LMFDB - Embedded newform 310.2.b.a.249.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(249,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("310.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.b (of order $2$, degree $1$, 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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			249.1
Root			$-1.49094 - 1.49094i$ of defining polynomial
Character	$\chi$	$=$	310.249
Dual form			310.2.b.a.249.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -3.44579i q^{3} -1.00000 q^{4} +(-1.82630 + 1.29021i) q^{5} -3.44579 q^{6} +2.40146i q^{7} +1.00000i q^{8} -8.87345 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -3.44579i q^{3} -1.00000 q^{4} +(-1.82630 + 1.29021i) q^{5} -3.44579 q^{6} +2.40146i q^{7} +1.00000i q^{8} -8.87345 q^{9} +(1.29021 + 1.82630i) q^{10} -1.80535 q^{11} +3.44579i q^{12} -1.79319i q^{13} +2.40146 q^{14} +(4.44579 + 6.29303i) q^{15} +1.00000 q^{16} -7.60418i q^{17} +8.87345i q^{18} -4.31116 q^{19} +(1.82630 - 1.29021i) q^{20} +8.27490 q^{21} +1.80535i q^{22} -4.98187i q^{23} +3.44579 q^{24} +(1.67072 - 4.71261i) q^{25} -1.79319 q^{26} +20.2387i q^{27} -2.40146i q^{28} +4.50580 q^{29} +(6.29303 - 4.44579i) q^{30} -1.00000 q^{31} -1.00000i q^{32} +6.22085i q^{33} -7.60418 q^{34} +(-3.09838 - 4.38577i) q^{35} +8.87345 q^{36} +1.48204i q^{37} +4.31116i q^{38} -6.17896 q^{39} +(-1.29021 - 1.82630i) q^{40} -4.44335 q^{41} -8.27490i q^{42} -0.243058i q^{43} +1.80535 q^{44} +(16.2055 - 11.4486i) q^{45} -4.98187 q^{46} -4.90373i q^{47} -3.44579i q^{48} +1.23301 q^{49} +(-4.71261 - 1.67072i) q^{50} -26.2024 q^{51} +1.79319i q^{52} -4.68477i q^{53} +20.2387 q^{54} +(3.29711 - 2.32928i) q^{55} -2.40146 q^{56} +14.8553i q^{57} -4.50580i q^{58} -0.802911 q^{59} +(-4.44579 - 6.29303i) q^{60} -3.57798 q^{61} +1.00000i q^{62} -21.3092i q^{63} -1.00000 q^{64} +(2.31360 + 3.27490i) q^{65} +6.22085 q^{66} +12.8134i q^{67} +7.60418i q^{68} -17.1665 q^{69} +(-4.38577 + 3.09838i) q^{70} -3.73074 q^{71} -8.87345i q^{72} -2.86184i q^{73} +1.48204 q^{74} +(-16.2387 - 5.75694i) q^{75} +4.31116 q^{76} -4.33547i q^{77} +6.17896i q^{78} +12.7110 q^{79} +(-1.82630 + 1.29021i) q^{80} +43.1177 q^{81} +4.44335i q^{82} -7.14027i q^{83} -8.27490 q^{84} +(9.81099 + 13.8875i) q^{85} -0.243058 q^{86} -15.5260i q^{87} -1.80535i q^{88} +9.26894 q^{89} +(-11.4486 - 16.2055i) q^{90} +4.30627 q^{91} +4.98187i q^{92} +3.44579i q^{93} -4.90373 q^{94} +(7.87345 - 5.56229i) q^{95} -3.44579 q^{96} -14.8069i q^{97} -1.23301i q^{98} +16.0197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} + 2 q^{10} - 16 q^{11} + 12 q^{14} + 16 q^{15} + 8 q^{16} - 12 q^{19} + 2 q^{20} - 4 q^{21} + 8 q^{24} + 12 q^{25} - 20 q^{26} + 12 q^{29} + 4 q^{30} - 8 q^{31} + 8 q^{34} + 20 q^{35} + 8 q^{36} - 40 q^{39} - 2 q^{40} + 16 q^{44} + 30 q^{45} - 16 q^{46} - 32 q^{49} - 8 q^{50} - 44 q^{51} + 44 q^{54} + 36 q^{55} - 12 q^{56} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 8 q^{64} + 12 q^{65} + 12 q^{66} - 28 q^{69} - 20 q^{70} - 24 q^{71} + 40 q^{74} - 12 q^{75} + 12 q^{76} + 32 q^{79} - 2 q^{80} + 88 q^{81} + 4 q^{84} + 4 q^{85} - 44 q^{86} - 24 q^{89} - 34 q^{90} - 20 q^{91} + 4 q^{94} - 8 q^{96} + 20 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9 + 2 * q^10 - 16 * q^11 + 12 * q^14 + 16 * q^15 + 8 * q^16 - 12 * q^19 + 2 * q^20 - 4 * q^21 + 8 * q^24 + 12 * q^25 - 20 * q^26 + 12 * q^29 + 4 * q^30 - 8 * q^31 + 8 * q^34 + 20 * q^35 + 8 * q^36 - 40 * q^39 - 2 * q^40 + 16 * q^44 + 30 * q^45 - 16 * q^46 - 32 * q^49 - 8 * q^50 - 44 * q^51 + 44 * q^54 + 36 * q^55 - 12 * q^56 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 8 * q^64 + 12 * q^65 + 12 * q^66 - 28 * q^69 - 20 * q^70 - 24 * q^71 + 40 * q^74 - 12 * q^75 + 12 * q^76 + 32 * q^79 - 2 * q^80 + 88 * q^81 + 4 * q^84 + 4 * q^85 - 44 * q^86 - 24 * q^89 - 34 * q^90 - 20 * q^91 + 4 * q^94 - 8 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	3.44579i		−	1.98943i	−0.102694	−	0.994713i	$-0.532746\pi$
$3$		−	3.44579i		−	1.98943i	0.102694	−	0.994713i	$-0.467254\pi$
$4$	−1.00000			−0.500000
$5$	−1.82630	+	1.29021i	−0.816745	+	0.576999i
$5$	−1.82630	+	1.29021i	−0.816745	+	0.576999i
$6$	−3.44579			−1.40674
$7$			2.40146i			0.907665i	0.891087	+	0.453832i	$0.149944\pi$
$7$			2.40146i			0.907665i	−0.891087	+	0.453832i	$0.850056\pi$
$8$			1.00000i			0.353553i
$9$	−8.87345			−2.95782
$10$	1.29021	+	1.82630i	0.408000	+	0.577526i
$11$	−1.80535			−0.544334			−0.272167	−	0.962250i	$-0.587740\pi$
$11$	−1.80535			−0.544334			−0.272167	+	0.962250i	$0.587740\pi$
$12$			3.44579i			0.994713i
$13$		−	1.79319i		−	0.497342i	−0.968588	−	0.248671i	$-0.920006\pi$
$13$		−	1.79319i		−	0.497342i	0.968588	−	0.248671i	$-0.0799939\pi$
$14$	2.40146			0.641816
$15$	4.44579	+	6.29303i	1.14790	+	1.62485i
$16$	1.00000			0.250000
$17$		−	7.60418i		−	1.84429i	−0.386850	−	0.922143i	$-0.626437\pi$
$17$		−	7.60418i		−	1.84429i	0.386850	−	0.922143i	$-0.373563\pi$
$18$			8.87345i			2.09149i
$19$	−4.31116			−0.989047			−0.494523	−	0.869164i	$-0.664657\pi$
$19$	−4.31116			−0.989047			−0.494523	+	0.869164i	$0.664657\pi$
$20$	1.82630	−	1.29021i	0.408372	−	0.288500i
$21$	8.27490			1.80573
$22$			1.80535i			0.384902i
$23$		−	4.98187i		−	1.03879i	−0.854533	−	0.519396i	$-0.826157\pi$
$23$		−	4.98187i		−	1.03879i	0.854533	−	0.519396i	$-0.173843\pi$
$24$	3.44579			0.703368
$25$	1.67072	−	4.71261i	0.334144	−	0.942522i
$26$	−1.79319			−0.351674
$27$			20.2387i			3.89493i
$28$		−	2.40146i		−	0.453832i
$29$	4.50580			0.836707			0.418353	−	0.908284i	$-0.362607\pi$
$29$	4.50580			0.836707			0.418353	+	0.908284i	$0.362607\pi$
$30$	6.29303	−	4.44579i	1.14894	−	0.811686i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$		−	1.00000i		−	0.176777i
$33$			6.22085i			1.08291i
$34$	−7.60418			−1.30411
$35$	−3.09838	−	4.38577i	−0.523722	−	0.741330i
$36$	8.87345			1.47891
$37$			1.48204i			0.243646i	0.992552	+	0.121823i	$0.0388740\pi$
$37$			1.48204i			0.243646i	−0.992552	+	0.121823i	$0.961126\pi$
$38$			4.31116i			0.699362i
$39$	−6.17896			−0.989426
$40$	−1.29021	−	1.82630i	−0.204000	−	0.288763i
$41$	−4.44335			−0.693934			−0.346967	−	0.937877i	$-0.612788\pi$
$41$	−4.44335			−0.693934			−0.346967	+	0.937877i	$0.612788\pi$
$42$		−	8.27490i		−	1.27685i
$43$		−	0.243058i		−	0.0370660i	−0.999828	−	0.0185330i	$-0.994100\pi$
$43$		−	0.243058i		−	0.0370660i	0.999828	−	0.0185330i	$-0.00589957\pi$
$44$	1.80535			0.272167
$45$	16.2055	−	11.4486i	2.41578	−	1.70666i
$46$	−4.98187			−0.734537
$47$		−	4.90373i		−	0.715283i	−0.933859	−	0.357641i	$-0.883581\pi$
$47$		−	4.90373i		−	0.715283i	0.933859	−	0.357641i	$-0.116419\pi$
$48$		−	3.44579i		−	0.497357i
$49$	1.23301			0.176145
$50$	−4.71261	−	1.67072i	−0.666464	−	0.236275i
$51$	−26.2024			−3.66907
$52$			1.79319i			0.248671i
$53$		−	4.68477i		−	0.643502i	−0.946824	−	0.321751i	$-0.895729\pi$
$53$		−	4.68477i		−	0.643502i	0.946824	−	0.321751i	$-0.104271\pi$
$54$	20.2387			2.75413
$55$	3.29711	−	2.32928i	0.444582	−	0.314080i
$56$	−2.40146			−0.320908
$57$			14.8553i			1.96764i
$58$		−	4.50580i		−	0.591641i
$59$	−0.802911			−0.104530			−0.0522650	−	0.998633i	$-0.516644\pi$
$59$	−0.802911			−0.104530			−0.0522650	+	0.998633i	$0.516644\pi$
$60$	−4.44579	−	6.29303i	−0.573949	−	0.812427i
$61$	−3.57798			−0.458113			−0.229057	−	0.973413i	$-0.573564\pi$
$61$	−3.57798			−0.458113			−0.229057	+	0.973413i	$0.573564\pi$
$62$			1.00000i			0.127000i
$63$		−	21.3092i		−	2.68471i
$64$	−1.00000			−0.125000
$65$	2.31360	+	3.27490i	0.286966	+	0.406202i
$66$	6.22085			0.765734
$67$			12.8134i			1.56541i	0.622393	+	0.782705i	$0.286161\pi$
$67$			12.8134i			1.56541i	−0.622393	+	0.782705i	$0.713839\pi$
$68$			7.60418i			0.922143i
$69$	−17.1665			−2.06660
$70$	−4.38577	+	3.09838i	−0.524200	+	0.370327i
$71$	−3.73074			−0.442757			−0.221378	−	0.975188i	$-0.571056\pi$
$71$	−3.73074			−0.442757			−0.221378	+	0.975188i	$0.571056\pi$
$72$		−	8.87345i		−	1.04575i
$73$		−	2.86184i		−	0.334953i	−0.985876	−	0.167477i	$-0.946438\pi$
$73$		−	2.86184i		−	0.334953i	0.985876	−	0.167477i	$-0.0535618\pi$
$74$	1.48204			0.172283
$75$	−16.2387	−	5.75694i	−1.87508	−	0.664754i
$76$	4.31116			0.494523
$77$		−	4.33547i		−	0.494073i
$78$			6.17896i			0.699630i
$79$	12.7110			1.43010			0.715048	−	0.699075i	$-0.246405\pi$
$79$	12.7110			1.43010			0.715048	+	0.699075i	$0.246405\pi$
$80$	−1.82630	+	1.29021i	−0.204186	+	0.144250i
$81$	43.1177			4.79086
$82$			4.44335i			0.490686i
$83$		−	7.14027i		−	0.783747i	−0.920019	−	0.391873i	$-0.871827\pi$
$83$		−	7.14027i		−	0.783747i	0.920019	−	0.391873i	$-0.128173\pi$
$84$	−8.27490			−0.902866
$85$	9.81099	+	13.8875i	1.06415	+	1.50631i
$86$	−0.243058			−0.0262096
$87$		−	15.5260i		−	1.66457i
$88$		−	1.80535i		−	0.192451i
$89$	9.26894			0.982505			0.491253	−	0.871017i	$-0.336539\pi$
$89$	9.26894			0.982505			0.491253	+	0.871017i	$0.336539\pi$
$90$	−11.4486	−	16.2055i	−1.20679	−	1.70821i
$91$	4.30627			0.451420
$92$			4.98187i			0.519396i
$93$			3.44579i			0.357311i
$94$	−4.90373			−0.505781
$95$	7.87345	−	5.56229i	0.807799	−	0.570679i
$96$	−3.44579			−0.351684
$97$		−	14.8069i		−	1.50341i	−0.659497	−	0.751707i	$-0.729231\pi$
$97$		−	14.8069i		−	1.50341i	0.659497	−	0.751707i	$-0.270769\pi$
$98$		−	1.23301i		−	0.124553i
$99$	16.0197			1.61004
$100$	−1.67072	+	4.71261i	−0.167072	+	0.471261i
$101$	−6.36357			−0.633199			−0.316599	−	0.948559i	$-0.602541\pi$
$101$	−6.36357			−0.633199			−0.316599	+	0.948559i	$0.602541\pi$
$102$			26.2024i			2.59442i
$103$			7.12459i			0.702006i	0.936374	+	0.351003i	$0.114159\pi$
$103$			7.12459i			0.702006i	−0.936374	+	0.351003i	$0.885841\pi$
$104$	1.79319			0.175837
$105$	−15.1124	+	10.6764i	−1.47482	+	1.04191i
$106$	−4.68477			−0.455025
$107$			5.50824i			0.532502i	0.963904	+	0.266251i	$0.0857850\pi$
$107$			5.50824i			0.532502i	−0.963904	+	0.266251i	$0.914215\pi$
$108$		−	20.2387i		−	1.94747i
$109$	3.47199			0.332557			0.166278	−	0.986079i	$-0.446825\pi$
$109$	3.47199			0.332557			0.166278	+	0.986079i	$0.446825\pi$
$110$	−2.32928	−	3.29711i	−0.222088	−	0.314367i
$111$	5.10679			0.484715
$112$			2.40146i			0.226916i
$113$		−	13.6461i		−	1.28371i	−0.766824	−	0.641857i	$-0.778164\pi$
$113$		−	13.6461i		−	1.28371i	0.766824	−	0.641857i	$-0.221836\pi$
$114$	14.8553			1.39133
$115$	6.42766	+	9.09838i	0.599383	+	0.848428i
$116$	−4.50580			−0.418353
$117$			15.9118i			1.47105i
$118$			0.802911i			0.0739139i
$119$	18.2611			1.67399
$120$	−6.29303	+	4.44579i	−0.574472	+	0.405843i
$121$	−7.74071			−0.703701
$122$			3.57798i			0.323935i
$123$			15.3108i			1.38053i
$124$	1.00000			0.0898027
$125$	3.02903	+	10.7622i	0.270924	+	0.962601i
$126$	−21.3092			−1.89837
$127$			6.89809i			0.612107i	0.952014	+	0.306053i	$0.0990086\pi$
$127$			6.89809i			0.612107i	−0.952014	+	0.306053i	$0.900991\pi$
$128$			1.00000i			0.0883883i
$129$	−0.837525			−0.0737400
$130$	3.27490	−	2.31360i	0.287228	−	0.202916i
$131$	−6.04189			−0.527883			−0.263941	−	0.964539i	$-0.585023\pi$
$131$	−6.04189			−0.527883			−0.263941	+	0.964539i	$0.585023\pi$
$132$		−	6.22085i		−	0.541456i
$133$		−	10.3530i		−	0.897723i
$134$	12.8134			1.10691
$135$	−26.1121	−	36.9618i	−2.24737	−	3.18116i
$136$	7.60418			0.652053
$137$		−	5.01813i		−	0.428727i	−0.976754	−	0.214364i	$-0.931232\pi$
$137$		−	5.01813i		−	0.428727i	0.976754	−	0.214364i	$-0.0687678\pi$
$138$			17.1665i			1.46131i
$139$	−8.09219			−0.686371			−0.343185	−	0.939268i	$-0.611506\pi$
$139$	−8.09219			−0.686371			−0.343185	+	0.939268i	$0.611506\pi$
$140$	3.09838	+	4.38577i	0.261861	+	0.370665i
$141$	−16.8972			−1.42300
$142$			3.73074i			0.313076i
$143$			3.23734i			0.270720i
$144$	−8.87345			−0.739454
$145$	−8.22894	+	5.81343i	−0.683376	+	0.482779i
$146$	−2.86184			−0.236848
$147$		−	4.24870i		−	0.350427i
$148$		−	1.48204i		−	0.121823i
$149$	3.07706			0.252082			0.126041	−	0.992025i	$-0.459773\pi$
$149$	3.07706			0.252082			0.126041	+	0.992025i	$0.459773\pi$
$150$	−5.75694	+	16.2387i	−0.470052	+	1.32588i
$151$	−4.59094			−0.373605			−0.186803	−	0.982397i	$-0.559813\pi$
$151$	−4.59094			−0.373605			−0.186803	+	0.982397i	$0.559813\pi$
$152$		−	4.31116i		−	0.349681i
$153$			67.4753i			5.45506i
$154$	−4.33547			−0.349362
$155$	1.82630	−	1.29021i	0.146692	−	0.103632i
$156$	6.17896			0.494713
$157$			1.09649i			0.0875093i	0.999042	+	0.0437547i	$0.0139320\pi$
$157$			1.09649i			0.0875093i	−0.999042	+	0.0437547i	$0.986068\pi$
$158$		−	12.7110i		−	1.01123i
$159$	−16.1427			−1.28020
$160$	1.29021	+	1.82630i	0.102000	+	0.144381i
$161$	11.9637			0.942875
$162$		−	43.1177i		−	3.38765i
$163$		−	3.40579i		−	0.266762i	−0.991065	−	0.133381i	$-0.957417\pi$
$163$		−	3.40579i		−	0.266762i	0.991065	−	0.133381i	$-0.0425834\pi$
$164$	4.44335			0.346967
$165$	−8.02621	−	11.3611i	−0.624839	−	0.884463i
$166$	−7.14027			−0.554193
$167$		−	19.7453i		−	1.52793i	−0.645255	−	0.763967i	$-0.723249\pi$
$167$		−	19.7453i		−	1.52793i	0.645255	−	0.763967i	$-0.276751\pi$
$168$			8.27490i			0.638423i
$169$	9.78446			0.752650
$170$	13.8875	−	9.81099i	1.06512	−	0.752469i
$171$	38.2548			2.92542
$172$			0.243058i			0.0185330i
$173$		−	13.5382i		−	1.02929i	−0.857403	−	0.514645i	$-0.827924\pi$
$173$		−	13.5382i		−	1.02929i	0.857403	−	0.514645i	$-0.172076\pi$
$174$	−15.5260			−1.17703
$175$	11.3171	+	4.01216i	0.855494	+	0.303291i
$176$	−1.80535			−0.136083
$177$			2.76666i			0.207955i
$178$		−	9.26894i		−	0.694736i
$179$	−18.8799			−1.41115			−0.705575	−	0.708636i	$-0.749311\pi$
$179$	−18.8799			−1.41115			−0.705575	+	0.708636i	$0.749311\pi$
$180$	−16.2055	+	11.4486i	−1.20789	+	0.853329i
$181$	−4.12703			−0.306759			−0.153380	−	0.988167i	$-0.549016\pi$
$181$	−4.12703			−0.306759			−0.153380	+	0.988167i	$0.549016\pi$
$182$		−	4.30627i		−	0.319202i
$183$			12.3290i			0.911382i
$184$	4.98187			0.367269
$185$	−1.91214	−	2.70664i	−0.140583	−	0.198996i
$186$	3.44579			0.252657
$187$			13.7282i			1.00391i
$188$			4.90373i			0.357641i
$189$	−48.6022			−3.53529
$190$	−5.56229	−	7.87345i	−0.403531	−	0.571200i
$191$	4.76502			0.344785			0.172392	−	0.985028i	$-0.444850\pi$
$191$	4.76502			0.344785			0.172392	+	0.985028i	$0.444850\pi$
$192$			3.44579i			0.248678i
$193$			14.1048i			1.01529i	0.861567	+	0.507644i	$0.169483\pi$
$193$			14.1048i			1.01529i	−0.861567	+	0.507644i	$0.830517\pi$
$194$	−14.8069			−1.06307
$195$	11.2846	−	7.97216i	0.808108	−	0.570898i
$196$	−1.23301			−0.0880723
$197$			10.6017i			0.755343i	0.925940	+	0.377672i	$0.123275\pi$
$197$			10.6017i			0.755343i	−0.925940	+	0.377672i	$0.876725\pi$
$198$		−	16.0197i		−	1.13847i
$199$	−15.7831			−1.11884			−0.559419	−	0.828885i	$-0.688976\pi$
$199$	−15.7831			−1.11884			−0.559419	+	0.828885i	$0.688976\pi$
$200$	4.71261	+	1.67072i	0.333232	+	0.118138i
$201$	44.1524			3.11427
$202$			6.36357i			0.447739i
$203$			10.8205i			0.759449i
$204$	26.2024			1.83453
$205$	8.11487	−	5.73285i	0.566767	−	0.400399i
$206$	7.12459			0.496393
$207$			44.2064i			3.07256i
$208$		−	1.79319i		−	0.124336i
$209$	7.78315			0.538372
$210$	10.6764	+	15.1124i	0.736739	+	1.04286i
$211$	2.01052			0.138410			0.0692050	−	0.997602i	$-0.477954\pi$
$211$	2.01052			0.138410			0.0692050	+	0.997602i	$0.477954\pi$
$212$			4.68477i			0.321751i
$213$			12.8553i			0.880832i
$214$	5.50824			0.376536
$215$	0.313595	+	0.443896i	0.0213870	+	0.0302734i
$216$	−20.2387			−1.37707
$217$		−	2.40146i		−	0.163021i
$218$		−	3.47199i		−	0.235153i
$219$	−9.86129			−0.666364
$220$	−3.29711	+	2.32928i	−0.222291	+	0.157040i
$221$	−13.6358			−0.917242
$222$		−	5.10679i		−	0.342745i
$223$		−	6.97699i		−	0.467214i	−0.972331	−	0.233607i	$-0.924947\pi$
$223$		−	6.97699i		−	0.467214i	0.972331	−	0.233607i	$-0.0750529\pi$
$224$	2.40146			0.160454
$225$	−14.8250	+	41.8171i	−0.988336	+	2.78781i
$226$	−13.6461			−0.907723
$227$			0.778596i			0.0516772i	0.999666	+	0.0258386i	$0.00822560\pi$
$227$			0.778596i			0.0516772i	−0.999666	+	0.0258386i	$0.991774\pi$
$228$		−	14.8553i		−	0.983818i
$229$	21.3368			1.40998			0.704988	−	0.709219i	$-0.250952\pi$
$229$	21.3368			1.40998			0.704988	+	0.709219i	$0.250952\pi$
$230$	9.09838	−	6.42766i	0.599929	−	0.423827i
$231$	−14.9391			−0.982921
$232$			4.50580i			0.295821i
$233$			12.2209i			0.800615i	0.916381	+	0.400307i	$0.131097\pi$
$233$			12.2209i			0.800615i	−0.916381	+	0.400307i	$0.868903\pi$
$234$	15.9118			1.04019
$235$	6.32684	+	8.95567i	0.412718	+	0.584203i
$236$	0.802911			0.0522650
$237$		−	43.7993i		−	2.84507i
$238$		−	18.2611i		−	1.18369i
$239$	−6.11298			−0.395416			−0.197708	−	0.980261i	$-0.563350\pi$
$239$	−6.11298			−0.395416			−0.197708	+	0.980261i	$0.563350\pi$
$240$	4.44579	+	6.29303i	0.286974	+	0.406213i
$241$	3.87181			0.249405			0.124703	−	0.992194i	$-0.460202\pi$
$241$	3.87181			0.249405			0.124703	+	0.992194i	$0.460202\pi$
$242$			7.74071i			0.497592i
$243$		−	87.8586i		−	5.63613i
$244$	3.57798			0.229057
$245$	−2.25185	+	1.59084i	−0.143865	+	0.101635i
$246$	15.3108			0.976183
$247$			7.73074i			0.491895i
$248$		−	1.00000i		−	0.0635001i
$249$	−24.6039			−1.55921
$250$	10.7622	−	3.02903i	0.680661	−	0.191572i
$251$	16.3390			1.03131			0.515654	−	0.856797i	$-0.327549\pi$
$251$	16.3390			1.03131			0.515654	+	0.856797i	$0.327549\pi$
$252$			21.3092i			1.34235i
$253$			8.99403i			0.565450i
$254$	6.89809			0.432825
$255$	47.8534	−	33.8066i	2.99669	−	2.11705i
$256$	1.00000			0.0625000
$257$		−	8.16757i		−	0.509479i	−0.967010	−	0.254739i	$-0.918010\pi$
$257$		−	8.16757i		−	0.509479i	0.967010	−	0.254739i	$-0.0819897\pi$
$258$			0.837525i			0.0521421i
$259$	−3.55905			−0.221149
$260$	−2.31360	−	3.27490i	−0.143483	−	0.203101i
$261$	−39.9820			−2.47482
$262$			6.04189i			0.373269i
$263$		−	18.7531i		−	1.15636i	−0.815908	−	0.578182i	$-0.803762\pi$
$263$		−	18.7531i		−	1.15636i	0.815908	−	0.578182i	$-0.196238\pi$
$264$	−6.22085			−0.382867
$265$	6.04433	+	8.55578i	0.371300	+	0.525577i
$266$	−10.3530			−0.634786
$267$		−	31.9388i		−	1.95462i
$268$		−	12.8134i		−	0.782705i
$269$	20.0859			1.22466			0.612329	−	0.790603i	$-0.290233\pi$
$269$	20.0859			1.22466			0.612329	+	0.790603i	$0.290233\pi$
$270$	−36.9618	+	26.1121i	−2.24942	+	1.58913i
$271$	11.3576			0.689925			0.344962	−	0.938616i	$-0.387892\pi$
$271$	11.3576			0.689925			0.344962	+	0.938616i	$0.387892\pi$
$272$		−	7.60418i		−	0.461071i
$273$		−	14.8385i		−	0.898067i
$274$	−5.01813			−0.303156
$275$	−3.01623	+	8.50792i	−0.181886	+	0.513047i
$276$	17.1665			1.03330
$277$		−	26.8815i		−	1.61515i	−0.589762	−	0.807577i	$-0.700778\pi$
$277$		−	26.8815i		−	1.61515i	0.589762	−	0.807577i	$-0.299222\pi$
$278$			8.09219i			0.485337i
$279$	8.87345			0.531239
$280$	4.38577	−	3.09838i	0.262100	−	0.185164i
$281$	28.3362			1.69040			0.845199	−	0.534452i	$-0.179482\pi$
$281$	28.3362			1.69040			0.845199	+	0.534452i	$0.179482\pi$
$282$			16.8972i			1.00621i
$283$			13.5090i			0.803027i	0.915853	+	0.401513i	$0.131516\pi$
$283$			13.5090i			0.803027i	−0.915853	+	0.401513i	$0.868484\pi$
$284$	3.73074			0.221378
$285$	−19.1665	−	27.1302i	−1.13532	−	1.60706i
$286$	3.23734			0.191428
$287$		−	10.6705i		−	0.629860i
$288$			8.87345i			0.522873i
$289$	−40.8236			−2.40139
$290$	5.81343	+	8.22894i	0.341376	+	0.483220i
$291$	−51.0215			−2.99093
$292$			2.86184i			0.167477i
$293$			31.9855i			1.86862i	0.356467	+	0.934308i	$0.383981\pi$
$293$			31.9855i			1.86862i	−0.356467	+	0.934308i	$0.616019\pi$
$294$	−4.24870			−0.247789
$295$	1.46635	−	1.03592i	0.0853744	−	0.0603138i
$296$	−1.48204			−0.0861417
$297$		−	36.5379i		−	2.12014i
$298$		−	3.07706i		−	0.178249i
$299$	−8.93347			−0.516636
$300$	16.2387	+	5.75694i	0.937539	+	0.332377i
$301$	0.583692			0.0336435
$302$			4.59094i			0.264179i
$303$			21.9275i			1.25970i
$304$	−4.31116			−0.247262
$305$	6.53445	−	4.61634i	0.374162	−	0.264331i
$306$	67.4753			3.85731
$307$			2.07487i			0.118419i	0.998246	+	0.0592095i	$0.0188580\pi$
$307$			2.07487i			0.118419i	−0.998246	+	0.0592095i	$0.981142\pi$
$308$			4.33547i			0.247036i
$309$	24.5498			1.39659
$310$	−1.29021	−	1.82630i	−0.0732790	−	0.103727i
$311$	−16.4611			−0.933426			−0.466713	−	0.884409i	$-0.654562\pi$
$311$	−16.4611			−0.933426			−0.466713	+	0.884409i	$0.654562\pi$
$312$		−	6.17896i		−	0.349815i
$313$		−	32.6087i		−	1.84315i	−0.388195	−	0.921577i	$-0.626901\pi$
$313$		−	32.6087i		−	1.84315i	0.388195	−	0.921577i	$-0.373099\pi$
$314$	1.09649			0.0618785
$315$	27.4933	+	38.9169i	1.54907	+	2.19272i
$316$	−12.7110			−0.715048
$317$			8.61743i			0.484003i	0.970276	+	0.242002i	$0.0778039\pi$
$317$			8.61743i			0.484003i	−0.970276	+	0.242002i	$0.922196\pi$
$318$			16.1427i			0.905238i
$319$	−8.13456			−0.455448
$320$	1.82630	−	1.29021i	0.102093	−	0.0721249i
$321$	18.9802			1.05937
$322$		−	11.9637i		−	0.666714i
$323$			32.7828i			1.82408i
$324$	−43.1177			−2.39543
$325$	−8.45062	−	2.99592i	−0.468756	−	0.166184i
$326$	−3.40579			−0.188629
$327$		−	11.9637i		−	0.661597i
$328$		−	4.44335i		−	0.245343i
$329$	11.7761			0.649237
$330$	−11.3611	+	8.02621i	−0.625409	+	0.441828i
$331$	−27.6618			−1.52043			−0.760214	−	0.649673i	$-0.774906\pi$
$331$	−27.6618			−1.52043			−0.760214	+	0.649673i	$0.774906\pi$
$332$			7.14027i			0.391873i
$333$		−	13.1508i		−	0.720659i
$334$	−19.7453			−1.08041
$335$	−16.5320	−	23.4011i	−0.903240	−	1.27854i
$336$	8.27490			0.451433
$337$			21.8929i			1.19258i	0.802769	+	0.596291i	$0.203359\pi$
$337$			21.8929i			1.19258i	−0.802769	+	0.596291i	$0.796641\pi$
$338$		−	9.78446i		−	0.532204i
$339$	−47.0215			−2.55386
$340$	−9.81099	−	13.8875i	−0.532076	−	0.753155i
$341$	1.80535			0.0977652
$342$		−	38.2548i		−	2.06858i
$343$			19.7712i			1.06755i
$344$	0.243058			0.0131048
$345$	31.3511	−	22.1484i	1.68789	−	1.19243i
$346$	−13.5382			−0.727818
$347$			6.46977i			0.347316i	0.984806	+	0.173658i	$0.0555587\pi$
$347$			6.46977i			0.347316i	−0.984806	+	0.173658i	$0.944441\pi$
$348$			15.5260i			0.832283i
$349$	28.3330			1.51663			0.758314	−	0.651889i	$-0.226023\pi$
$349$	28.3330			1.51663			0.758314	+	0.651889i	$0.226023\pi$
$350$	4.01216	−	11.3171i	0.214459	−	0.604926i
$351$	36.2918			1.93711
$352$			1.80535i			0.0962255i
$353$		−	9.08997i		−	0.483810i	−0.970300	−	0.241905i	$-0.922228\pi$
$353$		−	9.08997i		−	0.483810i	0.970300	−	0.241905i	$-0.0777723\pi$
$354$	2.76666			0.147046
$355$	6.81343	−	4.81343i	0.361619	−	0.255470i
$356$	−9.26894			−0.491253
$357$		−	62.9239i		−	3.33029i
$358$			18.8799i			0.997833i
$359$	32.2183			1.70042			0.850209	−	0.526445i	$-0.176475\pi$
$359$	32.2183			1.70042			0.850209	+	0.526445i	$0.176475\pi$
$360$	11.4486	+	16.2055i	0.603395	+	0.854107i
$361$	−0.413941			−0.0217864
$362$			4.12703i			0.216912i
$363$			26.6728i			1.39996i
$364$	−4.30627			−0.225710
$365$	3.69237	+	5.22657i	0.193268	+	0.273571i
$366$	12.3290			0.644445
$367$			11.8854i			0.620412i	0.950669	+	0.310206i	$0.100398\pi$
$367$			11.8854i			0.620412i	−0.950669	+	0.310206i	$0.899602\pi$
$368$		−	4.98187i		−	0.259698i
$369$	39.4278			2.05253
$370$	−2.70664	+	1.91214i	−0.140712	+	0.0994074i
$371$	11.2503			0.584084
$372$		−	3.44579i		−	0.178656i
$373$		−	32.7571i		−	1.69610i	−0.529918	−	0.848049i	$-0.677777\pi$
$373$		−	32.7571i		−	1.69610i	0.529918	−	0.848049i	$-0.322223\pi$
$374$	13.7282			0.709869
$375$	37.0843	−	10.4374i	1.91502	−	0.538984i
$376$	4.90373			0.252891
$377$		−	8.07978i		−	0.416130i
$378$			48.6022i			2.49983i
$379$	16.5217			0.848663			0.424332	−	0.905507i	$-0.360509\pi$
$379$	16.5217			0.848663			0.424332	+	0.905507i	$0.360509\pi$
$380$	−7.87345	+	5.56229i	−0.403899	+	0.285340i
$381$	23.7694			1.21774
$382$		−	4.76502i		−	0.243800i
$383$			19.0949i			0.975701i	0.872927	+	0.487851i	$0.162219\pi$
$383$			19.0949i			0.975701i	−0.872927	+	0.487851i	$0.837781\pi$
$384$	3.44579			0.175842
$385$	5.59366	+	7.91785i	0.285080	+	0.403531i
$386$	14.1048			0.717917
$387$			2.15676i			0.109634i
$388$			14.8069i			0.751707i
$389$	−10.8937			−0.552332			−0.276166	−	0.961110i	$-0.589064\pi$
$389$	−10.8937			−0.552332			−0.276166	+	0.961110i	$0.589064\pi$
$390$	−7.97216	−	11.2846i	−0.403686	−	0.571419i
$391$	−37.8831			−1.91583
$392$			1.23301i			0.0622765i
$393$			20.8191i			1.05018i
$394$	10.6017			0.534108
$395$	−23.2140	+	16.3998i	−1.16802	+	0.825164i
$396$	−16.0197			−0.805020
$397$		−	20.3049i		−	1.01907i	−0.860449	−	0.509536i	$-0.829817\pi$
$397$		−	20.3049i		−	1.01907i	0.860449	−	0.509536i	$-0.170183\pi$
$398$			15.7831i			0.791138i
$399$	−35.6744			−1.78595
$400$	1.67072	−	4.71261i	0.0835360	−	0.235631i
$401$	−19.1164			−0.954629			−0.477315	−	0.878733i	$-0.658390\pi$
$401$	−19.1164			−0.954629			−0.477315	+	0.878733i	$0.658390\pi$
$402$		−	44.1524i		−	2.20212i
$403$			1.79319i			0.0893253i
$404$	6.36357			0.316599
$405$	−78.7458	+	55.6309i	−3.91291	+	2.76432i
$406$	10.8205			0.537012
$407$		−	2.67560i		−	0.132625i
$408$		−	26.2024i		−	1.29721i
$409$	−5.87509			−0.290504			−0.145252	−	0.989395i	$-0.546399\pi$
$409$	−5.87509			−0.290504			−0.145252	+	0.989395i	$0.546399\pi$
$410$	−5.73285	−	8.11487i	−0.283125	−	0.400765i
$411$	−17.2914			−0.852922
$412$		−	7.12459i		−	0.351003i
$413$		−	1.92815i		−	0.0948783i
$414$	44.2064			2.17263
$415$	9.21245	+	13.0403i	0.452221	+	0.640121i
$416$	−1.79319			−0.0879186
$417$			27.8840i			1.36548i
$418$		−	7.78315i		−	0.380686i
$419$	−29.8880			−1.46012			−0.730061	−	0.683381i	$-0.760509\pi$
$419$	−29.8880			−1.46012			−0.730061	+	0.683381i	$0.760509\pi$
$420$	15.1124	−	10.6764i	0.737411	−	0.520953i
$421$	−8.55796			−0.417090			−0.208545	−	0.978013i	$-0.566873\pi$
$421$	−8.55796			−0.417090			−0.208545	+	0.978013i	$0.566873\pi$
$422$		−	2.01052i		−	0.0978706i
$423$			43.5130i			2.11567i
$424$	4.68477			0.227512
$425$	−35.8356	−	12.7045i	−1.73828	−	0.616257i
$426$	12.8553			0.622842
$427$		−	8.59236i		−	0.415813i
$428$		−	5.50824i		−	0.266251i
$429$	11.1552			0.538578
$430$	0.443896	−	0.313595i	0.0214065	−	0.0151229i
$431$	−23.4528			−1.12968			−0.564840	−	0.825200i	$-0.691062\pi$
$431$	−23.4528			−1.12968			−0.564840	+	0.825200i	$0.691062\pi$
$432$			20.2387i			0.973733i
$433$		−	11.1382i		−	0.535266i	−0.963521	−	0.267633i	$-0.913759\pi$
$433$		−	11.1382i		−	0.535266i	0.963521	−	0.267633i	$-0.0862414\pi$
$434$	−2.40146			−0.115274
$435$	20.0318	+	28.3552i	0.960453	+	1.35953i
$436$	−3.47199			−0.166278
$437$			21.4776i			1.02741i
$438$			9.86129i			0.471191i
$439$	33.0537			1.57757			0.788784	−	0.614670i	$-0.210711\pi$
$439$	33.0537			1.57757			0.788784	+	0.614670i	$0.210711\pi$
$440$	2.32928	+	3.29711i	0.111044	+	0.157183i
$441$	−10.9411			−0.521003
$442$			13.6358i			0.648588i
$443$			29.0715i			1.38123i	0.723223	+	0.690615i	$0.242660\pi$
$443$			29.0715i			1.38123i	−0.723223	+	0.690615i	$0.757340\pi$
$444$	−5.10679			−0.242357
$445$	−16.9278	+	11.9589i	−0.802456	+	0.566905i
$446$	−6.97699			−0.330370
$447$		−	10.6029i		−	0.501499i
$448$		−	2.40146i		−	0.113458i
$449$	−28.7466			−1.35663			−0.678317	−	0.734769i	$-0.737290\pi$
$449$	−28.7466			−1.35663			−0.678317	+	0.734769i	$0.737290\pi$
$450$	41.8171	+	14.8250i	1.97128	+	0.698859i
$451$	8.02180			0.377732
$452$			13.6461i			0.641857i
$453$			15.8194i			0.743260i
$454$	0.778596			0.0365413
$455$	−7.86453	+	5.55600i	−0.368695	+	0.260469i
$456$	−14.8553			−0.695664
$457$		−	14.2919i		−	0.668549i	−0.942476	−	0.334274i	$-0.891509\pi$
$457$		−	14.2919i		−	0.668549i	0.942476	−	0.334274i	$-0.108491\pi$
$458$		−	21.3368i		−	0.997004i
$459$	153.898			7.18336
$460$	−6.42766	−	9.09838i	−0.299691	−	0.424214i
$461$	−28.3156			−1.31879			−0.659395	−	0.751796i	$-0.729188\pi$
$461$	−28.3156			−1.31879			−0.659395	+	0.751796i	$0.729188\pi$
$462$			14.9391i			0.695030i
$463$		−	27.2987i		−	1.26868i	−0.773056	−	0.634338i	$-0.781273\pi$
$463$		−	27.2987i		−	1.26868i	0.773056	−	0.634338i	$-0.218727\pi$
$464$	4.50580			0.209177
$465$	−4.44579	−	6.29303i	−0.206168	−	0.291832i
$466$	12.2209			0.566120
$467$		−	25.3422i		−	1.17270i	−0.810059	−	0.586349i	$-0.800565\pi$
$467$		−	25.3422i		−	1.17270i	0.810059	−	0.586349i	$-0.199435\pi$
$468$		−	15.9118i		−	0.735524i
$469$	−30.7709			−1.42087
$470$	8.95567	−	6.32684i	0.413094	−	0.291835i
$471$	3.77827			0.174093
$472$		−	0.802911i		−	0.0369570i
$473$			0.438805i			0.0201763i
$474$	−43.7993			−2.01177
$475$	−7.20273	+	20.3168i	−0.330484	+	0.932198i
$476$	−18.2611			−0.836997
$477$			41.5700i			1.90336i
$478$			6.11298i			0.279601i
$479$	−1.77827			−0.0812511			−0.0406256	−	0.999174i	$-0.512935\pi$
$479$	−1.77827			−0.0812511			−0.0406256	+	0.999174i	$0.512935\pi$
$480$	6.29303	−	4.44579i	0.287236	−	0.202921i
$481$	2.65758			0.121175
$482$		−	3.87181i		−	0.176356i
$483$		−	41.2245i		−	1.87578i
$484$	7.74071			0.351850
$485$	19.1040	+	27.0418i	0.867469	+	1.22791i
$486$	−87.8586			−3.98535
$487$			22.9498i			1.03996i	0.854179	+	0.519978i	$0.174060\pi$
$487$			22.9498i			1.03996i	−0.854179	+	0.519978i	$0.825940\pi$
$488$		−	3.57798i		−	0.161967i
$489$	−11.7356			−0.530703
$490$	1.59084	+	2.25185i	0.0718670	+	0.101728i
$491$	−22.9557			−1.03597			−0.517987	−	0.855388i	$-0.673319\pi$
$491$	−22.9557			−1.03597			−0.517987	+	0.855388i	$0.673319\pi$
$492$		−	15.3108i		−	0.690265i
$493$		−	34.2630i		−	1.54313i
$494$	7.73074			0.347822
$495$	−29.2567	+	20.6688i	−1.31499	+	0.928991i
$496$	−1.00000			−0.0449013
$497$		−	8.95920i		−	0.401875i
$498$			24.6039i			1.10253i
$499$	−1.66588			−0.0745752			−0.0372876	−	0.999305i	$-0.511872\pi$
$499$	−1.66588			−0.0745752			−0.0372876	+	0.999305i	$0.511872\pi$
$500$	−3.02903	−	10.7622i	−0.135462	−	0.481300i
$501$	−68.0380			−3.03971
$502$		−	16.3390i		−	0.729245i
$503$			31.9394i			1.42411i	0.702124	+	0.712054i	$0.252235\pi$
$503$			31.9394i			1.42411i	−0.702124	+	0.712054i	$0.747765\pi$
$504$	21.3092			0.949187
$505$	11.6218	−	8.21033i	0.517162	−	0.365355i
$506$	8.99403			0.399833
$507$		−	33.7152i		−	1.49734i
$508$		−	6.89809i		−	0.306053i
$509$	16.6202			0.736677			0.368339	−	0.929692i	$-0.379927\pi$
$509$	16.6202			0.736677			0.368339	+	0.929692i	$0.379927\pi$
$510$	−33.8066	−	47.8534i	−1.49698	−	2.11898i
$511$	6.87258			0.304025
$512$		−	1.00000i		−	0.0441942i
$513$		−	87.2520i		−	3.85227i
$514$	−8.16757			−0.360256
$515$	−9.19221	−	13.0116i	−0.405057	−	0.573360i
$516$	0.837525			0.0368700
$517$			8.85296i			0.389353i
$518$			3.55905i			0.156376i
$519$	−46.6498			−2.04770
$520$	−3.27490	+	2.31360i	−0.143614	+	0.101458i
$521$	15.1852			0.665274			0.332637	−	0.943055i	$-0.392062\pi$
$521$	15.1852			0.665274			0.332637	+	0.943055i	$0.392062\pi$
$522$			39.9820i			1.74997i
$523$		−	24.9178i		−	1.08958i	−0.838573	−	0.544789i	$-0.816610\pi$
$523$		−	24.9178i		−	1.08958i	0.838573	−	0.544789i	$-0.183390\pi$
$524$	6.04189			0.263941
$525$	13.8250	−	38.9964i	0.603374	−	1.70194i
$526$	−18.7531			−0.817673
$527$			7.60418i			0.331243i
$528$			6.22085i			0.270728i
$529$	−1.81907			−0.0790900
$530$	8.55578	−	6.04433i	0.371639	−	0.262549i
$531$	7.12459			0.309181
$532$			10.3530i			0.448861i
$533$			7.96778i			0.345123i
$534$	−31.9388			−1.38213
$535$	−7.10679	−	10.0597i	−0.307253	−	0.434918i
$536$	−12.8134			−0.553456
$537$			65.0561i			2.80738i
$538$		−	20.0859i		−	0.865964i
$539$	−2.22602			−0.0958815
$540$	26.1121	+	36.9618i	1.12369	+	1.59058i
$541$	21.4114			0.920549			0.460275	−	0.887777i	$-0.347751\pi$
$541$	21.4114			0.920549			0.460275	+	0.887777i	$0.347751\pi$
$542$		−	11.3576i		−	0.487851i
$543$			14.2209i			0.610275i
$544$	−7.60418			−0.326027
$545$	−6.34089	+	4.47960i	−0.271614	+	0.191885i
$546$	−14.8385			−0.635029
$547$			9.13652i			0.390650i	0.980739	+	0.195325i	$0.0625761\pi$
$547$			9.13652i			0.390650i	−0.980739	+	0.195325i	$0.937424\pi$
$548$			5.01813i			0.214364i
$549$	31.7490			1.35501
$550$	8.50792	+	3.01623i	0.362779	+	0.128613i
$551$	−19.4252			−0.827542
$552$		−	17.1665i		−	0.730654i
$553$			30.5248i			1.29805i
$554$	−26.8815			−1.14209
$555$	−9.32651	+	6.58883i	−0.395888	+	0.279680i
$556$	8.09219			0.343185
$557$		−	23.6658i		−	1.00275i	−0.865230	−	0.501375i	$-0.832828\pi$
$557$		−	23.6658i		−	1.00275i	0.865230	−	0.501375i	$-0.167172\pi$
$558$		−	8.87345i		−	0.375643i
$559$	−0.435850			−0.0184345
$560$	−3.09838	−	4.38577i	−0.130930	−	0.185333i
$561$	47.3045			1.99720
$562$		−	28.3362i		−	1.19529i
$563$		−	19.0827i		−	0.804240i	−0.915587	−	0.402120i	$-0.868274\pi$
$563$		−	19.0827i		−	0.804240i	0.915587	−	0.402120i	$-0.131726\pi$
$564$	16.8972			0.711501
$565$	17.6063	+	24.9218i	0.740702	+	1.04847i
$566$	13.5090			0.567826
$567$			103.545i			4.34850i
$568$		−	3.73074i		−	0.156538i
$569$	−9.49067			−0.397869			−0.198935	−	0.980013i	$-0.563748\pi$
$569$	−9.49067			−0.397869			−0.198935	+	0.980013i	$0.563748\pi$
$570$	−27.1302	+	19.1665i	−1.13636	+	0.802795i
$571$	29.9771			1.25450			0.627252	−	0.778816i	$-0.284180\pi$
$571$	29.9771			1.25450			0.627252	+	0.778816i	$0.284180\pi$
$572$		−	3.23734i		−	0.135360i
$573$		−	16.4193i		−	0.685924i
$574$	−10.6705			−0.445378
$575$	−23.4776	−	8.32331i	−0.979085	−	0.347106i
$576$	8.87345			0.369727
$577$		−	28.6869i		−	1.19425i	−0.802148	−	0.597125i	$-0.796310\pi$
$577$		−	28.6869i		−	1.19425i	0.802148	−	0.597125i	$-0.203690\pi$
$578$			40.8236i			1.69804i
$579$	48.6022			2.01984
$580$	8.22894	−	5.81343i	0.341688	−	0.241390i
$581$	17.1470			0.711379
$582$			51.0215i			2.11491i
$583$			8.45765i			0.350280i
$584$	2.86184			0.118424
$585$	−20.5296	−	29.0597i	−0.848793	−	1.20147i
$586$	31.9855			1.32131
$587$			14.6971i			0.606616i	0.952893	+	0.303308i	$0.0980911\pi$
$587$			14.6971i			0.606616i	−0.952893	+	0.303308i	$0.901909\pi$
$588$			4.24870i			0.175213i
$589$	4.31116			0.177638
$590$	−1.03592	−	1.46635i	−0.0426483	−	0.0603688i
$591$	36.5314			1.50270
$592$			1.48204i			0.0609114i
$593$		−	13.2156i		−	0.542702i	−0.962481	−	0.271351i	$-0.912530\pi$
$593$		−	13.2156i		−	0.542702i	0.962481	−	0.271351i	$-0.0874703\pi$
$594$	−36.5379			−1.49917
$595$	−33.3502	+	23.5607i	−1.36723	+	0.965893i
$596$	−3.07706			−0.126041
$597$			54.3854i			2.22584i
$598$			8.93347i			0.365317i
$599$	6.47254			0.264461			0.132230	−	0.991219i	$-0.457786\pi$
$599$	6.47254			0.264461			0.132230	+	0.991219i	$0.457786\pi$
$600$	5.75694	−	16.2387i	0.235026	−	0.662940i
$601$	5.43826			0.221831			0.110916	−	0.993830i	$-0.464622\pi$
$601$	5.43826			0.221831			0.110916	+	0.993830i	$0.464622\pi$
$602$		−	0.583692i		−	0.0237895i
$603$		−	113.699i		−	4.63019i
$604$	4.59094			0.186803
$605$	14.1368	−	9.98713i	0.574744	−	0.406035i
$606$	21.9275			0.890744
$607$		−	5.64207i		−	0.229005i	−0.993423	−	0.114502i	$-0.963473\pi$
$607$		−	5.64207i		−	0.229005i	0.993423	−	0.114502i	$-0.0365273\pi$
$608$			4.31116i			0.174840i
$609$	37.2851			1.51087
$610$	−4.61634	−	6.53445i	−0.186910	−	0.264572i
$611$	−8.79334			−0.355740
$612$		−	67.4753i		−	2.72753i
$613$			7.10890i			0.287126i	0.989641	+	0.143563i	$0.0458559\pi$
$613$			7.10890i			0.287126i	−0.989641	+	0.143563i	$0.954144\pi$
$614$	2.07487			0.0837349
$615$	−19.7542	−	27.9621i	−0.796565	−	1.12754i
$616$	4.33547			0.174681
$617$			13.1003i			0.527397i	0.964605	+	0.263699i	$0.0849424\pi$
$617$			13.1003i			0.527397i	−0.964605	+	0.263699i	$0.915058\pi$
$618$		−	24.5498i		−	0.987538i
$619$	40.0788			1.61090			0.805452	−	0.592661i	$-0.201922\pi$
$619$	40.0788			1.61090			0.805452	+	0.592661i	$0.201922\pi$
$620$	−1.82630	+	1.29021i	−0.0733458	+	0.0518161i
$621$	100.826			4.04602
$622$			16.4611i			0.660032i
$623$			22.2589i			0.891785i
$624$	−6.17896			−0.247357
$625$	−19.4174	−	15.7469i	−0.776696	−	0.629876i
$626$	−32.6087			−1.30331
$627$		−	26.8191i		−	1.07105i
$628$		−	1.09649i		−	0.0437547i
$629$	11.2697			0.449352
$630$	38.9169	−	27.4933i	1.55049	−	1.09536i
$631$	16.9278			0.673886			0.336943	−	0.941525i	$-0.390607\pi$
$631$	16.9278			0.673886			0.336943	+	0.941525i	$0.390607\pi$
$632$			12.7110i			0.505615i
$633$		−	6.92783i		−	0.275356i
$634$	8.61743			0.342242
$635$	−8.89998	−	12.5980i	−0.353185	−	0.499935i
$636$	16.1427			0.640100
$637$		−	2.21103i		−	0.0876042i
$638$			8.13456i			0.322050i
$639$	33.1045			1.30959
$640$	−1.29021	−	1.82630i	−0.0510000	−	0.0721907i
$641$	−5.96863			−0.235747			−0.117873	−	0.993029i	$-0.537608\pi$
$641$	−5.96863			−0.235747			−0.117873	+	0.993029i	$0.537608\pi$
$642$		−	18.9802i		−	0.749090i
$643$		−	5.77074i		−	0.227576i	−0.993505	−	0.113788i	$-0.963702\pi$
$643$		−	5.77074i		−	0.227576i	0.993505	−	0.113788i	$-0.0362984\pi$
$644$	−11.9637			−0.471438
$645$	1.52957	−	1.08058i	0.0602268	−	0.0425479i
$646$	32.7828			1.28982
$647$		−	9.05045i		−	0.355810i	−0.984048	−	0.177905i	$-0.943068\pi$
$647$		−	9.05045i		−	0.355810i	0.984048	−	0.177905i	$-0.0569319\pi$
$648$			43.1177i			1.69382i
$649$	1.44954			0.0568992
$650$	−2.99592	+	8.45062i	−0.117510	+	0.331461i
$651$	−8.27490			−0.324319
$652$			3.40579i			0.133381i
$653$			27.7969i			1.08778i	0.839157	+	0.543889i	$0.183049\pi$
$653$			27.7969i			1.08778i	−0.839157	+	0.543889i	$0.816951\pi$
$654$	−11.9637			−0.467820
$655$	11.0343	−	7.79531i	0.431145	−	0.304588i
$656$	−4.44335			−0.173484
$657$			25.3944i			0.990729i
$658$		−	11.7761i		−	0.459080i
$659$	−18.9983			−0.740067			−0.370033	−	0.929018i	$-0.620654\pi$
$659$	−18.9983			−0.740067			−0.370033	+	0.929018i	$0.620654\pi$
$660$	8.02621	+	11.3611i	0.312420	+	0.442231i
$661$	−35.8244			−1.39341			−0.696703	−	0.717359i	$-0.745351\pi$
$661$	−35.8244			−1.39341			−0.696703	+	0.717359i	$0.745351\pi$
$662$			27.6618i			1.07510i
$663$			46.9860i			1.82478i
$664$	7.14027			0.277096
$665$	13.3576	+	18.9077i	0.517985	+	0.733210i
$666$	−13.1508			−0.509583
$667$		−	22.4473i		−	0.869165i
$668$			19.7453i			0.763967i
$669$	−24.0412			−0.929488
$670$	−23.4011	+	16.5320i	−0.904064	+	0.638687i
$671$	6.45951			0.249367
$672$		−	8.27490i		−	0.319211i
$673$			7.89449i			0.304310i	0.988357	+	0.152155i	$0.0486213\pi$
$673$			7.89449i			0.304310i	−0.988357	+	0.152155i	$0.951379\pi$
$674$	21.8929			0.843282
$675$	95.3769	+	33.8131i	3.67106	+	1.30147i
$676$	−9.78446			−0.376325
$677$		−	32.7728i		−	1.25956i	−0.776774	−	0.629780i	$-0.783145\pi$
$677$		−	32.7728i		−	1.25956i	0.776774	−	0.629780i	$-0.216855\pi$
$678$			47.0215i			1.80585i
$679$	35.5581			1.36460
$680$	−13.8875	+	9.81099i	−0.532561	+	0.376234i
$681$	2.68288			0.102808
$682$		−	1.80535i		−	0.0691305i
$683$			17.6856i			0.676720i	0.941017	+	0.338360i	$0.109872\pi$
$683$			17.6856i			0.676720i	−0.941017	+	0.338360i	$0.890128\pi$
$684$	−38.2548			−1.46271
$685$	6.47443	+	9.16459i	0.247375	+	0.350161i
$686$	19.7712			0.754868
$687$		−	73.5221i		−	2.80504i
$688$		−	0.243058i		−	0.00926649i
$689$	−8.40070			−0.320041
$690$	−22.1484	−	31.3511i	−0.843173	−	1.19352i
$691$	1.92262			0.0731398			0.0365699	−	0.999331i	$-0.488357\pi$
$691$	1.92262			0.0731398			0.0365699	+	0.999331i	$0.488357\pi$
$692$			13.5382i			0.514645i
$693$			38.4706i			1.46138i
$694$	6.46977			0.245589
$695$	14.7787	−	10.4406i	0.560590	−	0.396035i
$696$	15.5260			0.588513
$697$			33.7880i			1.27981i
$698$		−	28.3330i		−	1.07242i
$699$	42.1105			1.59276
$700$	−11.3171	−	4.01216i	−0.427747	−	0.151645i
$701$	12.2098			0.461158			0.230579	−	0.973054i	$-0.425938\pi$
$701$	12.2098			0.461158			0.230579	+	0.973054i	$0.425938\pi$
$702$		−	36.2918i		−	1.36975i
$703$		−	6.38930i		−	0.240977i
$704$	1.80535			0.0680417
$705$	30.8593	−	21.8009i	1.16223	−	0.821071i
$706$	−9.08997			−0.342106
$707$		−	15.2818i		−	0.574732i
$708$		−	2.76666i		−	0.103977i
$709$	−19.2662			−0.723556			−0.361778	−	0.932264i	$-0.617830\pi$
$709$	−19.2662			−0.723556			−0.361778	+	0.932264i	$0.617830\pi$
$710$	−4.81343	−	6.81343i	−0.180645	−	0.255704i
$711$	−112.790			−4.22996
$712$			9.26894i			0.347368i
$713$			4.98187i			0.186573i
$714$	−62.9239			−2.35487
$715$	−4.17685	−	5.91235i	−0.156205	−	0.221109i
$716$	18.8799			0.705575
$717$			21.0640i			0.786650i
$718$		−	32.2183i		−	1.20238i
$719$	−51.3607			−1.91543			−0.957716	−	0.287716i	$-0.907104\pi$
$719$	−51.3607			−1.91543			−0.957716	+	0.287716i	$0.907104\pi$
$720$	16.2055	−	11.4486i	0.603945	−	0.426664i
$721$	−17.1094			−0.637186
$722$			0.413941i			0.0154053i
$723$		−	13.3414i		−	0.496173i
$724$	4.12703			0.153380
$725$	7.52793	−	21.2341i	0.279580	−	0.788615i
$726$	26.6728			0.989922
$727$		−	14.3935i		−	0.533826i	−0.963721	−	0.266913i	$-0.913996\pi$
$727$		−	14.3935i		−	0.533826i	0.963721	−	0.266913i	$-0.0860037\pi$
$728$			4.30627i			0.159601i
$729$	−173.389			−6.42181
$730$	5.22657	−	3.69237i	0.193444	−	0.136661i
$731$	−1.84826			−0.0683602
$732$		−	12.3290i		−	0.455691i
$733$		−	27.4819i		−	1.01507i	−0.861632	−	0.507533i	$-0.830558\pi$
$733$		−	27.4819i		−	1.01507i	0.861632	−	0.507533i	$-0.169442\pi$
$734$	11.8854			0.438698
$735$	5.48171	+	7.75938i	0.202196	+	0.286209i
$736$	−4.98187			−0.183634
$737$		−	23.1327i		−	0.852105i
$738$		−	39.4278i		−	1.45136i
$739$	19.1330			0.703819			0.351909	−	0.936034i	$-0.385533\pi$
$739$	19.1330			0.703819			0.351909	+	0.936034i	$0.385533\pi$
$740$	1.91214	+	2.70664i	0.0702917	+	0.0994981i
$741$	26.6385			0.978589
$742$		−	11.2503i		−	0.413010i
$743$		−	30.1741i		−	1.10698i	−0.832856	−	0.553490i	$-0.813296\pi$
$743$		−	30.1741i		−	1.10698i	0.832856	−	0.553490i	$-0.186704\pi$
$744$	−3.44579			−0.126329
$745$	−5.61962	+	3.97005i	−0.205887	+	0.145451i
$746$	−32.7571			−1.19932
$747$			63.3588i			2.31818i
$748$		−	13.7282i		−	0.501954i
$749$	−13.2278			−0.483333
$750$	−10.4374	−	37.0843i	−0.381119	−	1.35413i
$751$	45.3067			1.65326			0.826632	−	0.562743i	$-0.190254\pi$
$751$	45.3067			1.65326			0.826632	+	0.562743i	$0.190254\pi$
$752$		−	4.90373i		−	0.178821i
$753$		−	56.3007i		−	2.05171i
$754$	−8.07978			−0.294248
$755$	8.38442	−	5.92327i	0.305140	−	0.215570i
$756$	48.6022			1.76765
$757$			42.3005i			1.53744i	0.639588	+	0.768718i	$0.279105\pi$
$757$			42.3005i			1.53744i	−0.639588	+	0.768718i	$0.720895\pi$
$758$		−	16.5217i		−	0.600096i
$759$	30.9915			1.12492
$760$	5.56229	+	7.87345i	0.201766	+	0.285600i
$761$	54.8028			1.98660			0.993299	−	0.115570i	$-0.0368696\pi$
$761$	54.8028			1.98660			0.993299	+	0.115570i	$0.0368696\pi$
$762$		−	23.7694i		−	0.861073i
$763$			8.33784i			0.301850i
$764$	−4.76502			−0.172392
$765$	−87.0573	−	123.230i	−3.14756	−	4.45539i
$766$	19.0949			0.689925
$767$			1.43977i			0.0519872i
$768$		−	3.44579i		−	0.124339i
$769$	−0.957560			−0.0345305			−0.0172652	−	0.999851i	$-0.505496\pi$
$769$	−0.957560			−0.0345305			−0.0172652	+	0.999851i	$0.505496\pi$
$770$	7.91785	−	5.59366i	0.285340	−	0.201582i
$771$	−28.1437			−1.01357
$772$		−	14.1048i		−	0.507644i
$773$		−	14.4365i		−	0.519246i	−0.965710	−	0.259623i	$-0.916402\pi$
$773$		−	14.4365i		−	0.519246i	0.965710	−	0.259623i	$-0.0835984\pi$
$774$	2.15676			0.0775232
$775$	−1.67072	+	4.71261i	−0.0600140	+	0.169282i
$776$	14.8069			0.531537
$777$			12.2637i			0.439959i
$778$			10.8937i			0.390558i
$779$	19.1560			0.686333
$780$	−11.2846	+	7.97216i	−0.404054	+	0.285449i
$781$	6.73529			0.241008
$782$			37.8831i			1.35470i
$783$			91.1914i			3.25891i
$784$	1.23301			0.0440362
$785$	−1.41470	−	2.00251i	−0.0504928	−	0.0714728i
$786$	20.8191			0.742592
$787$		−	7.58198i		−	0.270268i	−0.990827	−	0.135134i	$-0.956853\pi$
$787$		−	7.58198i		−	0.270268i	0.990827	−	0.135134i	$-0.0431466\pi$
$788$		−	10.6017i		−	0.377672i
$789$	−64.6191			−2.30050
$790$	16.3998	+	23.2140i	0.583479	+	0.825917i
$791$	32.7704			1.16518
$792$			16.0197i			0.569235i
$793$			6.41601i			0.227839i
$794$	−20.3049			−0.720592
$795$	29.4814	−	20.8275i	1.04560	−	0.738675i
$796$	15.7831			0.559419
$797$		−	11.9746i		−	0.424160i	−0.977252	−	0.212080i	$-0.931976\pi$
$797$		−	11.9746i		−	0.424160i	0.977252	−	0.212080i	$-0.0680238\pi$
$798$			35.6744i			1.26286i
$799$	−37.2889			−1.31919
$800$	−4.71261	−	1.67072i	−0.166616	−	0.0590688i
$801$	−82.2474			−2.90607
$802$			19.1164i			0.675025i
$803$			5.16663i			0.182326i
$804$	−44.1524			−1.55713
$805$	−21.8494	+	15.4357i	−0.770089	+	0.544038i
$806$	1.79319			0.0631626
$807$		−	69.2117i		−	2.43637i
$808$		−	6.36357i		−	0.223870i
$809$	−33.8232			−1.18916			−0.594580	−	0.804037i	$-0.702682\pi$
$809$	−33.8232			−1.18916			−0.594580	+	0.804037i	$0.702682\pi$
$810$	55.6309	+	78.7458i	1.95467	+	2.76684i
$811$	20.3341			0.714025			0.357013	−	0.934100i	$-0.383795\pi$
$811$	20.3341			0.714025			0.357013	+	0.934100i	$0.383795\pi$
$812$		−	10.8205i		−	0.379725i
$813$		−	39.1359i		−	1.37255i
$814$	−2.67560			−0.0937797
$815$	4.39418	+	6.21998i	0.153921	+	0.217876i
$816$	−26.2024			−0.917267
$817$			1.04786i			0.0366600i
$818$			5.87509i			0.205418i
$819$	−38.2115			−1.33522
$820$	−8.11487	+	5.73285i	−0.283384	+	0.200200i
$821$	18.8144			0.656629			0.328314	−	0.944569i	$-0.393519\pi$
$821$	18.8144			0.656629			0.328314	+	0.944569i	$0.393519\pi$
$822$			17.2914i			0.603107i
$823$			2.37084i			0.0826424i	0.999146	+	0.0413212i	$0.0131567\pi$
$823$			2.37084i			0.0826424i	−0.999146	+	0.0413212i	$0.986843\pi$
$824$	−7.12459			−0.248197
$825$	29.3165	+	10.3933i	1.02067	+	0.361848i
$826$	−1.92815			−0.0670891
$827$			32.8897i			1.14369i	0.820363	+	0.571843i	$0.193771\pi$
$827$			32.8897i			1.14369i	−0.820363	+	0.571843i	$0.806229\pi$
$828$		−	44.2064i		−	1.53628i
$829$	−2.93809			−0.102044			−0.0510221	−	0.998698i	$-0.516248\pi$
$829$	−2.93809			−0.102044			−0.0510221	+	0.998698i	$0.516248\pi$
$830$	13.0403	−	9.21245i	0.452634	−	0.319769i
$831$	−92.6280			−3.21323
$832$			1.79319i			0.0621678i
$833$		−	9.37605i		−	0.324861i
$834$	27.8840			0.965543
$835$	25.4755	+	36.0607i	0.881617	+	1.24793i
$836$	−7.78315			−0.269186
$837$		−	20.2387i		−	0.699550i
$838$			29.8880i			1.03246i
$839$	50.4951			1.74328			0.871642	−	0.490143i	$-0.163055\pi$
$839$	50.4951			1.74328			0.871642	+	0.490143i	$0.163055\pi$
$840$	−10.6764	−	15.1124i	−0.368369	−	0.521428i
$841$	−8.69773			−0.299922
$842$			8.55796i			0.294927i
$843$		−	97.6406i		−	3.36292i
$844$	−2.01052			−0.0692050
$845$	−17.8693	+	12.6240i	−0.614723	+	0.434279i
$846$	43.5130			1.49601
$847$		−	18.5890i		−	0.638724i
$848$		−	4.68477i		−	0.160876i
$849$	46.5492			1.59756
$850$	−12.7045	+	35.8356i	−0.435759	+	1.22915i
$851$	7.38333			0.253097
$852$		−	12.8553i		−	0.440416i
$853$		−	44.8933i		−	1.53712i	−0.639780	−	0.768558i	$-0.720974\pi$
$853$		−	44.8933i		−	1.53712i	0.639780	−	0.768558i	$-0.279026\pi$
$854$	−8.59236			−0.294024
$855$	−69.8646	+	49.3567i	−2.38932	+	1.68796i
$856$	−5.50824			−0.188268
$857$			34.7758i			1.18792i	0.804496	+	0.593959i	$0.202436\pi$
$857$			34.7758i			1.18792i	−0.804496	+	0.593959i	$0.797564\pi$
$858$		−	11.1552i		−	0.380832i
$859$	−19.4804			−0.664663			−0.332331	−	0.943163i	$-0.607835\pi$
$859$	−19.4804			−0.664663			−0.332331	+	0.943163i	$0.607835\pi$
$860$	−0.313595	−	0.443896i	−0.0106935	−	0.0151367i
$861$	−36.7683			−1.25306
$862$			23.4528i			0.798805i
$863$			13.3630i			0.454882i	0.973792	+	0.227441i	$0.0730360\pi$
$863$			13.3630i			0.454882i	−0.973792	+	0.227441i	$0.926964\pi$
$864$	20.2387			0.688533
$865$	17.4671	+	24.7248i	0.593900	+	0.840667i
$866$	−11.1382			−0.378490
$867$			140.670i			4.77739i
$868$			2.40146i			0.0815107i
$869$	−22.9478			−0.778450
$870$	28.3552	−	20.0318i	0.961330	−	0.679143i
$871$	22.9770			0.778545
$872$			3.47199i			0.117577i
$873$			131.388i			4.44682i
$874$	21.4776			0.726492
$875$	−25.8449	+	7.27407i	−0.873719	+	0.245908i
$876$	9.86129			0.333182
$877$			15.5220i			0.524142i	0.965049	+	0.262071i	$0.0844055\pi$
$877$			15.5220i			0.524142i	−0.965049	+	0.262071i	$0.915595\pi$
$878$		−	33.0537i		−	1.11551i
$879$	110.215			3.71747
$880$	3.29711	−	2.32928i	0.111145	−	0.0785200i
$881$	48.5335			1.63514			0.817568	−	0.575833i	$-0.195322\pi$
$881$	48.5335			1.63514			0.817568	+	0.575833i	$0.195322\pi$
$882$			10.9411i			0.368405i
$883$			21.0001i			0.706711i	0.935489	+	0.353356i	$0.114959\pi$
$883$			21.0001i			0.706711i	−0.935489	+	0.353356i	$0.885041\pi$
$884$	13.6358			0.458621
$885$	−3.56957	−	5.05274i	−0.119990	−	0.169846i
$886$	29.0715			0.976677
$887$			20.2441i			0.679729i	0.940474	+	0.339865i	$0.110381\pi$
$887$			20.2441i			0.679729i	−0.940474	+	0.339865i	$0.889619\pi$
$888$			5.10679i			0.171373i
$889$	−16.5655			−0.555588
$890$	11.9589	+	16.9278i	0.400862	+	0.567422i
$891$	−77.8427			−2.60783
$892$			6.97699i			0.233607i
$893$			21.1407i			0.707448i
$894$	−10.6029			−0.354613
$895$	34.4803	−	24.3590i	1.15255	−	0.814232i
$896$	−2.40146			−0.0802270
$897$			30.7828i			1.02781i
$898$			28.7466i			0.959285i
$899$	−4.50580			−0.150277
$900$	14.8250	−	41.8171i	0.494168	−	1.39390i
$901$	−35.6238			−1.18680
$902$		−	8.02180i		−	0.267097i
$903$		−	2.01128i		−	0.0669312i
$904$	13.6461			0.453862
$905$	7.53718	−	5.32473i	0.250544	−	0.177000i
$906$	15.8194			0.525564
$907$		−	51.6962i		−	1.71654i	−0.513195	−	0.858272i	$-0.671538\pi$
$907$		−	51.6962i		−	1.71654i	0.513195	−	0.858272i	$-0.328462\pi$
$908$		−	0.778596i		−	0.0258386i
$909$	56.4668			1.87288
$910$	5.55600	+	7.86453i	0.184179	+	0.260707i
$911$	56.5730			1.87435			0.937174	−	0.348862i	$-0.113432\pi$
$911$	56.5730			1.87435			0.937174	+	0.348862i	$0.113432\pi$
$912$			14.8553i			0.491909i
$913$			12.8907i			0.426620i
$914$	−14.2919			−0.472735
$915$	−15.9069	−	22.5163i	−0.525867	−	0.744367i
$916$	−21.3368			−0.704988
$917$		−	14.5093i		−	0.479140i
$918$		−	153.898i		−	5.07941i
$919$	34.2200			1.12881			0.564406	−	0.825497i	$-0.309105\pi$
$919$	34.2200			1.12881			0.564406	+	0.825497i	$0.309105\pi$
$920$	−9.09838	+	6.42766i	−0.299965	+	0.211914i
$921$	7.14956			0.235586
$922$			28.3156i			0.932526i
$923$			6.68993i			0.220202i
$924$	14.9391			0.491460
$925$	6.98427	+	2.47607i	0.229641	+	0.0814127i
$926$	−27.2987			−0.897090
$927$		−	63.2196i		−	2.07641i
$928$		−	4.50580i		−	0.147910i
$929$	−1.67344			−0.0549039			−0.0274520	−	0.999623i	$-0.508739\pi$
$929$	−1.67344			−0.0549039			−0.0274520	+	0.999623i	$0.508739\pi$
$930$	−6.29303	+	4.44579i	−0.206357	+	0.145783i
$931$	−5.31571			−0.174215
$932$		−	12.2209i		−	0.400307i
$933$			56.7216i			1.85698i
$934$	−25.3422			−0.829222
$935$	−17.7123	−	25.0718i	−0.579254	−	0.819936i
$936$	−15.9118			−0.520094
$937$		−	0.492515i		−	0.0160898i	−0.999968	−	0.00804488i	$-0.997439\pi$
$937$		−	0.492515i		−	0.0160898i	0.999968	−	0.00804488i	$-0.00256079\pi$
$938$			30.7709i			1.00470i
$939$	−112.363			−3.66682
$940$	−6.32684	−	8.95567i	−0.206359	−	0.292102i
$941$	−31.0467			−1.01209			−0.506047	−	0.862506i	$-0.668894\pi$
$941$	−31.0467			−1.01209			−0.506047	+	0.862506i	$0.668894\pi$
$942$		−	3.77827i		−	0.123103i
$943$			22.1362i			0.720854i
$944$	−0.802911			−0.0261325
$945$	88.7621	−	62.7070i	2.88743	−	2.03986i
$946$	0.438805			0.0142668
$947$			19.9076i			0.646910i	0.946244	+	0.323455i	$0.104844\pi$
$947$			19.9076i			0.646910i	−0.946244	+	0.323455i	$0.895156\pi$
$948$			43.7993i			1.42254i
$949$	−5.13183			−0.166586
$950$	20.3168	+	7.20273i	0.659164	+	0.233687i
$951$	29.6938			0.962888
$952$			18.2611i			0.591846i
$953$			3.40742i			0.110377i	0.998476	+	0.0551886i	$0.0175760\pi$
$953$			3.40742i			0.110377i	−0.998476	+	0.0551886i	$0.982424\pi$
$954$	41.5700			1.34588
$955$	−8.70234	+	6.14788i	−0.281601	+	0.198941i
$956$	6.11298			0.197708
$957$			28.0300i			0.906080i
$958$			1.77827i			0.0574532i
$959$	12.0508			0.389141
$960$	−4.44579	−	6.29303i	−0.143487	−	0.203107i
$961$	1.00000			0.0322581
$962$		−	2.65758i		−	0.0856839i
$963$		−	48.8771i		−	1.57504i
$964$	−3.87181			−0.124703
$965$	−18.1982	−	25.7596i	−0.585820	−	0.829231i
$966$	−41.2245			−1.32638
$967$		−	22.1065i		−	0.710896i	−0.934696	−	0.355448i	$-0.884328\pi$
$967$		−	22.1065i		−	0.710896i	0.934696	−	0.355448i	$-0.115672\pi$
$968$		−	7.74071i		−	0.248796i
$969$	112.963			3.62888
$970$	27.0418	−	19.1040i	0.868260	−	0.613393i
$971$	55.6954			1.78735			0.893676	−	0.448713i	$-0.148118\pi$
$971$	55.6954			1.78735			0.893676	+	0.448713i	$0.148118\pi$
$972$			87.8586i			2.81807i
$973$		−	19.4330i		−	0.622995i
$974$	22.9498			0.735361
$975$	−10.3233	+	29.1190i	−0.330611	+	0.932556i
$976$	−3.57798			−0.114528
$977$			24.8385i			0.794654i	0.917677	+	0.397327i	$0.130062\pi$
$977$			24.8385i			0.794654i	−0.917677	+	0.397327i	$0.869938\pi$
$978$			11.7356i			0.375264i
$979$	−16.7337			−0.534811
$980$	2.25185	−	1.59084i	0.0719326	−	0.0508177i
$981$	−30.8086			−0.983641
$982$			22.9557i			0.732545i
$983$			51.0142i			1.62710i	0.581495	+	0.813550i	$0.302468\pi$
$983$			51.0142i			1.62710i	−0.581495	+	0.813550i	$0.697532\pi$
$984$	−15.3108			−0.488091
$985$	−13.6785	−	19.3619i	−0.435832	−	0.616922i
$986$	−34.2630			−1.09116
$987$		−	40.5779i		−	1.29161i
$988$		−	7.73074i		−	0.245947i
$989$	−1.21088			−0.0385039
$990$	20.6688	+	29.2567i	0.656896	+	0.929839i
$991$	−35.5296			−1.12864			−0.564318	−	0.825558i	$-0.690861\pi$
$991$	−35.5296			−1.12864			−0.564318	+	0.825558i	$0.690861\pi$
$992$			1.00000i			0.0317500i
$993$			95.3165i			3.02478i
$994$	−8.95920			−0.284168
$995$	28.8247	−	20.3636i	0.913805	−	0.645568i
$996$	24.6039			0.779603
$997$		−	22.7086i		−	0.719189i	−0.933109	−	0.359594i	$-0.882915\pi$
$997$		−	22.7086i		−	0.719189i	0.933109	−	0.359594i	$-0.117085\pi$
$998$			1.66588i			0.0527326i
$999$	−29.9945			−0.948983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.b.a.249.1	✓	8
3.2	odd	2		2790.2.d.m.559.7		8
4.3	odd	2		2480.2.d.d.1489.8		8
5.2	odd	4		1550.2.a.p.1.1		4
5.3	odd	4		1550.2.a.o.1.4		4
5.4	even	2	inner	310.2.b.a.249.8	yes	8
15.14	odd	2		2790.2.d.m.559.3		8
20.19	odd	2		2480.2.d.d.1489.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.b.a.249.1	✓	8	1.1	even	1	trivial
310.2.b.a.249.8	yes	8	5.4	even	2	inner
1550.2.a.o.1.4		4	5.3	odd	4
1550.2.a.p.1.1		4	5.2	odd	4
2480.2.d.d.1489.1		8	20.19	odd	2
2480.2.d.d.1489.8		8	4.3	odd	2
2790.2.d.m.559.3		8	15.14	odd	2
2790.2.d.m.559.7		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -3.44579i q^{3} -1.00000 q^{4} +(-1.82630 + 1.29021i) q^{5} -3.44579 q^{6} +2.40146i q^{7} +1.00000i q^{8} -8.87345 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -3.44579i q^{3} -1.00000 q^{4} +(-1.82630 + 1.29021i) q^{5} -3.44579 q^{6} +2.40146i q^{7} +1.00000i q^{8} -8.87345 q^{9} +(1.29021 + 1.82630i) q^{10} -1.80535 q^{11} +3.44579i q^{12} -1.79319i q^{13} +2.40146 q^{14} +(4.44579 + 6.29303i) q^{15} +1.00000 q^{16} -7.60418i q^{17} +8.87345i q^{18} -4.31116 q^{19} +(1.82630 - 1.29021i) q^{20} +8.27490 q^{21} +1.80535i q^{22} -4.98187i q^{23} +3.44579 q^{24} +(1.67072 - 4.71261i) q^{25} -1.79319 q^{26} +20.2387i q^{27} -2.40146i q^{28} +4.50580 q^{29} +(6.29303 - 4.44579i) q^{30} -1.00000 q^{31} -1.00000i q^{32} +6.22085i q^{33} -7.60418 q^{34} +(-3.09838 - 4.38577i) q^{35} +8.87345 q^{36} +1.48204i q^{37} +4.31116i q^{38} -6.17896 q^{39} +(-1.29021 - 1.82630i) q^{40} -4.44335 q^{41} -8.27490i q^{42} -0.243058i q^{43} +1.80535 q^{44} +(16.2055 - 11.4486i) q^{45} -4.98187 q^{46} -4.90373i q^{47} -3.44579i q^{48} +1.23301 q^{49} +(-4.71261 - 1.67072i) q^{50} -26.2024 q^{51} +1.79319i q^{52} -4.68477i q^{53} +20.2387 q^{54} +(3.29711 - 2.32928i) q^{55} -2.40146 q^{56} +14.8553i q^{57} -4.50580i q^{58} -0.802911 q^{59} +(-4.44579 - 6.29303i) q^{60} -3.57798 q^{61} +1.00000i q^{62} -21.3092i q^{63} -1.00000 q^{64} +(2.31360 + 3.27490i) q^{65} +6.22085 q^{66} +12.8134i q^{67} +7.60418i q^{68} -17.1665 q^{69} +(-4.38577 + 3.09838i) q^{70} -3.73074 q^{71} -8.87345i q^{72} -2.86184i q^{73} +1.48204 q^{74} +(-16.2387 - 5.75694i) q^{75} +4.31116 q^{76} -4.33547i q^{77} +6.17896i q^{78} +12.7110 q^{79} +(-1.82630 + 1.29021i) q^{80} +43.1177 q^{81} +4.44335i q^{82} -7.14027i q^{83} -8.27490 q^{84} +(9.81099 + 13.8875i) q^{85} -0.243058 q^{86} -15.5260i q^{87} -1.80535i q^{88} +9.26894 q^{89} +(-11.4486 - 16.2055i) q^{90} +4.30627 q^{91} +4.98187i q^{92} +3.44579i q^{93} -4.90373 q^{94} +(7.87345 - 5.56229i) q^{95} -3.44579 q^{96} -14.8069i q^{97} -1.23301i q^{98} +16.0197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} + 2 q^{10} - 16 q^{11} + 12 q^{14} + 16 q^{15} + 8 q^{16} - 12 q^{19} + 2 q^{20} - 4 q^{21} + 8 q^{24} + 12 q^{25} - 20 q^{26} + 12 q^{29} + 4 q^{30} - 8 q^{31} + 8 q^{34} + 20 q^{35} + 8 q^{36} - 40 q^{39} - 2 q^{40} + 16 q^{44} + 30 q^{45} - 16 q^{46} - 32 q^{49} - 8 q^{50} - 44 q^{51} + 44 q^{54} + 36 q^{55} - 12 q^{56} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 8 q^{64} + 12 q^{65} + 12 q^{66} - 28 q^{69} - 20 q^{70} - 24 q^{71} + 40 q^{74} - 12 q^{75} + 12 q^{76} + 32 q^{79} - 2 q^{80} + 88 q^{81} + 4 q^{84} + 4 q^{85} - 44 q^{86} - 24 q^{89} - 34 q^{90} - 20 q^{91} + 4 q^{94} - 8 q^{96} + 20 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9 + 2 * q^10 - 16 * q^11 + 12 * q^14 + 16 * q^15 + 8 * q^16 - 12 * q^19 + 2 * q^20 - 4 * q^21 + 8 * q^24 + 12 * q^25 - 20 * q^26 + 12 * q^29 + 4 * q^30 - 8 * q^31 + 8 * q^34 + 20 * q^35 + 8 * q^36 - 40 * q^39 - 2 * q^40 + 16 * q^44 + 30 * q^45 - 16 * q^46 - 32 * q^49 - 8 * q^50 - 44 * q^51 + 44 * q^54 + 36 * q^55 - 12 * q^56 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 8 * q^64 + 12 * q^65 + 12 * q^66 - 28 * q^69 - 20 * q^70 - 24 * q^71 + 40 * q^74 - 12 * q^75 + 12 * q^76 + 32 * q^79 - 2 * q^80 + 88 * q^81 + 4 * q^84 + 4 * q^85 - 44 * q^86 - 24 * q^89 - 34 * q^90 - 20 * q^91 + 4 * q^94 - 8 * q^96 + 20 * q^99

Introduction

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