0.152301 + 0.152301i) q^{92} +(-6.29231 - 3.63287i) q^{93} +(-6.86325 - 3.96250i) q^{94} +(3.07198 - 2.01384i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-6.83472 - 11.8381i) q^{97} +(3.28429 + 5.68856i) q^{98} +(0.922576 - 0.922576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8}+O(q^{10}) $ 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8	$ 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8} + 12 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{16} - 4 q^{17} - 4 q^{19} + 4 q^{23} + 4 q^{25} + 4 q^{26} - 24 q^{28} - 48 q^{29} - 4 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 20 q^{34} - 12 q^{35} + 12 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} + 20 q^{43} - 12 q^{44} + 8 q^{45} - 4 q^{46} - 4 q^{49} - 16 q^{50} - 4 q^{52} + 32 q^{53} + 16 q^{55} - 24 q^{56} - 8 q^{57} - 48 q^{58} + 4 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 16 q^{64} - 8 q^{65} + 32 q^{66} - 28 q^{67} - 16 q^{68} + 4 q^{69} - 36 q^{71} + 32 q^{73} + 12 q^{74} - 24 q^{75} + 8 q^{76} + 4 q^{77} + 20 q^{78} + 8 q^{81} - 24 q^{82} + 52 q^{85} + 16 q^{86} + 36 q^{87} - 12 q^{88} - 24 q^{89} + 4 q^{90} - 8 q^{92} + 36 q^{94} - 40 q^{95} - 4 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8 + 12 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^16 - 4 * q^17 - 4 * q^19 + 4 * q^23 + 4 * q^25 + 4 * q^26 - 24 * q^28 - 48 * q^29 - 4 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 - 20 * q^34 - 12 * q^35 + 12 * q^37 + 4 * q^38 + 4 * q^39 - 12 * q^41 + 20 * q^43 - 12 * q^44 + 8 * q^45 - 4 * q^46 - 4 * q^49 - 16 * q^50 - 4 * q^52 + 32 * q^53 + 16 * q^55 - 24 * q^56 - 8 * q^57 - 48 * q^58 + 4 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 16 * q^64 - 8 * q^65 + 32 * q^66 - 28 * q^67 - 16 * q^68 + 4 * q^69 - 36 * q^71 + 32 * q^73 + 12 * q^74 - 24 * q^75 + 8 * q^76 + 4 * q^77 + 20 * q^78 + 8 * q^81 - 24 * q^82 + 52 * q^85 + 16 * q^86 + 36 * q^87 - 12 * q^88 - 24 * q^89 + 4 * q^90 - 8 * q^92 + 36 * q^94 - 40 * q^95 - 4 * q^97 + 4 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.66815	−	1.48905i	−0.746021	−	0.665922i
$5$	−1.66815	−	1.48905i	−0.746021	−	0.665922i
$6$	−0.965926	−	0.258819i	−0.394338	−	0.105662i
$7$	−0.568824	+	0.328411i	−0.214995	+	0.124128i	−0.603631	−	0.797264i	$-0.706280\pi$
$7$	−0.568824	+	0.328411i	−0.214995	+	0.124128i	0.388636	+	0.921392i	$0.372947\pi$
$8$	−1.00000			−0.353553
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	−2.12363	+	0.700141i	−0.671551	+	0.221404i
$11$	−1.26026	+	0.337686i	−0.379983	+	0.101816i	−0.443755	−	0.896148i	$-0.646354\pi$
$11$	−1.26026	+	0.337686i	−0.379983	+	0.101816i	0.0637713	+	0.997965i	$0.479687\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	0.656060	−	3.54536i	0.181958	−	0.983306i
$13$	0.656060	−	3.54536i	0.181958	−	0.983306i
$14$			0.656821i			0.175543i
$15$	−1.00656	+	1.99671i	−0.259892	+	0.515548i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.49364	−	1.47202i	−1.33240	−	0.357017i	−0.478793	−	0.877928i	$-0.658926\pi$
$17$	−5.49364	−	1.47202i	−1.33240	−	0.357017i	−0.853611	+	0.520911i	$0.825592\pi$
$18$			1.00000i			0.235702i
$19$	−0.425167	+	1.58674i	−0.0975399	+	0.364024i	−0.997392	−	0.0721707i	$-0.977007\pi$
$19$	−0.425167	+	1.58674i	−0.0975399	+	0.364024i	0.899852	+	0.436195i	$0.143674\pi$
$20$	−0.455475	+	2.18919i	−0.101847	+	0.489517i
$21$	0.464443	+	0.464443i	0.101350	+	0.101350i
$22$	−0.337686	+	1.26026i	−0.0719949	+	0.268689i
$23$	−0.208047	+	0.0557460i	−0.0433808	+	0.0116238i	−0.280444	−	0.959870i	$-0.590482\pi$
$23$	−0.208047	+	0.0557460i	−0.0433808	+	0.0116238i	0.237063	+	0.971494i	$0.423815\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$	0.565478	+	4.96792i	0.113096	+	0.993584i
$26$	−2.74234	−	2.34084i	−0.537818	−	0.459077i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	0.568824	+	0.328411i	0.107498	+	0.0620638i
$29$	−0.0656377	−	0.0378960i	−0.0121886	−	0.00703710i	0.493893	−	0.869523i	$-0.335573\pi$
$29$	−0.0656377	−	0.0378960i	−0.0121886	−	0.00703710i	−0.506082	+	0.862485i	$0.668907\pi$
$30$	1.22592	+	1.87006i	0.223821	+	0.341425i
$31$	5.13765	−	5.13765i	0.922749	−	0.922749i	−0.0744742	−	0.997223i	$-0.523728\pi$
$31$	5.13765	−	5.13765i	0.922749	−	0.922749i	0.997223	+	0.0744742i	$0.0237278\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.652360	+	1.12992i	0.113561	+	0.196694i
$34$	−4.02163	+	4.02163i	−0.689703	+	0.689703i
$35$	1.43790	+	0.299166i	0.243050	+	0.0505683i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	0.800508	+	0.462173i	0.131603	+	0.0759808i	0.564356	−	0.825532i	$-0.309125\pi$
$37$	0.800508	+	0.462173i	0.131603	+	0.0759808i	−0.432753	+	0.901512i	$0.642458\pi$
$38$	1.16158	+	1.16158i	0.188433	+	0.188433i
$39$	−3.59436	+	0.283902i	−0.575558	+	0.0454607i
$40$	1.66815	+	1.48905i	0.263758	+	0.235439i
$41$	−2.01318	−	7.51330i	−0.314406	−	1.17338i	−0.924541	−	0.381082i	$-0.875551\pi$
$41$	−2.01318	−	7.51330i	−0.314406	−	1.17338i	0.610135	−	0.792298i	$-0.291115\pi$
$42$	0.634441	−	0.169998i	0.0978963	−	0.0262312i
$43$	2.45871	−	9.17603i	0.374950	−	1.39933i	−0.478469	−	0.878105i	$-0.658808\pi$
$43$	2.45871	−	9.17603i	0.374950	−	1.39933i	0.853418	−	0.521226i	$-0.174525\pi$
$44$	0.922576	+	0.922576i	0.139084	+	0.139084i
$45$	2.18919	+	0.455475i	0.326345	+	0.0678983i
$46$	−0.0557460	+	0.208047i	−0.00821930	+	0.0306748i
$47$		−	7.92499i		−	1.15598i	−0.816044	−	0.577990i	$-0.803837\pi$
$47$		−	7.92499i		−	1.15598i	0.816044	−	0.577990i	$-0.196163\pi$
$48$	0.965926	+	0.258819i	0.139419	+	0.0373573i
$49$	−3.28429	+	5.68856i	−0.469185	+	0.812652i
$50$	4.58508	+	1.99424i	0.648429	+	0.282028i
$51$			5.68744i			0.796400i
$52$	−3.39840	+	1.20452i	−0.471274	+	0.167036i
$53$	2.58944	−	2.58944i	0.355687	−	0.355687i	−0.506533	−	0.862220i	$-0.669073\pi$
$53$	2.58944	−	2.58944i	0.355687	−	0.355687i	0.862220	+	0.506533i	$0.169073\pi$
$54$	0.965926	−	0.258819i	0.131446	−	0.0352208i
$55$	2.60514	+	1.31328i	0.351277	+	0.177082i
$56$	0.568824	−	0.328411i	0.0760123	−	0.0438857i
$57$	1.64272			0.217583
$58$	−0.0656377	+	0.0378960i	−0.00861866	+	0.00497598i
$59$	4.72918	+	1.26718i	0.615686	+	0.164973i	0.553166	−	0.833071i	$-0.313419\pi$
$59$	4.72918	+	1.26718i	0.615686	+	0.164973i	0.0625204	+	0.998044i	$0.480086\pi$
$60$	2.23248	−	0.126648i	0.288212	−	0.0163502i
$61$	1.60754	+	2.78433i	0.205824	+	0.356497i	0.950395	−	0.311046i	$-0.100679\pi$
$61$	1.60754	+	2.78433i	0.205824	+	0.356497i	−0.744571	+	0.667543i	$0.767346\pi$
$62$	−1.88051	−	7.01816i	−0.238825	−	0.891307i
$63$	0.328411	−	0.568824i	0.0413758	−	0.0716651i
$64$	1.00000			0.125000
$65$	−6.37362	+	4.93731i	−0.790550	+	0.612397i
$66$	1.30472			0.160600
$67$	6.64195	−	11.5042i	0.811443	−	1.40546i	−0.100411	−	0.994946i	$-0.532016\pi$
$67$	6.64195	−	11.5042i	0.811443	−	1.40546i	0.911854	−	0.410515i	$-0.134651\pi$
$68$	1.47202	+	5.49364i	0.178508	+	0.666202i
$69$	0.107693	+	0.186530i	0.0129647	+	0.0224555i
$70$	0.978038	−	1.09568i	0.116898	−	0.130959i
$71$	−3.94410	−	1.05682i	−0.468079	−	0.125421i	0.0170676	−	0.999854i	$-0.494567\pi$
$71$	−3.94410	−	1.05682i	−0.468079	−	0.125421i	−0.485146	+	0.874433i	$0.661234\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	3.44819			0.403581			0.201790	−	0.979429i	$-0.435324\pi$
$73$	3.44819			0.403581			0.201790	+	0.979429i	$0.435324\pi$
$74$	0.800508	−	0.462173i	0.0930571	−	0.0537265i
$75$	4.65229	−	1.83200i	0.537200	−	0.211541i
$76$	1.58674	−	0.425167i	0.182012	−	0.0487699i
$77$	0.605967	−	0.605967i	0.0690564	−	0.0690564i
$78$	−1.55131	+	3.25476i	−0.175651	+	0.368528i
$79$			11.0648i			1.24489i	0.782663	+	0.622446i	$0.213861\pi$
$79$			11.0648i			1.24489i	−0.782663	+	0.622446i	$0.786139\pi$
$80$	2.12363	−	0.700141i	0.237429	−	0.0782781i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−7.51330	−	2.01318i	−0.829705	−	0.222319i
$83$		−	2.20398i		−	0.241918i	−0.992658	−	0.120959i	$-0.961403\pi$
$83$		−	2.20398i		−	0.241918i	0.992658	−	0.120959i	$-0.0385969\pi$
$84$	0.169998	−	0.634441i	0.0185483	−	0.0692231i
$85$	6.97234	+	10.6358i	0.756257	+	1.15362i
$86$	−6.71732	−	6.71732i	−0.724347	−	0.724347i
$87$	−0.0196164	+	0.0732094i	−0.00210310	+	0.00784887i
$88$	1.26026	−	0.337686i	0.134344	−	0.0359975i
$89$	−1.59876	−	5.96664i	−0.169468	−	0.632462i	−0.997428	−	0.0716755i	$-0.977165\pi$
$89$	−1.59876	−	5.96664i	−0.169468	−	0.632462i	0.827960	−	0.560787i	$-0.189501\pi$
$90$	1.48905	−	1.66815i	0.156959	−	0.175839i
$91$	0.791152	+	2.23214i	0.0829352	+	0.233992i
$92$	0.152301	+	0.152301i	0.0158785	+	0.0158785i
$93$	−6.29231	−	3.63287i	−0.652482	−	0.376711i
$94$	−6.86325	−	3.96250i	−0.707890	−	0.408700i
$95$	3.07198	−	2.01384i	0.315178	−	0.206616i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−6.83472	−	11.8381i	−0.693961	−	1.20198i	−0.970530	−	0.240982i	$-0.922531\pi$
$97$	−6.83472	−	11.8381i	−0.693961	−	1.20198i	0.276569	−	0.960994i	$-0.410803\pi$
$98$	3.28429	+	5.68856i	0.331764	+	0.574632i
$99$	0.922576	−	0.922576i	0.0927224	−	0.0927224i
$100$	4.01961	−	2.97368i	0.401961	−	0.297368i
$101$	−9.11777	−	5.26415i	−0.907252	−	0.523802i	−0.0277059	−	0.999616i	$-0.508820\pi$
$101$	−9.11777	−	5.26415i	−0.907252	−	0.523802i	−0.879546	+	0.475814i	$0.842154\pi$
$102$	4.92547	+	2.84372i	0.487694	+	0.281570i
$103$	9.71646	+	9.71646i	0.957391	+	0.957391i	0.999129	−	0.0417373i	$-0.0132893\pi$
$103$	9.71646	+	9.71646i	0.957391	+	0.957391i	−0.0417373	+	0.999129i	$0.513289\pi$
$104$	−0.656060	+	3.54536i	−0.0643319	+	0.347651i
$105$	−0.0831851	−	1.46634i	−0.00811803	−	0.143100i
$106$	−0.947801	−	3.53724i	−0.0920586	−	0.343567i
$107$	12.3764	−	3.31625i	1.19647	−	0.320594i	0.395033	−	0.918667i	$-0.370733\pi$
$107$	12.3764	−	3.31625i	1.19647	−	0.320594i	0.801442	+	0.598073i	$0.204067\pi$
$108$	0.258819	−	0.965926i	0.0249049	−	0.0929463i
$109$	13.0240	+	13.0240i	1.24748	+	1.24748i	0.956831	+	0.290646i	$0.0938702\pi$
$109$	13.0240	+	13.0240i	1.24748	+	1.24748i	0.290646	+	0.956831i	$0.406130\pi$
$110$	2.43990	−	1.59948i	0.232636	−	0.152505i
$111$	0.239238	−	0.892850i	0.0227075	−	0.0847456i
$112$		−	0.656821i		−	0.0620638i
$113$	−2.25077	−	0.603092i	−0.211735	−	0.0567341i	0.151392	−	0.988474i	$-0.451624\pi$
$113$	−2.25077	−	0.603092i	−0.211735	−	0.0567341i	−0.363127	+	0.931740i	$0.618291\pi$
$114$	0.821359	−	1.42263i	0.0769273	−	0.133242i
$115$	0.430063	+	0.216799i	0.0401035	+	0.0202166i
$116$			0.0757919i			0.00703710i
$117$	1.20452	+	3.39840i	0.111358	+	0.314182i
$118$	3.46200	−	3.46200i	0.318703	−	0.318703i
$119$	3.60834	−	0.966852i	0.330776	−	0.0886312i
$120$	1.00656	−	1.99671i	0.0918858	−	0.182274i
$121$	−8.05205	+	4.64885i	−0.732005	+	0.422623i
$122$	3.21507			0.291079
$123$	−6.73624	+	3.88917i	−0.607386	+	0.350675i
$124$	−7.01816	−	1.88051i	−0.630249	−	0.168875i
$125$	6.45416	−	9.12928i	0.577278	−	0.816548i
$126$	−0.328411	−	0.568824i	−0.0292571	−	0.0506749i
$127$	−0.324813	−	1.21222i	−0.0288225	−	0.107567i	0.950016	−	0.312201i	$-0.101066\pi$
$127$	−0.324813	−	1.21222i	−0.0288225	−	0.107567i	−0.978839	+	0.204634i	$0.934400\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−9.49972			−0.836404
$130$	1.08902	+	7.98837i	0.0955136	+	0.700626i
$131$	14.7382			1.28768			0.643842	−	0.765159i	$-0.277340\pi$
$131$	14.7382			1.28768			0.643842	+	0.765159i	$0.277340\pi$
$132$	0.652360	−	1.12992i	0.0567806	−	0.0983469i
$133$	−0.279258	−	1.04221i	−0.0242148	−	0.0903708i
$134$	−6.64195	−	11.5042i	−0.573777	−	0.993811i
$135$	−0.126648	−	2.23248i	−0.0109001	−	0.192141i
$136$	5.49364	+	1.47202i	0.471076	+	0.126224i
$137$	−14.0629	+	8.11924i	−1.20148	+	0.693674i	−0.960884	−	0.276952i	$-0.910676\pi$
$137$	−14.0629	+	8.11924i	−1.20148	+	0.693674i	−0.240595	+	0.970626i	$0.577342\pi$
$138$	0.215386			0.0183349
$139$	−6.66282	+	3.84678i	−0.565133	+	0.326280i	−0.755203	−	0.655491i	$-0.772462\pi$
$139$	−6.66282	+	3.84678i	−0.565133	+	0.326280i	0.190070	+	0.981770i	$0.439128\pi$
$140$	−0.459867	−	1.39484i	−0.0388659	−	0.117886i
$141$	−7.65496	+	2.05114i	−0.644664	+	0.172737i
$142$	−2.88728	+	2.88728i	−0.242295	+	0.242295i
$143$	0.370412	+	4.68963i	0.0309754	+	0.392166i
$144$		−	1.00000i		−	0.0833333i
$145$	0.0530650	+	0.160954i	0.00440681	+	0.0133665i
$146$	1.72410	−	2.98622i	0.142687	−	0.247142i
$147$	6.34477	+	1.70008i	0.523308	+	0.140220i
$148$		−	0.924347i		−	0.0759808i
$149$	−3.77709	+	14.0963i	−0.309431	+	1.15481i	0.619632	+	0.784893i	$0.287282\pi$
$149$	−3.77709	+	14.0963i	−0.309431	+	1.15481i	−0.929063	+	0.369921i	$0.879385\pi$
$150$	0.739583	−	4.94500i	0.0603867	−	0.403757i
$151$	−8.69302	−	8.69302i	−0.707428	−	0.707428i	0.258566	−	0.965994i	$-0.416750\pi$
$151$	−8.69302	−	8.69302i	−0.707428	−	0.707428i	−0.965994	+	0.258566i	$0.916750\pi$
$152$	0.425167	−	1.58674i	0.0344856	−	0.128702i
$153$	5.49364	−	1.47202i	0.444135	−	0.119006i
$154$	−0.221799	−	0.827767i	−0.0178731	−	0.0667034i
$155$	−16.2206	+	0.920190i	−1.30287	+	0.0739114i
$156$	2.04304	+	2.97085i	0.163574	+	0.237859i
$157$	−3.31162	−	3.31162i	−0.264296	−	0.264296i	0.562501	−	0.826797i	$-0.309839\pi$
$157$	−3.31162	−	3.31162i	−0.264296	−	0.264296i	−0.826797	+	0.562501i	$0.809839\pi$
$158$	9.58244	+	5.53242i	0.762338	+	0.440136i
$159$	−3.17140	−	1.83101i	−0.251509	−	0.145209i
$160$	0.455475	−	2.18919i	0.0360085	−	0.173070i
$161$	0.100034	−	0.100034i	0.00788382	−	0.00788382i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	0.917052	+	1.58838i	0.0718291	+	0.124412i	0.899703	−	0.436503i	$-0.143783\pi$
$163$	0.917052	+	1.58838i	0.0718291	+	0.124412i	−0.827874	+	0.560914i	$0.810450\pi$
$164$	−5.50012	+	5.50012i	−0.429487	+	0.429487i
$165$	0.594268	−	2.85628i	0.0462637	−	0.222361i
$166$	−1.90870	−	1.10199i	−0.148144	−	0.0855309i
$167$	17.4905	+	10.0982i	1.35346	+	0.781420i	0.988732	−	0.149695i	$-0.0478292\pi$
$167$	17.4905	+	10.0982i	1.35346	+	0.781420i	0.364726	+	0.931115i	$0.381163\pi$
$168$	−0.464443	−	0.464443i	−0.0358325	−	0.0358325i
$169$	−12.1392	−	4.65194i	−0.933782	−	0.357841i
$170$	12.6971	−	0.720302i	0.973822	−	0.0552447i
$171$	−0.425167	−	1.58674i	−0.0325133	−	0.121341i
$172$	−9.17603	+	2.45871i	−0.699665	+	0.187475i
$173$	−2.62932	+	9.81276i	−0.199904	+	0.746051i	0.791039	+	0.611766i	$0.209540\pi$
$173$	−2.62932	+	9.81276i	−0.199904	+	0.746051i	−0.990943	+	0.134285i	$0.957126\pi$
$174$	0.0535930	+	0.0535930i	0.00406287	+	0.00406287i
$175$	−1.95317	−	2.64016i	−0.147646	−	0.199578i
$176$	0.337686	−	1.26026i	0.0254541	−	0.0949958i
$177$		−	4.89600i		−	0.368006i
$178$	−5.96664	−	1.59876i	−0.447218	−	0.119832i
$179$	−0.597467	+	1.03484i	−0.0446568	+	0.0773478i	−0.887490	−	0.460827i	$-0.847553\pi$
$179$	−0.597467	+	1.03484i	−0.0446568	+	0.0773478i	0.842833	+	0.538175i	$0.180886\pi$
$180$	−0.700141	−	2.12363i	−0.0521854	−	0.158286i
$181$			21.0296i			1.56312i	0.623831	+	0.781559i	$0.285575\pi$
$181$			21.0296i			1.56312i	−0.623831	+	0.781559i	$0.714425\pi$
$182$	2.32867	+	0.430914i	0.172612	+	0.0319415i
$183$	2.27340	−	2.27340i	0.168054	−	0.168054i
$184$	0.208047	−	0.0557460i	0.0153374	−	0.00410965i
$185$	−0.647172	−	1.96297i	−0.0475811	−	0.144320i
$186$	−6.29231	+	3.63287i	−0.461374	+	0.266375i
$187$	7.42051			0.542641
$188$	−6.86325	+	3.96250i	−0.500554	+	0.288995i
$189$	−0.634441	−	0.169998i	−0.0461488	−	0.0123655i
$190$	−0.208047	−	3.66733i	−0.0150933	−	0.266056i
$191$	4.06177	+	7.03518i	0.293899	+	0.509048i	0.974728	−	0.223394i	$-0.0717137\pi$
$191$	4.06177	+	7.03518i	0.293899	+	0.509048i	−0.680829	+	0.732442i	$0.738380\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	2.24370	−	3.88620i	0.161505	−	0.279735i	−0.773904	−	0.633303i	$-0.781698\pi$
$193$	2.24370	−	3.88620i	0.161505	−	0.279735i	0.935409	+	0.353568i	$0.115032\pi$
$194$	−13.6694			−0.981409
$195$	6.41869	+	4.87857i	0.459652	+	0.349362i
$196$	6.56859			0.469185
$197$	−5.75874	+	9.97443i	−0.410293	+	0.710649i	−0.994922	−	0.100652i	$-0.967907\pi$
$197$	−5.75874	+	9.97443i	−0.410293	+	0.710649i	0.584628	+	0.811301i	$0.301240\pi$
$198$	−0.337686	−	1.26026i	−0.0239983	−	0.0895629i
$199$	−1.75484	−	3.03947i	−0.124397	−	0.215462i	0.797100	−	0.603847i	$-0.206366\pi$
$199$	−1.75484	−	3.03947i	−0.124397	−	0.215462i	−0.921497	+	0.388385i	$0.873033\pi$
$200$	−0.565478	−	4.96792i	−0.0399853	−	0.351285i
$201$	−12.8313	−	3.43813i	−0.905047	−	0.242507i
$202$	−9.11777	+	5.26415i	−0.641524	+	0.370384i
$203$	0.0497817			0.00349399
$204$	4.92547	−	2.84372i	0.344852	−	0.199100i
$205$	−7.82935	+	15.5311i	−0.546826	+	1.08474i
$206$	13.2729	−	3.55647i	0.924769	−	0.247791i
$207$	0.152301	−	0.152301i	0.0105856	−	0.0105856i
$208$	2.74234	+	2.34084i	0.190147	+	0.162308i
$209$		−	2.14329i		−	0.148254i
$210$	−1.31148	−	0.661129i	−0.0905007	−	0.0456222i
$211$	9.02202	−	15.6266i	0.621102	−	1.07578i	−0.368179	−	0.929755i	$-0.620019\pi$
$211$	9.02202	−	15.6266i	0.621102	−	1.07578i	0.989281	−	0.146025i	$-0.0466479\pi$
$212$	−3.53724	−	0.947801i	−0.242939	−	0.0650952i
$213$			4.08323i			0.279778i
$214$	3.31625	−	12.3764i	0.226694	−	0.846035i
$215$	−17.7650	+	11.6459i	−1.21157	+	0.794243i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−1.23516	+	4.60967i	−0.0838480	+	0.312925i
$218$	17.7912	−	4.76713i	1.20497	−	0.322871i
$219$	−0.892458	−	3.33070i	−0.0603067	−	0.225068i
$220$	−0.165240	−	2.91276i	−0.0111405	−	0.196378i
$221$	−8.82299	+	18.5112i	−0.593498	+	1.24520i
$222$	−0.653612	−	0.653612i	−0.0438675	−	0.0438675i
$223$	−23.8968	−	13.7968i	−1.60025	−	0.923905i	−0.991436	−	0.130592i	$-0.958312\pi$
$223$	−23.8968	−	13.7968i	−1.60025	−	0.923905i	−0.608814	−	0.793313i	$-0.708354\pi$
$224$	−0.568824	−	0.328411i	−0.0380061	−	0.0219429i
$225$	−2.97368	−	4.01961i	−0.198245	−	0.267974i
$226$	−1.64768	+	1.64768i	−0.109602	+	0.109602i
$227$	6.22930	+	10.7895i	0.413453	+	0.716122i	0.995265	−	0.0972019i	$-0.0309893\pi$
$227$	6.22930	+	10.7895i	0.413453	+	0.716122i	−0.581812	+	0.813324i	$0.697656\pi$
$228$	−0.821359	−	1.42263i	−0.0543958	−	0.0942163i
$229$	12.4079	−	12.4079i	0.819937	−	0.819937i	−0.166162	−	0.986099i	$-0.553137\pi$
$229$	12.4079	−	12.4079i	0.819937	−	0.819937i	0.986099	+	0.166162i	$0.0531373\pi$
$230$	0.402784	−	0.264046i	0.0265588	−	0.0174107i
$231$	−0.742155	−	0.428484i	−0.0488302	−	0.0281922i
$232$	0.0656377	+	0.0378960i	0.00430933	+	0.00248799i
$233$	−21.0823	−	21.0823i	−1.38115	−	1.38115i	−0.842582	−	0.538567i	$-0.818966\pi$
$233$	−21.0823	−	21.0823i	−1.38115	−	1.38115i	−0.538567	−	0.842582i	$-0.681034\pi$
$234$	3.54536	+	0.656060i	0.231768	+	0.0428880i
$235$	−11.8007	+	13.2201i	−0.769792	+	0.862385i
$236$	−1.26718	−	4.72918i	−0.0824863	−	0.307843i
$237$	10.6878	−	2.86379i	0.694248	−	0.186023i
$238$	0.966852	−	3.60834i	0.0626717	−	0.233894i
$239$	−0.526226	−	0.526226i	−0.0340388	−	0.0340388i	0.689883	−	0.723921i	$-0.257662\pi$
$239$	−0.526226	−	0.526226i	−0.0340388	−	0.0340388i	−0.723921	+	0.689883i	$0.757662\pi$
$240$	−1.22592	−	1.87006i	−0.0791328	−	0.120712i
$241$	4.41998	−	16.4956i	0.284716	−	1.06258i	−0.664330	−	0.747439i	$-0.731283\pi$
$241$	4.41998	−	16.4956i	0.284716	−	1.06258i	0.949046	−	0.315136i	$-0.102050\pi$
$242$			9.29771i			0.597679i
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$	1.60754	−	2.78433i	0.102912	−	0.178249i
$245$	13.9492	−	4.59893i	0.891185	−	0.293815i
$246$			7.77834i			0.495929i
$247$	5.34664	+	2.54837i	0.340199	+	0.162149i
$248$	−5.13765	+	5.13765i	−0.326241	+	0.326241i
$249$	−2.12888	+	0.570431i	−0.134912	+	0.0361496i
$250$	−4.67911	−	10.1541i	−0.295933	−	0.642202i
$251$	−12.1516	+	7.01575i	−0.767004	+	0.442830i	−0.831805	−	0.555068i	$-0.812692\pi$
$251$	−12.1516	+	7.01575i	−0.767004	+	0.442830i	0.0648005	+	0.997898i	$0.479359\pi$
$252$	−0.656821			−0.0413758
$253$	0.243369	−	0.140509i	0.0153005	−	0.00883373i
$254$	−1.21222	−	0.324813i	−0.0760613	−	0.0203806i
$255$	8.46886	−	9.48752i	0.530341	−	0.594132i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.47521	+	16.7017i	0.279156	+	1.04182i	0.953005	+	0.302955i	$0.0979732\pi$
$257$	4.47521	+	16.7017i	0.279156	+	1.04182i	−0.673849	+	0.738869i	$0.735360\pi$
$258$	−4.74986	+	8.22700i	−0.295713	+	0.512191i
$259$	−0.607130			−0.0377252
$260$	7.46264	+	3.05106i	0.462813	+	0.189219i
$261$	0.0757919			0.00469140
$262$	7.36910	−	12.7637i	0.455265	−	0.788542i
$263$	6.72435	+	25.0956i	0.414641	+	1.54746i	0.785553	+	0.618794i	$0.212378\pi$
$263$	6.72435	+	25.0956i	0.414641	+	1.54746i	−0.370912	+	0.928668i	$0.620955\pi$
$264$	−0.652360	−	1.12992i	−0.0401500	−	0.0695418i
$265$	−8.17539	+	0.463788i	−0.502210	+	0.0284903i
$266$	−1.04221	−	0.279258i	−0.0639018	−	0.0171224i
$267$	−5.34954	+	3.08856i	−0.327387	+	0.189017i
$268$	−13.2839			−0.811443
$269$	21.6715	−	12.5121i	1.32134	−	0.762873i	0.337394	−	0.941364i	$-0.390455\pi$
$269$	21.6715	−	12.5121i	1.32134	−	0.762873i	0.983942	+	0.178490i	$0.0571214\pi$
$270$	−1.99671	−	1.00656i	−0.121516	−	0.0612572i
$271$	2.53478	−	0.679193i	0.153977	−	0.0412580i	−0.181007	−	0.983482i	$-0.557936\pi$
$271$	2.53478	−	0.679193i	0.153977	−	0.0412580i	0.334984	+	0.942224i	$0.391269\pi$
$272$	4.02163	−	4.02163i	0.243847	−	0.243847i
$273$	1.95132	−	1.34191i	0.118099	−	0.0812164i
$274$			16.2385i			0.981003i
$275$	−2.39025	−	6.06993i	−0.144137	−	0.366030i
$276$	0.107693	−	0.186530i	0.00648235	−	0.0112278i
$277$	−28.3973	−	7.60904i	−1.70623	−	0.457183i	−0.731735	−	0.681589i	$-0.761289\pi$
$277$	−28.3973	−	7.60904i	−1.70623	−	0.457183i	−0.974496	+	0.224406i	$0.927956\pi$
$278$			7.69356i			0.461429i
$279$	−1.88051	+	7.01816i	−0.112583	+	0.420166i
$280$	−1.43790	−	0.299166i	−0.0859312	−	0.0178786i
$281$	−10.3701	−	10.3701i	−0.618630	−	0.618630i	0.326550	−	0.945180i	$-0.394114\pi$
$281$	−10.3701	−	10.3701i	−0.618630	−	0.618630i	−0.945180	+	0.326550i	$0.894114\pi$
$282$	−2.05114	+	7.65496i	−0.122144	+	0.455846i
$283$	11.2809	−	3.02271i	0.670580	−	0.179681i	0.0925637	−	0.995707i	$-0.470494\pi$
$283$	11.2809	−	3.02271i	0.670580	−	0.179681i	0.578016	+	0.816025i	$0.303827\pi$
$284$	1.05682	+	3.94410i	0.0627106	+	0.234039i
$285$	−2.74031	−	2.44608i	−0.162322	−	0.144893i
$286$	4.24654	+	2.02403i	0.251103	+	0.119683i
$287$	3.61259	+	3.61259i	0.213245	+	0.213245i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	13.2908	+	7.67347i	0.781814	+	0.451381i
$290$	0.165923	+	0.0345214i	0.00974332	+	0.00202716i
$291$	−9.66576	+	9.66576i	−0.566617	+	0.566617i
$292$	−1.72410	−	2.98622i	−0.100895	−	0.174755i
$293$	−5.72033	−	9.90790i	−0.334185	−	0.578825i	0.649143	−	0.760666i	$-0.275128\pi$
$293$	−5.72033	−	9.90790i	−0.334185	−	0.578825i	−0.983328	+	0.181841i	$0.941794\pi$
$294$	4.64469	−	4.64469i	0.270884	−	0.270884i
$295$	−6.00211	−	9.15582i	−0.349456	−	0.533072i
$296$	−0.800508	−	0.462173i	−0.0465286	−	0.0268633i
$297$	−1.12992	−	0.652360i	−0.0655646	−	0.0378538i
$298$	10.3192	+	10.3192i	0.597775	+	0.597775i
$299$	0.0611485	+	0.774174i	0.00353631	+	0.0447716i
$300$	−3.91270	−	3.11300i	−0.225900	−	0.179729i
$301$	1.61493	+	6.02701i	0.0930831	+	0.347391i
$302$	−11.8749	+	3.18187i	−0.683323	+	0.183096i
$303$	−2.72492	+	10.1695i	−0.156543	+	0.584225i
$304$	−1.16158	−	1.16158i	−0.0666210	−	0.0666210i
$305$	1.46439	−	7.03839i	0.0838505	−	0.403017i
$306$	1.47202	−	5.49364i	0.0841496	−	0.314051i
$307$		−	26.9028i		−	1.53543i	−0.640794	−	0.767713i	$-0.721395\pi$
$307$		−	26.9028i		−	1.53543i	0.640794	−	0.767713i	$-0.278605\pi$
$308$	−0.827767	−	0.221799i	−0.0471664	−	0.0126382i
$309$	6.87058	−	11.9002i	0.390853	−	0.676978i
$310$	−7.31339	+	14.5075i	−0.415372	+	0.823973i
$311$			7.38647i			0.418849i	0.977825	+	0.209424i	$0.0671590\pi$
$311$			7.38647i			0.418849i	−0.977825	+	0.209424i	$0.932841\pi$
$312$	3.59436	−	0.283902i	0.203490	−	0.0160728i
$313$	13.9012	−	13.9012i	0.785742	−	0.785742i	−0.195051	−	0.980793i	$-0.562487\pi$
$313$	13.9012	−	13.9012i	0.785742	−	0.785742i	0.980793	+	0.195051i	$0.0624873\pi$
$314$	−4.52376	+	1.21214i	−0.255291	+	0.0684049i
$315$	−1.39484	+	0.459867i	−0.0785906	+	0.0259106i
$316$	9.58244	−	5.53242i	0.539054	−	0.311223i
$317$	24.2313			1.36097			0.680484	−	0.732763i	$-0.261770\pi$
$317$	24.2313			1.36097			0.680484	+	0.732763i	$0.261770\pi$
$318$	−3.17140	+	1.83101i	−0.177844	+	0.102678i
$319$	0.0955177	+	0.0255939i	0.00534797	+	0.00143298i
$320$	−1.66815	−	1.48905i	−0.0932527	−	0.0832403i
$321$	−6.40651	−	11.0964i	−0.357577	−	0.619341i
$322$	−0.0366151	−	0.136650i	−0.00204048	−	0.00761518i
$323$	4.67143	−	8.09115i	0.259925	−	0.450203i
$324$	−1.00000			−0.0555556
$325$	17.9841	+	1.25443i	0.997576	+	0.0695832i
$326$	1.83410			0.101582
$327$	9.20939	−	15.9511i	0.509280	−	0.882099i
$328$	2.01318	+	7.51330i	0.111159	+	0.414852i
$329$	2.60265	+	4.50793i	0.143489	+	0.248530i
$330$	−2.17647	−	1.94279i	−0.119811	−	0.106947i
$331$	7.54624	+	2.02201i	0.414779	+	0.111140i	0.460173	−	0.887830i	$-0.347788\pi$
$331$	7.54624	+	2.02201i	0.414779	+	0.111140i	−0.0453937	+	0.998969i	$0.514454\pi$
$332$	−1.90870	+	1.10199i	−0.104754	+	0.0604795i
$333$	−0.924347			−0.0506539
$334$	17.4905	−	10.0982i	0.957040	−	0.552547i
$335$	−28.2101	+	9.30059i	−1.54128	+	0.508146i
$336$	−0.634441	+	0.169998i	−0.0346116	+	0.00927414i
$337$	3.21147	−	3.21147i	0.174940	−	0.174940i	−0.614206	−	0.789146i	$-0.710524\pi$
$337$	3.21147	−	3.21147i	0.174940	−	0.174940i	0.789146	+	0.614206i	$0.210524\pi$
$338$	−10.0983	+	8.18686i	−0.549274	+	0.445307i
$339$			2.33017i			0.126557i
$340$	5.72474	−	11.3561i	0.310468	−	0.615873i
$341$	−4.73987	+	8.20970i	−0.256678	+	0.444580i
$342$	−1.58674	−	0.425167i	−0.0858012	−	0.0229904i
$343$		−	8.91213i		−	0.481210i
$344$	−2.45871	+	9.17603i	−0.132565	+	0.494738i
$345$	0.0981030	−	0.471520i	0.00528169	−	0.0253858i
$346$	7.18344	+	7.18344i	0.386184	+	0.386184i
$347$	−4.83017	+	18.0264i	−0.259297	+	0.967710i	0.706352	+	0.707861i	$0.250340\pi$
$347$	−4.83017	+	18.0264i	−0.259297	+	0.967710i	−0.965649	+	0.259849i	$0.916327\pi$
$348$	0.0732094	−	0.0196164i	0.00392444	−	0.00105155i
$349$	−0.712266	−	2.65821i	−0.0381267	−	0.142291i	0.944239	−	0.329261i	$-0.106800\pi$
$349$	−0.712266	−	2.65821i	−0.0381267	−	0.142291i	−0.982366	+	0.186971i	$0.940133\pi$
$350$	−3.26304	+	0.371418i	−0.174417	+	0.0198531i
$351$	2.97085	−	2.04304i	0.158572	−	0.109050i
$352$	−0.922576	−	0.922576i	−0.0491735	−	0.0491735i
$353$	2.10419	+	1.21485i	0.111995	+	0.0646602i	0.554951	−	0.831883i	$-0.312737\pi$
$353$	2.10419	+	1.21485i	0.111995	+	0.0646602i	−0.442956	+	0.896543i	$0.646070\pi$
$354$	−4.24006	−	2.44800i	−0.225357	−	0.130110i
$355$	5.00571	+	7.63589i	0.265676	+	0.405271i
$356$	−4.36788	+	4.36788i	−0.231497	+	0.231497i
$357$	−1.86781	−	3.23515i	−0.0988552	−	0.171222i
$358$	0.597467	+	1.03484i	0.0315771	+	0.0546931i
$359$	21.3084	−	21.3084i	1.12462	−	1.12462i	0.133578	−	0.991038i	$-0.457353\pi$
$359$	21.3084	−	21.3084i	1.12462	−	1.12462i	0.991038	−	0.133578i	$-0.0426466\pi$
$360$	−2.18919	−	0.455475i	−0.115380	−	0.0240057i
$361$	14.1175	+	8.15074i	0.743026	+	0.428986i
$362$	18.2122	+	10.5148i	0.957211	+	0.552646i
$363$	6.57447	+	6.57447i	0.345070	+	0.345070i
$364$	1.53752	−	1.80123i	0.0805878	−	0.0944100i
$365$	−5.75212	−	5.13452i	−0.301080	−	0.268753i
$366$	−0.832121	−	3.10552i	−0.0434957	−	0.162328i
$367$	10.6519	−	2.85418i	0.556027	−	0.148987i	0.0301464	−	0.999545i	$-0.490403\pi$
$367$	10.6519	−	2.85418i	0.556027	−	0.148987i	0.525880	+	0.850559i	$0.323736\pi$
$368$	0.0557460	−	0.208047i	0.00290596	−	0.0108452i
$369$	5.50012	+	5.50012i	0.286325	+	0.286325i
$370$	−2.02357	−	0.421017i	−0.105200	−	0.0218876i
$371$	−0.622536	+	2.32334i	−0.0323204	+	0.120622i
$372$			7.26573i			0.376711i
$373$	−2.85944	−	0.766184i	−0.148056	−	0.0396715i	0.184030	−	0.982921i	$-0.441086\pi$
$373$	−2.85944	−	0.766184i	−0.148056	−	0.0396715i	−0.332086	+	0.943249i	$0.607752\pi$
$374$	3.71025	−	6.42635i	0.191853	−	0.332299i
$375$	−10.4887	−	3.87141i	−0.541633	−	0.199919i
$376$			7.92499i			0.408700i
$377$	−0.177417	+	0.207847i	−0.00913745	+	0.0107047i
$378$	−0.464443	+	0.464443i	−0.0238884	+	0.0238884i
$379$	19.7782	−	5.29955i	1.01594	−	0.272220i	0.287830	−	0.957682i	$-0.407066\pi$
$379$	19.7782	−	5.29955i	1.01594	−	0.272220i	0.728109	+	0.685462i	$0.240400\pi$
$380$	−3.28003	−	1.65349i	−0.168262	−	0.0848223i
$381$	−1.08684	+	0.627490i	−0.0556807	+	0.0321473i
$382$	8.12353			0.415636
$383$	21.6891	−	12.5222i	1.10826	−	0.639855i	0.169882	−	0.985464i	$-0.445661\pi$
$383$	21.6891	−	12.5222i	1.10826	−	0.639855i	0.938378	+	0.345610i	$0.112328\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	−1.91316	+	0.108533i	−0.0975037	+	0.00553136i
$386$	−2.24370	−	3.88620i	−0.114201	−	0.197803i
$387$	2.45871	+	9.17603i	0.124983	+	0.466444i
$388$	−6.83472	+	11.8381i	−0.346981	+	0.600988i
$389$	13.9873			0.709182			0.354591	−	0.935022i	$-0.384620\pi$
$389$	13.9873			0.709182			0.354591	+	0.935022i	$0.384620\pi$
$390$	7.43431	−	3.11946i	0.376451	−	0.157960i
$391$	1.22499			0.0619506
$392$	3.28429	−	5.68856i	0.165882	−	0.287316i
$393$	−3.81453	−	14.2360i	−0.192418	−	0.718112i
$394$	5.75874	+	9.97443i	0.290121	+	0.502505i
$395$	16.4761	−	18.4579i	0.829001	−	0.928716i
$396$	−1.26026	−	0.337686i	−0.0633306	−	0.0169694i
$397$	−18.1215	+	10.4625i	−0.909494	+	0.525096i	−0.880268	−	0.474476i	$-0.842637\pi$
$397$	−18.1215	+	10.4625i	−0.909494	+	0.525096i	−0.0292254	+	0.999573i	$0.509304\pi$
$398$	−3.50967			−0.175924
$399$	−0.934417	+	0.539486i	−0.0467793	+	0.0270081i
$400$	−4.58508	−	1.99424i	−0.229254	−	0.0997121i
$401$	28.6705	−	7.68224i	1.43174	−	0.383633i	0.542105	−	0.840311i	$-0.317628\pi$
$401$	28.6705	−	7.68224i	1.43174	−	0.383633i	0.889632	+	0.456678i	$0.150961\pi$
$402$	−9.39313	+	9.39313i	−0.468487	+	0.468487i
$403$	−14.8442	−	21.5854i	−0.739443	−	1.07525i
$404$			10.5283i			0.523802i
$405$	−2.12363	+	0.700141i	−0.105524	+	0.0347903i
$406$	0.0248909	−	0.0431123i	0.00123531	−	0.00213963i
$407$	−1.16492	−	0.312139i	−0.0577429	−	0.0154722i
$408$		−	5.68744i		−	0.281570i
$409$	3.61041	−	13.4742i	0.178523	−	0.666259i	−0.817401	−	0.576069i	$-0.804586\pi$
$409$	3.61041	−	13.4742i	0.178523	−	0.666259i	0.995925	−	0.0901897i	$-0.0287473\pi$
$410$	9.53562	+	14.5460i	0.470931	+	0.718373i
$411$	11.4823	+	11.4823i	0.566382	+	0.566382i
$412$	3.55647	−	13.2729i	0.175215	−	0.653910i
$413$	−3.10622	+	0.832310i	−0.152847	+	0.0409553i
$414$	−0.0557460	−	0.208047i	−0.00273977	−	0.0102249i
$415$	−3.28183	+	3.67657i	−0.161098	+	0.180476i
$416$	3.39840	−	1.20452i	0.166620	−	0.0590563i
$417$	5.44017	+	5.44017i	0.266406	+	0.266406i
$418$	−1.85614	−	1.07164i	−0.0907867	−	0.0524158i
$419$	−6.36248	−	3.67338i	−0.310827	−	0.179456i	0.336469	−	0.941694i	$-0.390767\pi$
$419$	−6.36248	−	3.67338i	−0.310827	−	0.179456i	−0.647297	+	0.762238i	$0.724101\pi$
$420$	−1.22829	+	0.805210i	−0.0599346	+	0.0392902i
$421$	11.2103	−	11.2103i	0.546356	−	0.546356i	−0.379029	−	0.925385i	$-0.623742\pi$
$421$	11.2103	−	11.2103i	0.546356	−	0.546356i	0.925385	+	0.379029i	$0.123742\pi$
$422$	−9.02202	−	15.6266i	−0.439185	−	0.760691i
$423$	3.96250	+	6.86325i	0.192663	+	0.333702i
$424$	−2.58944	+	2.58944i	−0.125754	+	0.125754i
$425$	4.20633	−	28.1244i	0.204037	−	1.36423i
$426$	3.53618	+	2.04162i	0.171329	+	0.0989166i
$427$	−1.82881	−	1.05586i	−0.0885022	−	0.0510968i
$428$	−9.06017	−	9.06017i	−0.437940	−	0.437940i
$429$	4.43396	−	1.57156i	0.214074	−	0.0758754i
$430$	1.20312	+	21.2079i	0.0580196	+	1.02274i
$431$	9.52492	+	35.5475i	0.458799	+	1.71226i	0.676672	+	0.736285i	$0.263422\pi$
$431$	9.52492	+	35.5475i	0.458799	+	1.71226i	−0.217872	+	0.975977i	$0.569912\pi$
$432$	−0.965926	+	0.258819i	−0.0464731	+	0.0124524i
$433$	2.19180	−	8.17993i	0.105331	−	0.393102i	−0.893051	−	0.449955i	$-0.851440\pi$
$433$	2.19180	−	8.17993i	0.105331	−	0.393102i	0.998383	+	0.0568530i	$0.0181066\pi$
$434$	3.37452	+	3.37452i	0.161982	+	0.161982i
$435$	0.141735	−	0.0929148i	0.00679569	−	0.00445492i
$436$	4.76713	−	17.7912i	0.228304	−	0.852042i
$437$		−	0.353818i		−	0.0169254i
$438$	−3.33070	−	0.892458i	−0.159147	−	0.0426433i
$439$	−8.93023	+	15.4676i	−0.426216	+	0.738229i	−0.996533	−	0.0831963i	$-0.973487\pi$
$439$	−8.93023	+	15.4676i	−0.426216	+	0.738229i	0.570317	+	0.821425i	$0.306820\pi$
$440$	−2.60514	−	1.31328i	−0.124195	−	0.0626080i
$441$		−	6.56859i		−	0.312790i
$442$	11.6197	+	16.8965i	0.552692	+	0.803686i
$443$	−2.70502	+	2.70502i	−0.128519	+	0.128519i	−0.768440	−	0.639921i	$-0.778967\pi$
$443$	−2.70502	+	2.70502i	−0.128519	+	0.128519i	0.639921	+	0.768440i	$0.278967\pi$
$444$	−0.892850	+	0.239238i	−0.0423728	+	0.0113538i
$445$	−6.21763	+	12.3339i	−0.294744	+	0.584683i
$446$	−23.8968	+	13.7968i	−1.13155	+	0.653299i
$447$	14.5936			0.690252
$448$	−0.568824	+	0.328411i	−0.0268744	+	0.0155159i
$449$	11.5315	+	3.08986i	0.544205	+	0.145819i	0.520440	−	0.853898i	$-0.325768\pi$
$449$	11.5315	+	3.08986i	0.544205	+	0.145819i	0.0237652	+	0.999718i	$0.492435\pi$
$450$	−4.96792	+	0.565478i	−0.234190	+	0.0266569i
$451$	5.07427	+	8.78890i	0.238938	+	0.413853i
$452$	0.603092	+	2.25077i	0.0283671	+	0.105867i
$453$	−6.14689	+	10.6467i	−0.288806	+	0.500227i
$454$	12.4586			0.584711
$455$	2.00400	−	4.90162i	0.0939491	−	0.229792i
$456$	−1.64272			−0.0769273
$457$	−20.3307	+	35.2137i	−0.951028	+	1.64723i	−0.207821	+	0.978167i	$0.566637\pi$
$457$	−20.3307	+	35.2137i	−0.951028	+	1.64723i	−0.743207	+	0.669062i	$0.766696\pi$
$458$	−4.54161	−	16.9495i	−0.212215	−	0.791998i
$459$	−2.84372	−	4.92547i	−0.132733	−	0.229901i
$460$	−0.0272782	−	0.480844i	−0.00127185	−	0.0224195i
$461$	30.0601	+	8.05459i	1.40004	+	0.375139i	0.878359	−	0.478001i	$-0.158639\pi$
$461$	30.0601	+	8.05459i	1.40004	+	0.375139i	0.521681	+	0.853141i	$0.325305\pi$
$462$	−0.742155	+	0.428484i	−0.0345282	+	0.0199349i
$463$	−13.3638			−0.621069			−0.310534	−	0.950562i	$-0.600508\pi$
$463$	−13.3638			−0.621069			−0.310534	+	0.950562i	$0.600508\pi$
$464$	0.0656377	−	0.0378960i	0.00304716	−	0.00175928i
$465$	5.08703	+	15.4297i	0.235905	+	0.715536i
$466$	−28.7990	+	7.71667i	−1.33409	+	0.357468i
$467$	15.7888	−	15.7888i	0.730619	−	0.730619i	−0.240123	−	0.970742i	$-0.577188\pi$
$467$	15.7888	−	15.7888i	0.730619	−	0.730619i	0.970742	+	0.240123i	$0.0771878\pi$
$468$	2.34084	−	2.74234i	0.108206	−	0.126765i
$469$			8.72514i			0.402890i
$470$	5.54861	+	16.8298i	0.255938	+	0.776299i
$471$	−2.34167	+	4.05589i	−0.107898	+	0.186886i
$472$	−4.72918	−	1.26718i	−0.217678	−	0.0583267i
$473$			12.3945i			0.569898i
$474$	2.86379	−	10.6878i	0.131538	−	0.490908i
$475$	−8.12324	−	1.21493i	−0.372720	−	0.0557446i
$476$	−2.64149	−	2.64149i	−0.121072	−	0.121072i
$477$	−0.947801	+	3.53724i	−0.0433968	+	0.161959i
$478$	−0.718839	+	0.192612i	−0.0328789	+	0.00880988i
$479$	−8.34864	−	31.1575i	−0.381459	−	1.42362i	−0.843674	−	0.536856i	$-0.819612\pi$
$479$	−8.34864	−	31.1575i	−0.381459	−	1.42362i	0.462215	−	0.886768i	$-0.347055\pi$
$480$	−2.23248	+	0.126648i	−0.101898	+	0.00578066i
$481$	2.16375	−	2.53488i	0.0986586	−	0.115580i
$482$	−12.0756	−	12.0756i	−0.550029	−	0.550029i
$483$	−0.122517	−	0.0707350i	−0.00557470	−	0.00321855i
$484$	8.05205	+	4.64885i	0.366002	+	0.211312i
$485$	−6.22610	+	29.9250i	−0.282713	+	1.35882i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	−6.60545	−	11.4410i	−0.299321	−	0.518440i	0.676659	−	0.736296i	$-0.263427\pi$
$487$	−6.60545	−	11.4410i	−0.299321	−	0.518440i	−0.975981	+	0.217856i	$0.930094\pi$
$488$	−1.60754	−	2.78433i	−0.0727697	−	0.126041i
$489$	1.29691	−	1.29691i	0.0586482	−	0.0586482i
$490$	2.99183	−	14.3799i	0.135157	−	0.649616i
$491$	−21.0123	−	12.1315i	−0.948274	−	0.547486i	−0.0557297	−	0.998446i	$-0.517749\pi$
$491$	−21.0123	−	12.1315i	−0.948274	−	0.547486i	−0.892544	+	0.450960i	$0.851082\pi$
$492$	6.73624	+	3.88917i	0.303693	+	0.175337i
$493$	0.304807	+	0.304807i	0.0137278	+	0.0137278i
$494$	4.88027	−	3.35614i	0.219574	−	0.151000i
$495$	−2.91276	+	0.165240i	−0.130919	+	0.00742699i
$496$	1.88051	+	7.01816i	0.0844374	+	0.315125i
$497$	2.59057	−	0.694141i	0.116203	−	0.0311365i
$498$	−0.570431	+	2.12888i	−0.0255616	+	0.0953973i
$499$	−23.6665	−	23.6665i	−1.05946	−	1.05946i	−0.998117	−	0.0613431i	$-0.980462\pi$
$499$	−23.6665	−	23.6665i	−1.05946	−	1.05946i	−0.0613431	−	0.998117i	$-0.519538\pi$
$500$	−11.1333	−	1.02483i	−0.497895	−	0.0458317i
$501$	5.22720	−	19.5082i	0.233534	−	0.871560i
$502$			14.0315i			0.626257i
$503$	−21.3318	−	5.71583i	−0.951137	−	0.254856i	−0.250292	−	0.968170i	$-0.580527\pi$
$503$	−21.3318	−	5.71583i	−0.951137	−	0.254856i	−0.700845	+	0.713314i	$0.747193\pi$
$504$	−0.328411	+	0.568824i	−0.0146286	+	0.0253374i
$505$	7.37128	+	22.3582i	0.328018	+	0.994926i
$506$		−	0.281018i		−	0.0124928i
$507$	−1.35158	+	12.9295i	−0.0600256	+	0.574221i
$508$	−0.887405	+	0.887405i	−0.0393722	+	0.0393722i
$509$	17.4786	−	4.68339i	0.774727	−	0.207588i	0.150268	−	0.988645i	$-0.451986\pi$
$509$	17.4786	−	4.68339i	0.774727	−	0.207588i	0.624459	+	0.781058i	$0.285320\pi$
$510$	−3.98201	−	12.0780i	−0.176326	−	0.534823i
$511$	−1.96141	+	1.13242i	−0.0867679	+	0.0500955i
$512$	−1.00000			−0.0441942
$513$	−1.42263	+	0.821359i	−0.0628109	+	0.0362639i
$514$	16.7017	+	4.47521i	0.736681	+	0.197393i
$515$	−1.74029	−	30.6768i	−0.0766863	−	1.35178i
$516$	4.74986	+	8.22700i	0.209101	+	0.362173i
$517$	2.67616	+	9.98757i	0.117697	+	0.439253i
$518$	−0.303565	+	0.525790i	−0.0133379	+	0.0231019i
$519$	10.1589			0.445927
$520$	6.37362	−	4.93731i	0.279502	−	0.216515i
$521$	30.3276			1.32868			0.664339	−	0.747432i	$-0.268713\pi$
$521$	30.3276			1.32868			0.664339	+	0.747432i	$0.268713\pi$
$522$	0.0378960	−	0.0656377i	0.00165866	−	0.00287289i
$523$	11.7984	+	44.0321i	0.515906	+	1.92539i	0.336905	+	0.941539i	$0.390620\pi$
$523$	11.7984	+	44.0321i	0.515906	+	1.92539i	0.179001	+	0.983849i	$0.442713\pi$
$524$	−7.36910	−	12.7637i	−0.321921	−	0.557583i
$525$	−2.04468	+	2.56995i	−0.0892373	+	0.112162i
$526$	25.0956	+	6.72435i	1.09422	+	0.293196i
$527$	−35.7871	+	20.6617i	−1.55891	+	0.900038i
$528$	−1.30472			−0.0567806
$529$	−19.8784	+	11.4768i	−0.864279	+	0.498991i
$530$	−3.68604	+	7.31199i	−0.160111	+	0.317612i
$531$	−4.72918	+	1.26718i	−0.205229	+	0.0549909i
$532$	−0.762948	+	0.762948i	−0.0330780	+	0.0330780i
$533$	−27.9581	+	2.20829i	−1.21100	+	0.0956515i
$534$			6.17712i			0.267310i
$535$	−25.5839	−	12.8971i	−1.10609	−	0.557589i
$536$	−6.64195	+	11.5042i	−0.286888	+	0.496905i
$537$	1.15422	+	0.309271i	0.0498081	+	0.0133461i
$538$		−	25.0241i		−	1.07887i
$539$	2.21812	−	8.27814i	0.0955412	−	0.356565i
$540$	−1.87006	+	1.22592i	−0.0804745	+	0.0527552i
$541$	−7.31140	−	7.31140i	−0.314342	−	0.314342i	0.532247	−	0.846589i	$-0.321348\pi$
$541$	−7.31140	−	7.31140i	−0.314342	−	0.314342i	−0.846589	+	0.532247i	$0.821348\pi$
$542$	0.679193	−	2.53478i	0.0291738	−	0.108878i
$543$	20.3130	−	5.44286i	0.871716	−	0.233576i
$544$	−1.47202	−	5.49364i	−0.0631122	−	0.235538i
$545$	−2.33270	−	41.1195i	−0.0999219	−	1.76137i
$546$	−0.186473	−	2.36085i	−0.00798030	−	0.101035i
$547$	−30.7225	−	30.7225i	−1.31360	−	1.31360i	−0.918742	−	0.394857i	$-0.870794\pi$
$547$	−30.7225	−	30.7225i	−1.31360	−	1.31360i	−0.394857	−	0.918742i	$-0.629206\pi$
$548$	14.0629	+	8.11924i	0.600739	+	0.346837i
$549$	−2.78433	−	1.60754i	−0.118832	−	0.0686079i
$550$	−6.45184	−	0.964948i	−0.275107	−	0.0411455i
$551$	0.0880381	−	0.0880381i	0.00375055	−	0.00375055i
$552$	−0.107693	−	0.186530i	−0.00458372	−	0.00793923i
$553$	−3.63381	−	6.29395i	−0.154525	−	0.267646i
$554$	−20.7883	+	20.7883i	−0.883210	+	0.883210i
$555$	−1.72858	+	1.13317i	−0.0733742	+	0.0481006i
$556$	6.66282	+	3.84678i	0.282566	+	0.163140i
$557$	−14.1530	−	8.17126i	−0.599683	−	0.346227i	0.169234	−	0.985576i	$-0.445871\pi$
$557$	−14.1530	−	8.17126i	−0.599683	−	0.346227i	−0.768917	+	0.639349i	$0.779204\pi$
$558$	5.13765	+	5.13765i	0.217494	+	0.217494i
$559$	−30.9193	−	14.7370i	−1.30775	−	0.623310i
$560$	−0.978038	+	1.09568i	−0.0413296	+	0.0463009i
$561$	−1.92057	−	7.16766i	−0.0810865	−	0.302619i
$562$	−14.1659	+	3.79573i	−0.597551	+	0.160113i
$563$	4.87699	−	18.2012i	0.205541	−	0.767088i	−0.783743	−	0.621085i	$-0.786692\pi$
$563$	4.87699	−	18.2012i	0.205541	−	0.767088i	0.989284	−	0.146003i	$-0.0466410\pi$
$564$	5.60382	+	5.60382i	0.235963	+	0.235963i
$565$	2.85660	+	4.35755i	0.120178	+	0.183324i
$566$	3.02271	−	11.2809i	0.127054	−	0.474171i
$567$			0.656821i			0.0275839i
$568$	3.94410	+	1.05682i	0.165491	+	0.0443431i
$569$	−5.61694	+	9.72882i	−0.235474	+	0.407853i	−0.959410	−	0.282014i	$-0.908998\pi$
$569$	−5.61694	+	9.72882i	−0.235474	+	0.407853i	0.723936	+	0.689867i	$0.242331\pi$
$570$	−3.48852	+	1.15013i	−0.146118	+	0.0481738i
$571$			38.3139i			1.60339i	0.597735	+	0.801693i	$0.296067\pi$
$571$			38.3139i			1.60339i	−0.597735	+	0.801693i	$0.703933\pi$
$572$	3.87613	−	2.66560i	0.162069	−	0.111454i
$573$	5.74420	−	5.74420i	0.239968	−	0.239968i
$574$	4.93489	−	1.32230i	0.205978	−	0.0551918i
$575$	−0.394587	−	1.00204i	−0.0164554	−	0.0417878i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	−18.0766			−0.752540			−0.376270	−	0.926510i	$-0.622793\pi$
$577$	−18.0766			−0.752540			−0.376270	+	0.926510i	$0.622793\pi$
$578$	13.2908	−	7.67347i	0.552826	−	0.319174i
$579$	−4.33450	−	1.16143i	−0.180136	−	0.0482672i
$580$	0.112858	−	0.126433i	0.00468616	−	0.00524983i
$581$	0.723809	+	1.25367i	0.0300287	+	0.0520112i
$582$	3.53791	+	13.2037i	0.146651	+	0.547310i
$583$	−2.38896	+	4.13779i	−0.0989404	+	0.171370i
$584$	−3.44819			−0.142687
$585$	3.05106	−	7.46264i	0.126146	−	0.308542i
$586$	−11.4407			−0.472609
$587$	−7.51880	+	13.0229i	−0.310334	+	0.537514i	−0.978435	−	0.206557i	$-0.933774\pi$
$587$	−7.51880	+	13.0229i	−0.310334	+	0.537514i	0.668101	+	0.744071i	$0.267108\pi$
$588$	−1.70008	−	6.34477i	−0.0701099	−	0.261654i
$589$	5.96777	+	10.3365i	0.245898	+	0.425907i
$590$	−10.9302	+	0.620069i	−0.449990	+	0.0255278i
$591$	11.1250	+	2.98094i	0.457623	+	0.122620i
$592$	−0.800508	+	0.462173i	−0.0329007	+	0.0189952i
$593$	−36.6579			−1.50536			−0.752680	−	0.658387i	$-0.771239\pi$
$593$	−36.6579			−1.50536			−0.752680	+	0.658387i	$0.771239\pi$
$594$	−1.12992	+	0.652360i	−0.0463612	+	0.0267666i
$595$	−7.45896	−	3.76013i	−0.305787	−	0.154150i
$596$	14.0963	−	3.77709i	0.577407	−	0.154716i
$597$	−2.48171	+	2.48171i	−0.101570	+	0.101570i
$598$	0.701028	+	0.334131i	0.0286672	+	0.0136636i
$599$		−	9.07935i		−	0.370972i	−0.982647	−	0.185486i	$-0.940614\pi$
$599$		−	9.07935i		−	0.370972i	0.982647	−	0.185486i	$-0.0593860\pi$
$600$	−4.65229	+	1.83200i	−0.189929	+	0.0747912i
$601$	17.2295	−	29.8423i	0.702805	−	1.21729i	−0.264673	−	0.964338i	$-0.585264\pi$
$601$	17.2295	−	29.8423i	0.702805	−	1.21729i	0.967478	−	0.252956i	$-0.0814027\pi$
$602$	6.02701	+	1.61493i	0.245643	+	0.0658197i
$603$			13.2839i			0.540962i
$604$	−3.18187	+	11.8749i	−0.129468	+	0.483182i
$605$	20.3544	+	4.23488i	0.827525	+	0.172172i
$606$	7.44463	+	7.44463i	0.302417	+	0.302417i
$607$	−7.45542	+	27.8240i	−0.302606	+	1.12934i	0.632381	+	0.774658i	$0.282078\pi$
$607$	−7.45542	+	27.8240i	−0.302606	+	1.12934i	−0.934987	+	0.354683i	$0.884589\pi$
$608$	−1.58674	+	0.425167i	−0.0643509	+	0.0172428i
$609$	−0.0128845	−	0.0480855i	−0.000522105	−	0.00194852i
$610$	−5.36323	−	4.78739i	−0.217151	−	0.193836i
$611$	−28.0970	−	5.19927i	−1.13668	−	0.210340i
$612$	−4.02163	−	4.02163i	−0.162565	−	0.162565i
$613$	13.8536	+	7.99836i	0.559540	+	0.323051i	0.752961	−	0.658065i	$-0.228625\pi$
$613$	13.8536	+	7.99836i	0.559540	+	0.323051i	−0.193421	+	0.981116i	$0.561958\pi$
$614$	−23.2985	−	13.4514i	−0.940253	−	0.542855i
$615$	17.0282	+	3.54284i	0.686645	+	0.142861i
$616$	−0.605967	+	0.605967i	−0.0244151	+	0.0244151i
$617$	−3.05979	−	5.29972i	−0.123183	−	0.213359i	0.797838	−	0.602871i	$-0.205977\pi$
$617$	−3.05979	−	5.29972i	−0.123183	−	0.213359i	−0.921021	+	0.389513i	$0.872643\pi$
$618$	−6.87058	−	11.9002i	−0.276375	−	0.478696i
$619$	1.83202	−	1.83202i	0.0736353	−	0.0736353i	−0.669330	−	0.742965i	$-0.733419\pi$
$619$	1.83202	−	1.83202i	0.0736353	−	0.0736353i	0.742965	+	0.669330i	$0.233419\pi$
$620$	8.90720	+	13.5873i	0.357722	+	0.545681i
$621$	−0.186530	−	0.107693i	−0.00748518	−	0.00432157i
$622$	6.39687	+	3.69324i	0.256491	+	0.148085i
$623$	2.86892	+	2.86892i	0.114941	+	0.114941i
$624$	1.55131	−	3.25476i	0.0621022	−	0.130294i
$625$	−24.3605	+	5.61850i	−0.974419	+	0.224740i
$626$	−5.08819	−	18.9894i	−0.203365	−	0.758968i
$627$	−2.07025	+	0.554723i	−0.0826780	+	0.0221535i
$628$	−1.21214	+	4.52376i	−0.0483696	+	0.180518i
$629$	−3.71738	−	3.71738i	−0.148221	−	0.148221i
$630$	−0.299166	+	1.43790i	−0.0119191	+	0.0572875i
$631$	7.50451	−	28.0072i	0.298750	−	1.11495i	−0.639444	−	0.768838i	$-0.720835\pi$
$631$	7.50451	−	28.0072i	0.298750	−	1.11495i	0.938193	−	0.346111i	$-0.112498\pi$
$632$		−	11.0648i		−	0.440136i
$633$	−17.4292	−	4.67014i	−0.692749	−	0.185622i
$634$	12.1157	−	20.9850i	0.481175	−	0.833419i
$635$	−1.26321	+	2.50583i	−0.0501290	+	0.0994408i
$636$			3.66202i			0.145209i
$637$	18.0133	+	15.3760i	0.713714	+	0.609221i
$638$	0.0699238	−	0.0699238i	0.00276831	−	0.00276831i
$639$	3.94410	−	1.05682i	0.156026	−	0.0418071i
$640$	−2.12363	+	0.700141i	−0.0839438	+	0.0276755i
$641$	−18.3265	+	10.5808i	−0.723851	+	0.417916i	−0.816169	−	0.577814i	$-0.803906\pi$
$641$	−18.3265	+	10.5808i	−0.723851	+	0.417916i	0.0923172	+	0.995730i	$0.470573\pi$
$642$	−12.8130			−0.505690
$643$	11.7319	−	6.77343i	0.462662	−	0.267118i	−0.250501	−	0.968116i	$-0.580595\pi$
$643$	11.7319	−	6.77343i	0.462662	−	0.267118i	0.713163	+	0.700998i	$0.247262\pi$
$644$	−0.136650	−	0.0366151i	−0.00538475	−	0.00144284i
$645$	15.8470	+	14.1455i	0.623975	+	0.556980i
$646$	−4.67143	−	8.09115i	−0.183795	−	0.318342i
$647$	−10.1296	−	37.8041i	−0.398235	−	1.48623i	−0.816200	−	0.577769i	$-0.803923\pi$
$647$	−10.1296	−	37.8041i	−0.398235	−	1.48623i	0.417966	−	0.908463i	$-0.362743\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−6.38791			−0.250747
$650$	10.0784	−	14.9474i	0.395307	−	0.586287i
$651$	4.77229			0.187041
$652$	0.917052	−	1.58838i	0.0359145	−	0.0622058i
$653$	3.12337	+	11.6566i	0.122227	+	0.456157i	0.999726	−	0.0234221i	$-0.00745618\pi$
$653$	3.12337	+	11.6566i	0.122227	+	0.456157i	−0.877499	+	0.479579i	$0.840790\pi$
$654$	−9.20939	−	15.9511i	−0.360115	−	0.623738i
$655$	−24.5856	−	21.9459i	−0.960639	−	0.857497i
$656$	7.51330	+	2.01318i	0.293345	+	0.0786015i
$657$	−2.98622	+	1.72410i	−0.116504	+	0.0672634i
$658$	5.20530			0.202924
$659$	−18.1821	+	10.4974i	−0.708273	+	0.408921i	−0.810421	−	0.585848i	$-0.800762\pi$
$659$	−18.1821	+	10.4974i	−0.708273	+	0.408921i	0.102149	+	0.994769i	$0.467428\pi$
$660$	−2.77074	+	0.913487i	−0.107851	+	0.0355574i
$661$	−20.7944	+	5.57184i	−0.808808	+	0.216719i	−0.639448	−	0.768835i	$-0.720837\pi$
$661$	−20.7944	+	5.57184i	−0.808808	+	0.216719i	−0.169360	+	0.985554i	$0.554170\pi$
$662$	5.52423	−	5.52423i	0.214705	−	0.214705i
$663$	20.1640	+	3.73130i	0.783106	+	0.144912i
$664$			2.20398i			0.0855309i
$665$	−1.08605	+	2.15439i	−0.0421151	+	0.0835437i
$666$	−0.462173	+	0.800508i	−0.0179088	+	0.0310190i
$667$	0.0157683	+	0.00422510i	0.000610550	+	0.000163596i
$668$		−	20.1963i		−	0.781420i
$669$	−7.14177	+	26.6535i	−0.276117	+	1.03048i
$670$	−6.05049	+	29.0809i	−0.233751	+	1.12349i
$671$	−2.96615	−	2.96615i	−0.114507	−	0.114507i
$672$	−0.169998	+	0.634441i	−0.00655781	+	0.0244741i
$673$	13.8145	−	3.70159i	0.532511	−	0.142686i	0.0174635	−	0.999848i	$-0.494441\pi$
$673$	13.8145	−	3.70159i	0.532511	−	0.142686i	0.515048	+	0.857162i	$0.327774\pi$
$674$	−1.17548	−	4.38695i	−0.0452778	−	0.168979i
$675$	−3.11300	+	3.91270i	−0.119819	+	0.150600i
$676$	2.04089	+	12.8388i	0.0784958	+	0.493800i
$677$	−23.0498	−	23.0498i	−0.885875	−	0.885875i	0.108249	−	0.994124i	$-0.465476\pi$
$677$	−23.0498	−	23.0498i	−0.885875	−	0.885875i	−0.994124	+	0.108249i	$0.965476\pi$
$678$	2.01799	+	1.16508i	0.0775003	+	0.0447448i
$679$	7.77551	+	4.48919i	0.298397	+	0.172279i
$680$	−6.97234	−	10.6358i	−0.267377	−	0.407866i
$681$	8.80956	−	8.80956i	0.337583	−	0.337583i
$682$	4.73987	+	8.20970i	0.181499	+	0.314366i
$683$	5.14139	+	8.90514i	0.196730	+	0.340746i	0.947466	−	0.319856i	$-0.103635\pi$
$683$	5.14139	+	8.90514i	0.196730	+	0.340746i	−0.750736	+	0.660602i	$0.770301\pi$
$684$	−1.16158	+	1.16158i	−0.0444140	+	0.0444140i
$685$	35.5491	+	7.39623i	1.35826	+	0.282596i
$686$	−7.71813	−	4.45607i	−0.294680	−	0.170133i
$687$	−15.1965	−	8.77371i	−0.579783	−	0.334738i
$688$	6.71732	+	6.71732i	0.256095	+	0.256095i
$689$	−7.48168	−	10.8793i	−0.285029	−	0.414469i
$690$	−0.359297	−	0.320720i	−0.0136782	−	0.0122096i
$691$	2.69876	+	10.0719i	0.102666	+	0.383153i	0.998070	−	0.0621008i	$-0.0197800\pi$
$691$	2.69876	+	10.0719i	0.102666	+	0.383153i	−0.895404	+	0.445254i	$0.853113\pi$
$692$	9.81276	−	2.62932i	0.373025	−	0.0999518i
$693$	−0.221799	+	0.827767i	−0.00842546	+	0.0314443i
$694$	13.1963	+	13.1963i	0.500923	+	0.500923i
$695$	16.8426	+	3.50423i	0.638878	+	0.132923i
$696$	0.0196164	−	0.0732094i	0.000743558	−	0.00277499i
$697$			44.2388i			1.67566i
$698$	−2.65821	−	0.712266i	−0.100615	−	0.0269597i
$699$	−14.9075	+	25.8205i	−0.563852	+	0.976620i
$700$	−1.30986	+	3.01158i	−0.0495081	+	0.113827i
$701$		−	48.0206i		−	1.81371i	−0.421440	−	0.906856i	$-0.638475\pi$
$701$		−	48.0206i		−	1.81371i	0.421440	−	0.906856i	$-0.361525\pi$
$702$	−0.283902	−	3.59436i	−0.0107152	−	0.135660i
$703$	−1.07370	+	1.07370i	−0.0404953	+	0.0404953i
$704$	−1.26026	+	0.337686i	−0.0474979	+	0.0127270i
$705$	15.8239	+	7.97697i	0.595962	+	0.300430i
$706$	2.10419	−	1.21485i	0.0791922	−	0.0457217i
$707$	6.91520			0.260073
$708$	−4.24006	+	2.44800i	−0.159351	+	0.0920016i
$709$	16.6659	+	4.46562i	0.625901	+	0.167710i	0.557809	−	0.829969i	$-0.311642\pi$
$709$	16.6659	+	4.46562i	0.625901	+	0.167710i	0.0680921	+	0.997679i	$0.478309\pi$
$710$	9.11573	−	0.517133i	0.342107	−	0.0194077i
$711$	−5.53242	−	9.58244i	−0.207482	−	0.359369i
$712$	1.59876	+	5.96664i	0.0599159	+	0.223609i
$713$	−0.782468	+	1.35527i	−0.0293037	+	0.0507554i
$714$	−3.73563			−0.139802
$715$	6.36517	−	8.37458i	0.238044	−	0.313192i
$716$	1.19493			0.0446568
$717$	−0.372098	+	0.644493i	−0.0138963	+	0.0240690i
$718$	−7.79943	−	29.1079i	−0.291072	−	1.08630i
$719$	9.27325	+	16.0617i	0.345834	+	0.599002i	0.985505	−	0.169647i	$-0.0542627\pi$
$719$	9.27325	+	16.0617i	0.345834	+	0.599002i	−0.639671	+	0.768649i	$0.720929\pi$
$720$	−1.48905	+	1.66815i	−0.0554935	+	0.0621684i
$721$	−8.71794	−	2.33597i	−0.324673	−	0.0869959i
$722$	14.1175	−	8.15074i	0.525399	−	0.303339i
$723$	−17.0775			−0.635119
$724$	18.2122	−	10.5148i	0.676850	−	0.390780i
$725$	0.151147	−	0.347512i	0.00561348	−	0.0129063i
$726$	8.98090	−	2.40642i	0.333312	−	0.0893108i
$727$	−3.86950	+	3.86950i	−0.143512	+	0.143512i	−0.775212	−	0.631701i	$-0.782357\pi$
$727$	−3.86950	+	3.86950i	−0.143512	+	0.143512i	0.631701	+	0.775212i	$0.282357\pi$
$728$	−0.791152	−	2.23214i	−0.0293220	−	0.0827287i
$729$			1.00000i			0.0370370i
$730$	−7.32269	+	2.41422i	−0.271025	+	0.0893543i
$731$	−27.0145	+	46.7905i	−0.999169	+	1.73061i
$732$	−3.10552	−	0.832121i	−0.114783	−	0.0307561i
$733$			45.7696i			1.69054i	0.534339	+	0.845270i	$0.320561\pi$
$733$			45.7696i			1.69054i	−0.534339	+	0.845270i	$0.679439\pi$
$734$	2.85418	−	10.6519i	0.105350	−	0.393170i
$735$	−8.05256	−	12.2836i	−0.297023	−	0.453089i
$736$	−0.152301	−	0.152301i	−0.00561388	−	0.00561388i
$737$	−4.48579	+	16.7412i	−0.165236	+	0.616670i
$738$	7.51330	−	2.01318i	0.276568	−	0.0741063i
$739$	2.54621	+	9.50257i	0.0936637	+	0.349558i	0.996813	−	0.0797679i	$-0.0254179\pi$
$739$	2.54621	+	9.50257i	0.0936637	+	0.349558i	−0.903150	+	0.429326i	$0.858751\pi$
$740$	−1.37640	+	1.54195i	−0.0505973	+	0.0566833i
$741$	1.07772	−	5.82403i	0.0395911	−	0.213951i
$742$	1.70080	+	1.70080i	0.0624383	+	0.0624383i
$743$	26.9827	+	15.5785i	0.989899	+	0.571518i	0.905244	−	0.424892i	$-0.139688\pi$
$743$	26.9827	+	15.5785i	0.989899	+	0.571518i	0.0846546	+	0.996410i	$0.473021\pi$
$744$	6.29231	+	3.63287i	0.230687	+	0.133187i
$745$	27.2908	−	17.8905i	0.999858	−	0.655458i
$746$	−2.09325	+	2.09325i	−0.0766395	+	0.0766395i
$747$	1.10199	+	1.90870i	0.0403196	+	0.0698357i
$748$	−3.71025	−	6.42635i	−0.135660	−	0.234971i
$749$	−5.95091	+	5.95091i	−0.217442	+	0.217442i
$750$	−8.59707	+	7.14775i	−0.313921	+	0.260999i
$751$	13.1964	+	7.61892i	0.481542	+	0.278018i	0.721059	−	0.692874i	$-0.243656\pi$
$751$	13.1964	+	7.61892i	0.481542	+	0.278018i	−0.239517	+	0.970892i	$0.576989\pi$
$752$	6.86325	+	3.96250i	0.250277	+	0.144497i
$753$	9.92177	+	9.92177i	0.361569	+	0.361569i
$754$	0.0912926	+	0.257572i	0.00332468	+	0.00938020i
$755$	1.55698	+	27.4456i	0.0566644	+	0.998848i
$756$	0.169998	+	0.634441i	0.00618276	+	0.0230744i
$757$	46.2033	−	12.3801i	1.67929	−	0.449964i	0.711696	−	0.702487i	$-0.247927\pi$
$757$	46.2033	−	12.3801i	1.67929	−	0.449964i	0.967591	+	0.252524i	$0.0812606\pi$
$758$	5.29955	−	19.7782i	0.192488	−	0.718377i
$759$	−0.198710	−	0.198710i	−0.00721271	−	0.00721271i
$760$	−3.07198	+	2.01384i	−0.111432	+	0.0730496i
$761$	5.54307	−	20.6870i	0.200936	−	0.749904i	−0.789714	−	0.613476i	$-0.789771\pi$
$761$	5.54307	−	20.6870i	0.200936	−	0.749904i	0.990650	−	0.136429i	$-0.0435624\pi$
$762$			1.25498i			0.0454631i
$763$	−11.6856	−	3.13115i	−0.423048	−	0.113355i
$764$	4.06177	−	7.03518i	0.146950	−	0.254524i
$765$	−11.3561	−	5.72474i	−0.410582	−	0.206978i
$766$		−	25.0444i		−	0.904891i
$767$	7.59523	−	15.9353i	0.274248	−	0.575390i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−22.8775	+	6.13001i	−0.824984	+	0.221054i	−0.646524	−	0.762893i	$-0.723778\pi$
$769$	−22.8775	+	6.13001i	−0.824984	+	0.221054i	−0.178460	+	0.983947i	$0.557111\pi$
$770$	−0.862588	+	1.71111i	−0.0310855	+	0.0616642i
$771$	14.9743	−	8.64544i	0.539288	−	0.311358i
$772$	−4.48740			−0.161505
$773$	−25.1486	+	14.5195i	−0.904531	+	0.522231i	−0.878668	−	0.477434i	$-0.841567\pi$
$773$	−25.1486	+	14.5195i	−0.904531	+	0.522231i	−0.0258639	+	0.999665i	$0.508234\pi$
$774$	9.17603	+	2.45871i	0.329825	+	0.0883765i
$775$	28.4287	+	22.6182i	1.02119	+	0.812470i
$776$	6.83472	+	11.8381i	0.245352	+	0.424963i
$777$	0.157137	+	0.586443i	0.00563725	+	0.0210385i
$778$	6.99363	−	12.1133i	0.250734	−	0.434283i
$779$	12.7776			0.457805
$780$	1.01563	−	7.99803i	0.0363653	−	0.286375i
$781$	5.32747			0.190632
$782$	0.612497	−	1.06088i	0.0219028	−	0.0379368i
$783$	−0.0196164	−	0.0732094i	−0.000701033	−	0.00261629i
$784$	−3.28429	−	5.68856i	−0.117296	−	0.203163i
$785$	0.593136	+	10.4555i	0.0211699	+	0.373171i
$786$	−14.2360	−	3.81453i	−0.507782	−	0.136060i
$787$	29.4456	−	17.0004i	1.04962	−	0.605999i	0.127078	−	0.991893i	$-0.459440\pi$
$787$	29.4456	−	17.0004i	1.04962	−	0.605999i	0.922543	+	0.385894i	$0.126107\pi$
$788$	11.5175			0.410293
$789$	22.5001	−	12.9904i	0.801025	−	0.462472i
$790$	−7.74695	−	23.4976i	−0.275624	−	0.836008i
$791$	1.47835	−	0.396124i	0.0525642	−	0.0140845i
$792$	−0.922576	+	0.922576i	−0.0327823	+	0.0327823i
$793$	10.9261	−	3.87260i	0.387997	−	0.137520i
$794$			20.9249i			0.742598i
$795$	2.56393	+	7.77678i	0.0909332	+	0.275814i
$796$	−1.75484	+	3.03947i	−0.0621985	+	0.107731i
$797$	29.2332	+	7.83302i	1.03549	+	0.277460i	0.736245	−	0.676715i	$-0.236597\pi$
$797$	29.2332	+	7.83302i	1.03549	+	0.277460i	0.299249	+	0.954175i	$0.403264\pi$
$798$			1.07897i			0.0381952i
$799$	−11.6657	+	43.5371i	−0.412704	+	1.54023i
$800$	−4.01961	+	2.97368i	−0.142115	+	0.105135i
$801$	4.36788	+	4.36788i	0.154331	+	0.154331i
$802$	7.68224	−	28.6705i	0.271269	−	1.01239i
$803$	−4.34563	+	1.16441i	−0.153354	+	0.0410911i
$804$	3.43813	+	12.8313i	0.121253	+	0.452524i
$805$	−0.315829	+	0.0179169i	−0.0111315	+	0.000631487i
$806$	−26.1156	+	2.06276i	−0.919884	+	0.0726575i
$807$	−17.6947	−	17.6947i	−0.622883	−	0.622883i
$808$	9.11777	+	5.26415i	0.320762	+	0.185192i
$809$	−11.2881	−	6.51717i	−0.396868	−	0.229132i	0.288264	−	0.957551i	$-0.406922\pi$
$809$	−11.2881	−	6.51717i	−0.396868	−	0.229132i	−0.685132	+	0.728419i	$0.740255\pi$
$810$	−0.455475	+	2.18919i	−0.0160038	+	0.0769202i
$811$	−2.31200	+	2.31200i	−0.0811854	+	0.0811854i	−0.746533	−	0.665348i	$-0.768283\pi$
$811$	−2.31200	+	2.31200i	−0.0811854	+	0.0811854i	0.665348	+	0.746533i	$0.268283\pi$
$812$	−0.0248909	−	0.0431123i	−0.000873498	−	0.00151294i
$813$	−1.31210	−	2.27262i	−0.0460174	−	0.0797044i
$814$	−0.852780	+	0.852780i	−0.0298899	+	0.0298899i
$815$	0.835390	−	4.01520i	0.0292624	−	0.140646i
$816$	−4.92547	−	2.84372i	−0.172426	−	0.0995501i
$817$	13.5146	+	7.80268i	0.472817	+	0.272981i
$818$	−9.86383	−	9.86383i	−0.344881	−	0.344881i
$819$	−1.80123	−	1.53752i	−0.0629400	−	0.0537252i
$820$	17.3650	−	0.985111i	0.606411	−	0.0344016i
$821$	6.24607	+	23.3107i	0.217989	+	0.813548i	0.985093	+	0.172024i	$0.0550307\pi$
$821$	6.24607	+	23.3107i	0.217989	+	0.813548i	−0.767103	+	0.641524i	$0.778303\pi$
$822$	15.6852	−	4.20283i	0.547083	−	0.146591i
$823$	−8.18088	+	30.5314i	−0.285167	+	1.06426i	0.663549	+	0.748132i	$0.269049\pi$
$823$	−8.18088	+	30.5314i	−0.285167	+	1.06426i	−0.948717	+	0.316127i	$0.897617\pi$
$824$	−9.71646	−	9.71646i	−0.338489	−	0.338489i
$825$	−5.24446	+	3.87982i	−0.182589	+	0.135078i
$826$	−0.832310	+	3.10622i	−0.0289598	+	0.108079i
$827$			37.1285i			1.29108i	0.763725	+	0.645542i	$0.223369\pi$
$827$			37.1285i			1.29108i	−0.763725	+	0.645542i	$0.776631\pi$
$828$	−0.208047	−	0.0557460i	−0.00723013	−	0.00193731i
$829$	4.87650	−	8.44635i	0.169368	−	0.293354i	−0.768830	−	0.639453i	$-0.779161\pi$
$829$	4.87650	−	8.44635i	0.169368	−	0.293354i	0.938198	+	0.346100i	$0.112494\pi$
$830$	1.54309	+	4.68043i	0.0535616	+	0.162460i
$831$			29.3991i			1.01984i
$832$	0.656060	−	3.54536i	0.0227448	−	0.122913i
$833$	26.4164	−	26.4164i	0.915274	−	0.915274i
$834$	7.43141	−	1.99124i	0.257329	−	0.0689510i
$835$	−14.1403	−	42.8895i	−0.489344	−	1.48425i
$836$	−1.85614	+	1.07164i	−0.0641959	+	0.0370635i
$837$	7.26573			0.251140
$838$	−6.36248	+	3.67338i	−0.219788	+	0.126895i
$839$	26.3259	+	7.05401i	0.908871	+	0.243531i	0.682822	−	0.730585i	$-0.260752\pi$
$839$	26.3259	+	7.05401i	0.908871	+	0.243531i	0.226049	+	0.974116i	$0.427419\pi$
$840$	0.0831851	+	1.46634i	0.00287016	+	0.0505935i
$841$	−14.4971	−	25.1098i	−0.499901	−	0.865854i
$842$	−4.10325	−	15.3136i	−0.141407	−	0.527740i
$843$	−7.33279	+	12.7008i	−0.252555	+	0.437438i
$844$	−18.0440			−0.621102
$845$	13.3231	+	25.8359i	0.458327	+	0.888784i
$846$	7.92499			0.272467
$847$	3.05347	−	5.28876i	0.104918	−	0.181724i
$848$	0.947801	+	3.53724i	0.0325476	+	0.121469i
$849$	−5.83942	−	10.1142i	−0.200408	−	0.347118i
$850$	−22.2533	−	17.7050i	−0.763280	−	0.607276i
$851$	−0.192307	−	0.0515286i	−0.00659221	−	0.00176638i
$852$	3.53618	−	2.04162i	0.121148	−	0.0699446i
$853$	17.3357			0.593563			0.296782	−	0.954945i	$-0.404087\pi$
$853$	17.3357			0.593563			0.296782	+	0.954945i	$0.404087\pi$
$854$	−1.82881	+	1.05586i	−0.0625805	+	0.0361309i
$855$	−1.65349	+	3.28003i	−0.0565482	+	0.112174i
$856$	−12.3764	+	3.31625i	−0.423018	+	0.113347i
$857$	26.5534	−	26.5534i	0.907048	−	0.907048i	−0.0889851	−	0.996033i	$-0.528362\pi$
$857$	26.5534	−	26.5534i	0.907048	−	0.907048i	0.996033	+	0.0889851i	$0.0283623\pi$
$858$	0.855974	−	4.62570i	0.0292225	−	0.157919i
$859$		−	28.0469i		−	0.956949i	−0.878101	−	0.478475i	$-0.841190\pi$
$859$		−	28.0469i		−	0.956949i	0.878101	−	0.478475i	$-0.158810\pi$
$860$	18.9682	+	9.56203i	0.646809	+	0.326062i
$861$	2.55449	−	4.42450i	0.0870567	−	0.150787i
$862$	35.5475	+	9.52492i	1.21075	+	0.324420i
$863$			55.7475i			1.89767i	0.315775	+	0.948834i	$0.397736\pi$
$863$			55.7475i			1.89767i	−0.315775	+	0.948834i	$0.602264\pi$
$864$	−0.258819	+	0.965926i	−0.00880520	+	0.0328615i
$865$	18.9978	−	12.4540i	0.645944	−	0.423449i
$866$	−5.98812	−	5.98812i	−0.203485	−	0.203485i
$867$	3.97208	−	14.8240i	0.134899	−	0.503450i
$868$	4.60967	−	1.23516i	0.156463	−	0.0419240i
$869$	−3.73645	−	13.9446i	−0.126750	−	0.473038i
$870$	−0.00959890	−	0.169204i	−0.000325433	−	0.00573655i
$871$	−36.4290	−	31.0955i	−1.23435	−	1.05363i
$872$	−13.0240	−	13.0240i	−0.441050	−	0.441050i
$873$	11.8381	+	6.83472i	0.400659	+	0.231320i
$874$	−0.306416	−	0.176909i	−0.0103647	−	0.00598404i
$875$	−0.673129	+	7.31257i	−0.0227559	+	0.247210i
$876$	−2.43824	+	2.43824i	−0.0823805	+	0.0823805i
$877$	−8.32925	−	14.4267i	−0.281259	−	0.487155i	0.690436	−	0.723393i	$-0.257419\pi$
$877$	−8.32925	−	14.4267i	−0.281259	−	0.487155i	−0.971695	+	0.236239i	$0.924085\pi$
$878$	8.93023	+	15.4676i	0.301381	+	0.522006i
$879$	−8.08976	+	8.08976i	−0.272861	+	0.272861i
$880$	−2.43990	+	1.59948i	−0.0822491	+	0.0539185i
$881$	15.4667	+	8.92971i	0.521087	+	0.300850i	0.737379	−	0.675479i	$-0.236063\pi$
$881$	15.4667	+	8.92971i	0.521087	+	0.300850i	−0.216292	+	0.976329i	$0.569396\pi$
$882$	−5.68856	−	3.28429i	−0.191544	−	0.110588i
$883$	18.4830	+	18.4830i	0.622003	+	0.622003i	0.946043	−	0.324040i	$-0.105041\pi$
$883$	18.4830	+	18.4830i	0.622003	+	0.622003i	−0.324040	+	0.946043i	$0.605041\pi$
$884$	20.4427	−	1.61467i	0.687562	−	0.0543074i
$885$	−7.29038	+	8.16729i	−0.245063	+	0.274540i
$886$	0.990104	+	3.69512i	0.0332632	+	0.124140i
$887$	24.6672	−	6.60955i	0.828243	−	0.221927i	0.180296	−	0.983612i	$-0.442294\pi$
$887$	24.6672	−	6.60955i	0.828243	−	0.221927i	0.647947	+	0.761685i	$0.275628\pi$
$888$	−0.239238	+	0.892850i	−0.00802832	+	0.0299621i
$889$	0.582866	+	0.582866i	0.0195487	+	0.0195487i
$890$	7.57265	+	11.5516i	0.253836	+	0.387210i
$891$	−0.337686	+	1.26026i	−0.0113129	+	0.0422204i
$892$			27.5937i			0.923905i
$893$	12.5749	+	3.36944i	0.420804	+	0.112754i
$894$	7.29678	−	12.6384i	0.244041	−	0.422691i
$895$	2.53760	−	0.836621i	0.0848225	−	0.0279652i
$896$			0.656821i			0.0219429i
$897$	0.731968	−	0.259436i	0.0244397	−	0.00866231i
$898$	8.44165	−	8.44165i	0.281701	−	0.281701i
$899$	−0.531920	+	0.142527i	−0.0177405	+	0.00475356i
$900$	−1.99424	+	4.58508i	−0.0664747	+	0.152836i
$901$	−18.0372	+	10.4138i	−0.600905	+	0.346933i
$902$	10.1485			0.337910
$903$	5.40367	−	3.11981i	0.179823	−	0.103821i
$904$	2.25077	+	0.603092i	0.0748595	+	0.0200585i
$905$	31.3141	−	35.0806i	1.04092	−	1.16612i
$906$	6.14689	+	10.6467i	0.204217	+	0.353714i
$907$	−12.6212	−	47.1031i	−0.419081	−	1.56403i	−0.776518	−	0.630095i	$-0.783016\pi$
$907$	−12.6212	−	47.1031i	−0.419081	−	1.56403i	0.357437	−	0.933937i	$-0.383651\pi$
$908$	6.22930	−	10.7895i	0.206727	−	0.358061i
$909$	10.5283			0.349201
$910$	−3.24293	−	4.18633i	−0.107502	−	0.138775i
$911$	2.26572			0.0750665			0.0375333	−	0.999295i	$-0.488050\pi$
$911$	2.26572			0.0750665			0.0375333	+	0.999295i	$0.488050\pi$
$912$	−0.821359	+	1.42263i	−0.0271979	+	0.0471081i
$913$	0.744253	+	2.77759i	0.0246312	+	0.0919248i
$914$	20.3307	+	35.2137i	0.672478	+	1.16477i
$915$	−7.17757	+	0.407182i	−0.237283	+	0.0134610i
$916$	−16.9495	−	4.54161i	−0.560027	−	0.150059i
$917$	−8.38344	+	4.84018i	−0.276846	+	0.159837i
$918$	−5.68744			−0.187713
$919$	−26.0297	+	15.0283i	−0.858642	+	0.495737i	−0.863557	−	0.504251i	$-0.831769\pi$
$919$	−26.0297	+	15.0283i	−0.858642	+	0.495737i	0.00491537	+	0.999988i	$0.498435\pi$
$920$	−0.430063	−	0.216799i	−0.0141787	−	0.00714764i
$921$	−25.9862	+	6.96297i	−0.856273	+	0.229438i
$922$	22.0055	−	22.0055i	0.724714	−	0.724714i
$923$	−6.33437	+	13.2899i	−0.208498	+	0.437443i
$924$			0.856967i			0.0281922i
$925$	−1.84337	+	4.23821i	−0.0606097	+	0.139351i
$926$	−6.68190	+	11.5734i	−0.219581	+	0.380325i
$927$	−13.2729	−	3.55647i	−0.435940	−	0.116810i
$928$		−	0.0757919i		−	0.00248799i
$929$	−8.62799	+	32.2001i	−0.283075	+	1.05645i	0.667159	+	0.744915i	$0.267510\pi$
$929$	−8.62799	+	32.2001i	−0.283075	+	1.05645i	−0.950234	+	0.311536i	$0.899157\pi$
$930$	15.9060	+	3.30936i	0.521580	+	0.108518i
$931$	−7.62992	−	7.62992i	−0.250060	−	0.250060i
$932$	−7.71667	+	28.7990i	−0.252768	+	0.943343i
$933$	7.13479	−	1.91176i	0.233582	−	0.0625882i
$934$	−5.77911	−	21.5679i	−0.189098	−	0.705724i
$935$	−12.3786	−	11.0495i	−0.404822	−	0.361357i
$936$	−1.20452	−	3.39840i	−0.0393708	−	0.111080i
$937$	−13.8622	−	13.8622i	−0.452860	−	0.452860i	0.443443	−	0.896303i	$-0.353757\pi$
$937$	−13.8622	−	13.8622i	−0.452860	−	0.452860i	−0.896303	+	0.443443i	$0.853757\pi$
$938$	7.55620	+	4.36257i	0.246719	+	0.142443i
$939$	−17.0254	−	9.82963i	−0.555603	−	0.320778i
$940$	17.3493	+	3.60964i	0.565872	+	0.117733i
$941$	−3.41512	+	3.41512i	−0.111330	+	0.111330i	−0.760577	−	0.649248i	$-0.775084\pi$
$941$	−3.41512	+	3.41512i	−0.111330	+	0.111330i	0.649248	+	0.760577i	$0.275084\pi$
$942$	2.34167	+	4.05589i	0.0762958	+	0.132148i
$943$	0.837672	+	1.45089i	0.0272784	+	0.0472475i
$944$	−3.46200	+	3.46200i	−0.112678	+	0.112678i
$945$	0.805210	+	1.22829i	0.0261935	+	0.0399564i
$946$	10.7339	+	6.19724i	0.348990	+	0.201490i
$947$	−42.5076	−	24.5418i	−1.38131	−	0.797501i	−0.388998	−	0.921239i	$-0.627179\pi$
$947$	−42.5076	−	24.5418i	−1.38131	−	0.797501i	−0.992315	+	0.123738i	$0.960512\pi$
$948$	−7.82403	−	7.82403i	−0.254113	−	0.254113i
$949$	2.26222	−	12.2251i	0.0734348	−	0.396843i
$950$	−5.11377	+	6.42747i	−0.165913	+	0.208535i
$951$	−6.27153	−	23.4057i	−0.203368	−	0.758981i
$952$	−3.60834	+	0.966852i	−0.116947	+	0.0313359i
$953$	9.99546	−	37.3036i	0.323785	−	1.20838i	−0.591743	−	0.806126i	$-0.701560\pi$
$953$	9.99546	−	37.3036i	0.323785	−	1.20838i	0.915528	−	0.402254i	$-0.131773\pi$
$954$	2.58944	+	2.58944i	0.0838362	+	0.0838362i
$955$	3.70007	−	17.7839i	0.119731	−	0.575475i
$956$	−0.192612	+	0.718839i	−0.00622952	+	0.0232489i
$957$		−	0.0988872i		−	0.00319657i
$958$	−31.1575	−	8.34864i	−1.00665	−	0.269732i
$959$	5.33289	−	9.23684i	0.172208	−	0.298273i
$960$	−1.00656	+	1.99671i	−0.0324865	+	0.0644434i
$961$		−	21.7908i		−	0.702931i
$962$	−1.11339	−	3.14130i	−0.0358971	−	0.101280i
$963$	−9.06017	+	9.06017i	−0.291960	+	0.291960i
$964$	−16.4956	+	4.41998i	−0.531288	+	0.142358i
$965$	−9.52958	+	3.14181i	−0.306768	+	0.101139i
$966$	−0.122517	+	0.0707350i	−0.00394191	+	0.00227586i
$967$	26.5516			0.853843			0.426922	−	0.904289i	$-0.359598\pi$
$967$	26.5516			0.853843			0.426922	+	0.904289i	$0.359598\pi$
$968$	8.05205	−	4.64885i	0.258803	−	0.149420i
$969$	−9.02450	−	2.41811i	−0.289909	−	0.0776808i
$970$	22.8027	+	20.3545i	0.732152	+	0.653542i
$971$	−0.859329	−	1.48840i	−0.0275772	−	0.0477651i	0.851907	−	0.523692i	$-0.175446\pi$
$971$	−0.859329	−	1.48840i	−0.0275772	−	0.0477651i	−0.879485	+	0.475927i	$0.842113\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	2.52665	−	4.37628i	0.0810006	−	0.140297i
$974$	−13.2109			−0.423304
$975$	−3.44293	−	17.6959i	−0.110262	−	0.566724i
$976$	−3.21507			−0.102912
$977$	−7.11901	+	12.3305i	−0.227757	+	0.394487i	−0.957143	−	0.289615i	$-0.906473\pi$
$977$	−7.11901	+	12.3305i	−0.227757	+	0.394487i	0.729386	+	0.684103i	$0.239806\pi$
$978$	−0.474701	−	1.77161i	−0.0151793	−	0.0566498i
$979$	4.02970	+	6.97965i	0.128790	+	0.223071i
$980$	−10.9574	−	9.78093i	−0.350022	−	0.312440i
$981$	−17.7912	−	4.76713i	−0.568028	−	0.152203i
$982$	−21.0123	+	12.1315i	−0.670531	+	0.387131i
$983$	−11.3280			−0.361307			−0.180653	−	0.983547i	$-0.557821\pi$
$983$	−11.3280			−0.361307			−0.180653	+	0.983547i	$0.557821\pi$
$984$	6.73624	−	3.88917i	0.214743	−	0.123982i
$985$	24.4589	−	8.06386i	0.779324	−	0.256936i
$986$	0.416374	−	0.111567i	0.0132600	−	0.00355302i
$987$	3.68071	−	3.68071i	0.117158	−	0.117158i
$988$	−0.466371	−	5.90451i	−0.0148372	−	0.187848i
$989$			2.04611i			0.0650624i
$990$	−1.31328	+	2.60514i	−0.0417387	+	0.0827969i
$991$	−11.0414	+	19.1243i	−0.350743	+	0.607505i	−0.986380	−	0.164484i	$-0.947404\pi$
$991$	−11.0414	+	19.1243i	−0.350743	+	0.607505i	0.635637	+	0.771988i	$0.280738\pi$
$992$	7.01816	+	1.88051i	0.222827	+	0.0597062i
$993$		−	7.81244i		−	0.247920i
$994$	0.694141	−	2.59057i	0.0220168	−	0.0821678i
$995$	−1.59857	+	7.68333i	−0.0506781	+	0.243578i
$996$	1.55845	+	1.55845i	0.0493813	+	0.0493813i
$997$	−1.98144	+	7.39482i	−0.0627527	+	0.234196i	−0.990178	−	0.139812i	$-0.955350\pi$
$997$	−1.98144	+	7.39482i	−0.0627527	+	0.234196i	0.927425	+	0.374008i	$0.122017\pi$
$998$	−32.3291	+	8.66256i	−1.02336	+	0.274208i
$999$	0.239238	+	0.892850i	0.00756917	+	0.0282485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bn.b.97.1	yes	16
5.3	odd	4		390.2.bd.b.253.3	yes	16
13.11	odd	12		390.2.bd.b.37.3	✓	16
65.63	even	12	inner	390.2.bn.b.193.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.b.37.3	✓	16	13.11	odd	12
390.2.bd.b.253.3	yes	16	5.3	odd	4
390.2.bn.b.97.1	yes	16	1.1	even	1	trivial
390.2.bn.b.193.1	yes	16	65.63	even	12	inner

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.66815 - 1.48905i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-0.568824 + 0.328411i) q^{7} -1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.66815 - 1.48905i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-0.568824 + 0.328411i) q^{7} -1.00000 q^{8} +(-0.866025 + 0.500000i) q^{9} +(-2.12363 + 0.700141i) q^{10} +(-1.26026 + 0.337686i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(0.656060 - 3.54536i) q^{13} +0.656821i q^{14} +(-1.00656 + 1.99671i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.49364 - 1.47202i) q^{17} +1.00000i q^{18} +(-0.425167 + 1.58674i) q^{19} +(-0.455475 + 2.18919i) q^{20} +(0.464443 + 0.464443i) q^{21} +(-0.337686 + 1.26026i) q^{22} +(-0.208047 + 0.0557460i) q^{23} +(0.258819 + 0.965926i) q^{24} +(0.565478 + 4.96792i) q^{25} +(-2.74234 - 2.34084i) q^{26} +(0.707107 + 0.707107i) q^{27} +(0.568824 + 0.328411i) q^{28} +(-0.0656377 - 0.0378960i) q^{29} +(1.22592 + 1.87006i) q^{30} +(5.13765 - 5.13765i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.652360 + 1.12992i) q^{33} +(-4.02163 + 4.02163i) q^{34} +(1.43790 + 0.299166i) q^{35} +(0.866025 + 0.500000i) q^{36} +(0.800508 + 0.462173i) q^{37} +(1.16158 + 1.16158i) q^{38} +(-3.59436 + 0.283902i) q^{39} +(1.66815 + 1.48905i) q^{40} +(-2.01318 - 7.51330i) q^{41} +(0.634441 - 0.169998i) q^{42} +(2.45871 - 9.17603i) q^{43} +(0.922576 + 0.922576i) q^{44} +(2.18919 + 0.455475i) q^{45} +(-0.0557460 + 0.208047i) q^{46} -7.92499i q^{47} +(0.965926 + 0.258819i) q^{48} +(-3.28429 + 5.68856i) q^{49} +(4.58508 + 1.99424i) q^{50} +5.68744i q^{51} +(-3.39840 + 1.20452i) q^{52} +(2.58944 - 2.58944i) q^{53} +(0.965926 - 0.258819i) q^{54} +(2.60514 + 1.31328i) q^{55} +(0.568824 - 0.328411i) q^{56} +1.64272 q^{57} +(-0.0656377 + 0.0378960i) q^{58} +(4.72918 + 1.26718i) q^{59} +(2.23248 - 0.126648i) q^{60} +(1.60754 + 2.78433i) q^{61} +(-1.88051 - 7.01816i) q^{62} +(0.328411 - 0.568824i) q^{63} +1.00000 q^{64} +(-6.37362 + 4.93731i) q^{65} +1.30472 q^{66} +(6.64195 - 11.5042i) q^{67} +(1.47202 + 5.49364i) q^{68} +(0.107693 + 0.186530i) q^{69} +(0.978038 - 1.09568i) q^{70} +(-3.94410 - 1.05682i) q^{71} +(0.866025 - 0.500000i) q^{72} +3.44819 q^{73} +(0.800508 - 0.462173i) q^{74} +(4.65229 - 1.83200i) q^{75} +(1.58674 - 0.425167i) q^{76} +(0.605967 - 0.605967i) q^{77} +(-1.55131 + 3.25476i) q^{78} +11.0648i q^{79} +(2.12363 - 0.700141i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-7.51330 - 2.01318i) q^{82} -2.20398i q^{83} +(0.169998 - 0.634441i) q^{84} +(6.97234 + 10.6358i) q^{85} +(-6.71732 - 6.71732i) q^{86} +(-0.0196164 + 0.0732094i) q^{87} +(1.26026 - 0.337686i) q^{88} +(-1.59876 - 5.96664i) q^{89} +(1.48905 - 1.66815i) q^{90} +(0.791152 + 2.23214i) q^{91} +(0.152301 + 0.152301i) q^{92} +(-6.29231 - 3.63287i) q^{93} +(-6.86325 - 3.96250i) q^{94} +(3.07198 - 2.01384i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-6.83472 - 11.8381i) q^{97} +(3.28429 + 5.68856i) q^{98} +(0.922576 - 0.922576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8}+O(q^{10}) \) 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8	\( 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8} + 12 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{16} - 4 q^{17} - 4 q^{19} + 4 q^{23} + 4 q^{25} + 4 q^{26} - 24 q^{28} - 48 q^{29} - 4 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 20 q^{34} - 12 q^{35} + 12 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} + 20 q^{43} - 12 q^{44} + 8 q^{45} - 4 q^{46} - 4 q^{49} - 16 q^{50} - 4 q^{52} + 32 q^{53} + 16 q^{55} - 24 q^{56} - 8 q^{57} - 48 q^{58} + 4 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 16 q^{64} - 8 q^{65} + 32 q^{66} - 28 q^{67} - 16 q^{68} + 4 q^{69} - 36 q^{71} + 32 q^{73} + 12 q^{74} - 24 q^{75} + 8 q^{76} + 4 q^{77} + 20 q^{78} + 8 q^{81} - 24 q^{82} + 52 q^{85} + 16 q^{86} + 36 q^{87} - 12 q^{88} - 24 q^{89} + 4 q^{90} - 8 q^{92} + 36 q^{94} - 40 q^{95} - 4 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8 + 12 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^16 - 4 * q^17 - 4 * q^19 + 4 * q^23 + 4 * q^25 + 4 * q^26 - 24 * q^28 - 48 * q^29 - 4 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 - 20 * q^34 - 12 * q^35 + 12 * q^37 + 4 * q^38 + 4 * q^39 - 12 * q^41 + 20 * q^43 - 12 * q^44 + 8 * q^45 - 4 * q^46 - 4 * q^49 - 16 * q^50 - 4 * q^52 + 32 * q^53 + 16 * q^55 - 24 * q^56 - 8 * q^57 - 48 * q^58 + 4 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 16 * q^64 - 8 * q^65 + 32 * q^66 - 28 * q^67 - 16 * q^68 + 4 * q^69 - 36 * q^71 + 32 * q^73 + 12 * q^74 - 24 * q^75 + 8 * q^76 + 4 * q^77 + 20 * q^78 + 8 * q^81 - 24 * q^82 + 52 * q^85 + 16 * q^86 + 36 * q^87 - 12 * q^88 - 24 * q^89 + 4 * q^90 - 8 * q^92 + 36 * q^94 - 40 * q^95 - 4 * q^97 + 4 * q^98 - 12 * q^99

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