# Properties

 Label 725.2.j.a.418.1 Level $725$ Weight $2$ Character 725.418 Analytic conductor $5.789$ Analytic rank $0$ Dimension $4$ Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(307,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("725.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$725 = 5^{2} \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 725.j (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$5.78915414654$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(i, \sqrt{5})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 3x^{2} + 1$$ x^4 + 3*x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 418.1 Root $$-1.61803i$$ of defining polynomial Character $$\chi$$ $$=$$ 725.418 Dual form 725.2.j.a.307.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-2.23607 q^{2} +3.00000 q^{4} +(2.23607 - 2.23607i) q^{7} -2.23607 q^{8} +3.00000 q^{9} +O(q^{10})$$ $$q-2.23607 q^{2} +3.00000 q^{4} +(2.23607 - 2.23607i) q^{7} -2.23607 q^{8} +3.00000 q^{9} +(4.00000 + 4.00000i) q^{11} +(-4.47214 + 4.47214i) q^{13} +(-5.00000 + 5.00000i) q^{14} -1.00000 q^{16} +4.47214 q^{17} -6.70820 q^{18} +(2.00000 - 2.00000i) q^{19} +(-8.94427 - 8.94427i) q^{22} +(-2.23607 - 2.23607i) q^{23} +(10.0000 - 10.0000i) q^{26} +(6.70820 - 6.70820i) q^{28} +(-2.00000 + 5.00000i) q^{29} +(-4.00000 - 4.00000i) q^{31} +6.70820 q^{32} -10.0000 q^{34} +9.00000 q^{36} +4.47214i q^{37} +(-4.47214 + 4.47214i) q^{38} +(1.00000 - 1.00000i) q^{41} +4.47214i q^{43} +(12.0000 + 12.0000i) q^{44} +(5.00000 + 5.00000i) q^{46} -4.47214i q^{47} -3.00000i q^{49} +(-13.4164 + 13.4164i) q^{52} +(8.94427 + 8.94427i) q^{53} +(-5.00000 + 5.00000i) q^{56} +(4.47214 - 11.1803i) q^{58} +(-9.00000 - 9.00000i) q^{61} +(8.94427 + 8.94427i) q^{62} +(6.70820 - 6.70820i) q^{63} -13.0000 q^{64} +(2.23607 + 2.23607i) q^{67} +13.4164 q^{68} +12.0000i q^{71} -6.70820 q^{72} +4.47214 q^{73} -10.0000i q^{74} +(6.00000 - 6.00000i) q^{76} +17.8885 q^{77} +(2.00000 - 2.00000i) q^{79} +9.00000 q^{81} +(-2.23607 + 2.23607i) q^{82} +(6.70820 + 6.70820i) q^{83} -10.0000i q^{86} +(-8.94427 - 8.94427i) q^{88} +(7.00000 - 7.00000i) q^{89} +20.0000i q^{91} +(-6.70820 - 6.70820i) q^{92} +10.0000i q^{94} -4.47214i q^{97} +6.70820i q^{98} +(12.0000 + 12.0000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 12 q^{4} + 12 q^{9}+O(q^{10})$$ 4 * q + 12 * q^4 + 12 * q^9 $$4 q + 12 q^{4} + 12 q^{9} + 16 q^{11} - 20 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 8 q^{29} - 16 q^{31} - 40 q^{34} + 36 q^{36} + 4 q^{41} + 48 q^{44} + 20 q^{46} - 20 q^{56} - 36 q^{61} - 52 q^{64} + 24 q^{76} + 8 q^{79} + 36 q^{81} + 28 q^{89} + 48 q^{99}+O(q^{100})$$ 4 * q + 12 * q^4 + 12 * q^9 + 16 * q^11 - 20 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 8 * q^29 - 16 * q^31 - 40 * q^34 + 36 * q^36 + 4 * q^41 + 48 * q^44 + 20 * q^46 - 20 * q^56 - 36 * q^61 - 52 * q^64 + 24 * q^76 + 8 * q^79 + 36 * q^81 + 28 * q^89 + 48 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$$.

 $$n$$ $$176$$ $$552$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$e\left(\frac{3}{4}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.23607 −1.58114 −0.790569 0.612372i $$-0.790215\pi$$
−0.790569 + 0.612372i $$0.790215\pi$$
$$3$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$4$$ 3.00000 1.50000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.23607 2.23607i 0.845154 0.845154i −0.144370 0.989524i $$-0.546115\pi$$
0.989524 + 0.144370i $$0.0461154\pi$$
$$8$$ −2.23607 −0.790569
$$9$$ 3.00000 1.00000
$$10$$ 0 0
$$11$$ 4.00000 + 4.00000i 1.20605 + 1.20605i 0.972297 + 0.233748i $$0.0750991\pi$$
0.233748 + 0.972297i $$0.424901\pi$$
$$12$$ 0 0
$$13$$ −4.47214 + 4.47214i −1.24035 + 1.24035i −0.280491 + 0.959857i $$0.590497\pi$$
−0.959857 + 0.280491i $$0.909503\pi$$
$$14$$ −5.00000 + 5.00000i −1.33631 + 1.33631i
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ 4.47214 1.08465 0.542326 0.840168i $$-0.317544\pi$$
0.542326 + 0.840168i $$0.317544\pi$$
$$18$$ −6.70820 −1.58114
$$19$$ 2.00000 2.00000i 0.458831 0.458831i −0.439440 0.898272i $$-0.644823\pi$$
0.898272 + 0.439440i $$0.144823\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −8.94427 8.94427i −1.90693 1.90693i
$$23$$ −2.23607 2.23607i −0.466252 0.466252i 0.434446 0.900698i $$-0.356944\pi$$
−0.900698 + 0.434446i $$0.856944\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 10.0000 10.0000i 1.96116 1.96116i
$$27$$ 0 0
$$28$$ 6.70820 6.70820i 1.26773 1.26773i
$$29$$ −2.00000 + 5.00000i −0.371391 + 0.928477i
$$30$$ 0 0
$$31$$ −4.00000 4.00000i −0.718421 0.718421i 0.249861 0.968282i $$-0.419615\pi$$
−0.968282 + 0.249861i $$0.919615\pi$$
$$32$$ 6.70820 1.18585
$$33$$ 0 0
$$34$$ −10.0000 −1.71499
$$35$$ 0 0
$$36$$ 9.00000 1.50000
$$37$$ 4.47214i 0.735215i 0.929981 + 0.367607i $$0.119823\pi$$
−0.929981 + 0.367607i $$0.880177\pi$$
$$38$$ −4.47214 + 4.47214i −0.725476 + 0.725476i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 1.00000 1.00000i 0.156174 0.156174i −0.624695 0.780869i $$-0.714777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ 0 0
$$43$$ 4.47214i 0.681994i 0.940064 + 0.340997i $$0.110765\pi$$
−0.940064 + 0.340997i $$0.889235\pi$$
$$44$$ 12.0000 + 12.0000i 1.80907 + 1.80907i
$$45$$ 0 0
$$46$$ 5.00000 + 5.00000i 0.737210 + 0.737210i
$$47$$ 4.47214i 0.652328i −0.945313 0.326164i $$-0.894244\pi$$
0.945313 0.326164i $$-0.105756\pi$$
$$48$$ 0 0
$$49$$ 3.00000i 0.428571i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −13.4164 + 13.4164i −1.86052 + 1.86052i
$$53$$ 8.94427 + 8.94427i 1.22859 + 1.22859i 0.964497 + 0.264093i $$0.0850726\pi$$
0.264093 + 0.964497i $$0.414927\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −5.00000 + 5.00000i −0.668153 + 0.668153i
$$57$$ 0 0
$$58$$ 4.47214 11.1803i 0.587220 1.46805i
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ −9.00000 9.00000i −1.15233 1.15233i −0.986084 0.166248i $$-0.946835\pi$$
−0.166248 0.986084i $$-0.553165\pi$$
$$62$$ 8.94427 + 8.94427i 1.13592 + 1.13592i
$$63$$ 6.70820 6.70820i 0.845154 0.845154i
$$64$$ −13.0000 −1.62500
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 2.23607 + 2.23607i 0.273179 + 0.273179i 0.830379 0.557199i $$-0.188124\pi$$
−0.557199 + 0.830379i $$0.688124\pi$$
$$68$$ 13.4164 1.62698
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.0000i 1.42414i 0.702109 + 0.712069i $$0.252242\pi$$
−0.702109 + 0.712069i $$0.747758\pi$$
$$72$$ −6.70820 −0.790569
$$73$$ 4.47214 0.523424 0.261712 0.965146i $$-0.415713\pi$$
0.261712 + 0.965146i $$0.415713\pi$$
$$74$$ 10.0000i 1.16248i
$$75$$ 0 0
$$76$$ 6.00000 6.00000i 0.688247 0.688247i
$$77$$ 17.8885 2.03859
$$78$$ 0 0
$$79$$ 2.00000 2.00000i 0.225018 0.225018i −0.585590 0.810607i $$-0.699137\pi$$
0.810607 + 0.585590i $$0.199137\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ −2.23607 + 2.23607i −0.246932 + 0.246932i
$$83$$ 6.70820 + 6.70820i 0.736321 + 0.736321i 0.971864 0.235543i $$-0.0756868\pi$$
−0.235543 + 0.971864i $$0.575687\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 10.0000i 1.07833i
$$87$$ 0 0
$$88$$ −8.94427 8.94427i −0.953463 0.953463i
$$89$$ 7.00000 7.00000i 0.741999 0.741999i −0.230964 0.972962i $$-0.574188\pi$$
0.972962 + 0.230964i $$0.0741879\pi$$
$$90$$ 0 0
$$91$$ 20.0000i 2.09657i
$$92$$ −6.70820 6.70820i −0.699379 0.699379i
$$93$$ 0 0
$$94$$ 10.0000i 1.03142i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 4.47214i 0.454077i −0.973886 0.227038i $$-0.927096\pi$$
0.973886 0.227038i $$-0.0729043\pi$$
$$98$$ 6.70820i 0.677631i
$$99$$ 12.0000 + 12.0000i 1.20605 + 1.20605i
$$100$$ 0 0
$$101$$ −1.00000 1.00000i −0.0995037 0.0995037i 0.655602 0.755106i $$-0.272415\pi$$
−0.755106 + 0.655602i $$0.772415\pi$$
$$102$$ 0 0
$$103$$ −6.70820 6.70820i −0.660979 0.660979i 0.294632 0.955611i $$-0.404803\pi$$
−0.955611 + 0.294632i $$0.904803\pi$$
$$104$$ 10.0000 10.0000i 0.980581 0.980581i
$$105$$ 0 0
$$106$$ −20.0000 20.0000i −1.94257 1.94257i
$$107$$ 6.70820 6.70820i 0.648507 0.648507i −0.304125 0.952632i $$-0.598364\pi$$
0.952632 + 0.304125i $$0.0983642\pi$$
$$108$$ 0 0
$$109$$ 10.0000 0.957826 0.478913 0.877862i $$-0.341031\pi$$
0.478913 + 0.877862i $$0.341031\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −2.23607 + 2.23607i −0.211289 + 0.211289i
$$113$$ 4.47214 0.420703 0.210352 0.977626i $$-0.432539\pi$$
0.210352 + 0.977626i $$0.432539\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −6.00000 + 15.0000i −0.557086 + 1.39272i
$$117$$ −13.4164 + 13.4164i −1.24035 + 1.24035i
$$118$$ 0 0
$$119$$ 10.0000 10.0000i 0.916698 0.916698i
$$120$$ 0 0
$$121$$ 21.0000i 1.90909i
$$122$$ 20.1246 + 20.1246i 1.82200 + 1.82200i
$$123$$ 0 0
$$124$$ −12.0000 12.0000i −1.07763 1.07763i
$$125$$ 0 0
$$126$$ −15.0000 + 15.0000i −1.33631 + 1.33631i
$$127$$ 4.47214 0.396838 0.198419 0.980117i $$-0.436419\pi$$
0.198419 + 0.980117i $$0.436419\pi$$
$$128$$ 15.6525 1.38350
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 14.0000 14.0000i 1.22319 1.22319i 0.256693 0.966493i $$-0.417367\pi$$
0.966493 0.256693i $$-0.0826328\pi$$
$$132$$ 0 0
$$133$$ 8.94427i 0.775567i
$$134$$ −5.00000 5.00000i −0.431934 0.431934i
$$135$$ 0 0
$$136$$ −10.0000 −0.857493
$$137$$ −13.4164 −1.14624 −0.573121 0.819471i $$-0.694267\pi$$
−0.573121 + 0.819471i $$0.694267\pi$$
$$138$$ 0 0
$$139$$ 4.00000i 0.339276i 0.985506 + 0.169638i $$0.0542598\pi$$
−0.985506 + 0.169638i $$0.945740\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 26.8328i 2.25176i
$$143$$ −35.7771 −2.99183
$$144$$ −3.00000 −0.250000
$$145$$ 0 0
$$146$$ −10.0000 −0.827606
$$147$$ 0 0
$$148$$ 13.4164i 1.10282i
$$149$$ −20.0000 −1.63846 −0.819232 0.573462i $$-0.805600\pi$$
−0.819232 + 0.573462i $$0.805600\pi$$
$$150$$ 0 0
$$151$$ 12.0000i 0.976546i −0.872691 0.488273i $$-0.837627\pi$$
0.872691 0.488273i $$-0.162373\pi$$
$$152$$ −4.47214 + 4.47214i −0.362738 + 0.362738i
$$153$$ 13.4164 1.08465
$$154$$ −40.0000 −3.22329
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 13.4164i 1.07075i −0.844616 0.535373i $$-0.820171\pi$$
0.844616 0.535373i $$-0.179829\pi$$
$$158$$ −4.47214 + 4.47214i −0.355784 + 0.355784i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −10.0000 −0.788110
$$162$$ −20.1246 −1.58114
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 3.00000 3.00000i 0.234261 0.234261i
$$165$$ 0 0
$$166$$ −15.0000 15.0000i −1.16423 1.16423i
$$167$$ −6.70820 6.70820i −0.519096 0.519096i 0.398202 0.917298i $$-0.369634\pi$$
−0.917298 + 0.398202i $$0.869634\pi$$
$$168$$ 0 0
$$169$$ 27.0000i 2.07692i
$$170$$ 0 0
$$171$$ 6.00000 6.00000i 0.458831 0.458831i
$$172$$ 13.4164i 1.02299i
$$173$$ −13.4164 + 13.4164i −1.02003 + 1.02003i −0.0202354 + 0.999795i $$0.506442\pi$$
−0.999795 + 0.0202354i $$0.993558\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −4.00000 4.00000i −0.301511 0.301511i
$$177$$ 0 0
$$178$$ −15.6525 + 15.6525i −1.17320 + 1.17320i
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ −20.0000 −1.48659 −0.743294 0.668965i $$-0.766738\pi$$
−0.743294 + 0.668965i $$0.766738\pi$$
$$182$$ 44.7214i 3.31497i
$$183$$ 0 0
$$184$$ 5.00000 + 5.00000i 0.368605 + 0.368605i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 17.8885 + 17.8885i 1.30814 + 1.30814i
$$188$$ 13.4164i 0.978492i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 6.00000 + 6.00000i 0.434145 + 0.434145i 0.890036 0.455891i $$-0.150679\pi$$
−0.455891 + 0.890036i $$0.650679\pi$$
$$192$$ 0 0
$$193$$ 4.47214i 0.321911i −0.986962 0.160956i $$-0.948542\pi$$
0.986962 0.160956i $$-0.0514576\pi$$
$$194$$ 10.0000i 0.717958i
$$195$$ 0 0
$$196$$ 9.00000i 0.642857i
$$197$$ 13.4164 13.4164i 0.955879 0.955879i −0.0431875 0.999067i $$-0.513751\pi$$
0.999067 + 0.0431875i $$0.0137513\pi$$
$$198$$ −26.8328 26.8328i −1.90693 1.90693i
$$199$$ 20.0000i 1.41776i 0.705328 + 0.708881i $$0.250800\pi$$
−0.705328 + 0.708881i $$0.749200\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 2.23607 + 2.23607i 0.157329 + 0.157329i
$$203$$ 6.70820 + 15.6525i 0.470824 + 1.09859i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 15.0000 + 15.0000i 1.04510 + 1.04510i
$$207$$ −6.70820 6.70820i −0.466252 0.466252i
$$208$$ 4.47214 4.47214i 0.310087 0.310087i
$$209$$ 16.0000 1.10674
$$210$$ 0 0
$$211$$ 16.0000 16.0000i 1.10149 1.10149i 0.107254 0.994232i $$-0.465794\pi$$
0.994232 0.107254i $$-0.0342057\pi$$
$$212$$ 26.8328 + 26.8328i 1.84289 + 1.84289i
$$213$$ 0 0
$$214$$ −15.0000 + 15.0000i −1.02538 + 1.02538i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −17.8885 −1.21435
$$218$$ −22.3607 −1.51446
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −20.0000 + 20.0000i −1.34535 + 1.34535i
$$222$$ 0 0
$$223$$ 11.1803 + 11.1803i 0.748691 + 0.748691i 0.974233 0.225542i $$-0.0724154\pi$$
−0.225542 + 0.974233i $$0.572415\pi$$
$$224$$ 15.0000 15.0000i 1.00223 1.00223i
$$225$$ 0 0
$$226$$ −10.0000 −0.665190
$$227$$ −6.70820 + 6.70820i −0.445239 + 0.445239i −0.893768 0.448529i $$-0.851948\pi$$
0.448529 + 0.893768i $$0.351948\pi$$
$$228$$ 0 0
$$229$$ 3.00000 + 3.00000i 0.198246 + 0.198246i 0.799248 0.601002i $$-0.205232\pi$$
−0.601002 + 0.799248i $$0.705232\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 4.47214 11.1803i 0.293610 0.734025i
$$233$$ −8.94427 8.94427i −0.585959 0.585959i 0.350576 0.936534i $$-0.385986\pi$$
−0.936534 + 0.350576i $$0.885986\pi$$
$$234$$ 30.0000 30.0000i 1.96116 1.96116i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ −22.3607 + 22.3607i −1.44943 + 1.44943i
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 8.00000i 0.515325i 0.966235 + 0.257663i $$0.0829523\pi$$
−0.966235 + 0.257663i $$0.917048\pi$$
$$242$$ 46.9574i 3.01854i
$$243$$ 0 0
$$244$$ −27.0000 27.0000i −1.72850 1.72850i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 17.8885i 1.13822i
$$248$$ 8.94427 + 8.94427i 0.567962 + 0.567962i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 4.00000 + 4.00000i 0.252478 + 0.252478i 0.821986 0.569508i $$-0.192866\pi$$
−0.569508 + 0.821986i $$0.692866\pi$$
$$252$$ 20.1246 20.1246i 1.26773 1.26773i
$$253$$ 17.8885i 1.12464i
$$254$$ −10.0000 −0.627456
$$255$$ 0 0
$$256$$ −9.00000 −0.562500
$$257$$ −4.47214 + 4.47214i −0.278964 + 0.278964i −0.832695 0.553731i $$-0.813203\pi$$
0.553731 + 0.832695i $$0.313203\pi$$
$$258$$ 0 0
$$259$$ 10.0000 + 10.0000i 0.621370 + 0.621370i
$$260$$ 0 0
$$261$$ −6.00000 + 15.0000i −0.371391 + 0.928477i
$$262$$ −31.3050 + 31.3050i −1.93403 + 1.93403i
$$263$$ 8.94427i 0.551527i −0.961225 0.275764i $$-0.911069\pi$$
0.961225 0.275764i $$-0.0889307\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 20.0000i 1.22628i
$$267$$ 0 0
$$268$$ 6.70820 + 6.70820i 0.409769 + 0.409769i
$$269$$ 7.00000 + 7.00000i 0.426798 + 0.426798i 0.887536 0.460738i $$-0.152415\pi$$
−0.460738 + 0.887536i $$0.652415\pi$$
$$270$$ 0 0
$$271$$ 14.0000 14.0000i 0.850439 0.850439i −0.139748 0.990187i $$-0.544629\pi$$
0.990187 + 0.139748i $$0.0446292\pi$$
$$272$$ −4.47214 −0.271163
$$273$$ 0 0
$$274$$ 30.0000 1.81237
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −8.94427 + 8.94427i −0.537409 + 0.537409i −0.922767 0.385358i $$-0.874078\pi$$
0.385358 + 0.922767i $$0.374078\pi$$
$$278$$ 8.94427i 0.536442i
$$279$$ −12.0000 12.0000i −0.718421 0.718421i
$$280$$ 0 0
$$281$$ −12.0000 −0.715860 −0.357930 0.933748i $$-0.616517\pi$$
−0.357930 + 0.933748i $$0.616517\pi$$
$$282$$ 0 0
$$283$$ 11.1803 11.1803i 0.664602 0.664602i −0.291859 0.956461i $$-0.594274\pi$$
0.956461 + 0.291859i $$0.0942738\pi$$
$$284$$ 36.0000i 2.13621i
$$285$$ 0 0
$$286$$ 80.0000 4.73050
$$287$$ 4.47214i 0.263982i
$$288$$ 20.1246 1.18585
$$289$$ 3.00000 0.176471
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 13.4164 0.785136
$$293$$ 4.47214i 0.261265i −0.991431 0.130632i $$-0.958299\pi$$
0.991431 0.130632i $$-0.0417008\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 10.0000i 0.581238i
$$297$$ 0 0
$$298$$ 44.7214 2.59064
$$299$$ 20.0000 1.15663
$$300$$ 0 0
$$301$$ 10.0000 + 10.0000i 0.576390 + 0.576390i
$$302$$ 26.8328i 1.54406i
$$303$$ 0 0
$$304$$ −2.00000 + 2.00000i −0.114708 + 0.114708i
$$305$$ 0 0
$$306$$ −30.0000 −1.71499
$$307$$ −31.3050 −1.78667 −0.893334 0.449393i $$-0.851640\pi$$
−0.893334 + 0.449393i $$0.851640\pi$$
$$308$$ 53.6656 3.05788
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −4.00000 4.00000i −0.226819 0.226819i 0.584543 0.811363i $$-0.301274\pi$$
−0.811363 + 0.584543i $$0.801274\pi$$
$$312$$ 0 0
$$313$$ −22.3607 22.3607i −1.26390 1.26390i −0.949187 0.314714i $$-0.898091\pi$$
−0.314714 0.949187i $$-0.601909\pi$$
$$314$$ 30.0000i 1.69300i
$$315$$ 0 0
$$316$$ 6.00000 6.00000i 0.337526 0.337526i
$$317$$ 31.3050i 1.75826i 0.476581 + 0.879131i $$0.341876\pi$$
−0.476581 + 0.879131i $$0.658124\pi$$
$$318$$ 0 0
$$319$$ −28.0000 + 12.0000i −1.56770 + 0.671871i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 22.3607 1.24611
$$323$$ 8.94427 8.94427i 0.497673 0.497673i
$$324$$ 27.0000 1.50000
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ −2.23607 + 2.23607i −0.123466 + 0.123466i
$$329$$ −10.0000 10.0000i −0.551318 0.551318i
$$330$$ 0 0
$$331$$ −6.00000 + 6.00000i −0.329790 + 0.329790i −0.852506 0.522717i $$-0.824919\pi$$
0.522717 + 0.852506i $$0.324919\pi$$
$$332$$ 20.1246 + 20.1246i 1.10448 + 1.10448i
$$333$$ 13.4164i 0.735215i
$$334$$ 15.0000 + 15.0000i 0.820763 + 0.820763i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 13.4164i 0.730838i −0.930843 0.365419i $$-0.880926\pi$$
0.930843 0.365419i $$-0.119074\pi$$
$$338$$ 60.3738i 3.28390i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 32.0000i 1.73290i
$$342$$ −13.4164 + 13.4164i −0.725476 + 0.725476i
$$343$$ 8.94427 + 8.94427i 0.482945 + 0.482945i
$$344$$ 10.0000i 0.539164i
$$345$$ 0 0
$$346$$ 30.0000 30.0000i 1.61281 1.61281i
$$347$$ −15.6525 15.6525i −0.840269 0.840269i 0.148625 0.988894i $$-0.452515\pi$$
−0.988894 + 0.148625i $$0.952515\pi$$
$$348$$ 0 0
$$349$$ 30.0000i 1.60586i −0.596071 0.802932i $$-0.703272\pi$$
0.596071 0.802932i $$-0.296728\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 26.8328 + 26.8328i 1.43019 + 1.43019i
$$353$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 21.0000 21.0000i 1.11300 1.11300i
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −12.0000 + 12.0000i −0.633336 + 0.633336i −0.948903 0.315567i $$-0.897805\pi$$
0.315567 + 0.948903i $$0.397805\pi$$
$$360$$ 0 0
$$361$$ 11.0000i 0.578947i
$$362$$ 44.7214 2.35050
$$363$$ 0 0
$$364$$ 60.0000i 3.14485i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 26.8328 1.40066 0.700331 0.713818i $$-0.253036\pi$$
0.700331 + 0.713818i $$0.253036\pi$$
$$368$$ 2.23607 + 2.23607i 0.116563 + 0.116563i
$$369$$ 3.00000 3.00000i 0.156174 0.156174i
$$370$$ 0 0
$$371$$ 40.0000 2.07670
$$372$$ 0 0
$$373$$ −13.4164 13.4164i −0.694675 0.694675i 0.268582 0.963257i $$-0.413445\pi$$
−0.963257 + 0.268582i $$0.913445\pi$$
$$374$$ −40.0000 40.0000i −2.06835 2.06835i
$$375$$ 0 0
$$376$$ 10.0000i 0.515711i
$$377$$ −13.4164 31.3050i −0.690980 1.61229i
$$378$$ 0 0
$$379$$ −12.0000 + 12.0000i −0.616399 + 0.616399i −0.944606 0.328207i $$-0.893556\pi$$
0.328207 + 0.944606i $$0.393556\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −13.4164 13.4164i −0.686443 0.686443i
$$383$$ 11.1803 11.1803i 0.571289 0.571289i −0.361200 0.932488i $$-0.617633\pi$$
0.932488 + 0.361200i $$0.117633\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 10.0000i 0.508987i
$$387$$ 13.4164i 0.681994i
$$388$$ 13.4164i 0.681115i
$$389$$ −7.00000 7.00000i −0.354914 0.354914i 0.507020 0.861934i $$-0.330747\pi$$
−0.861934 + 0.507020i $$0.830747\pi$$
$$390$$ 0 0
$$391$$ −10.0000 10.0000i −0.505722 0.505722i
$$392$$ 6.70820i 0.338815i
$$393$$ 0 0
$$394$$ −30.0000 + 30.0000i −1.51138 + 1.51138i
$$395$$ 0 0
$$396$$ 36.0000 + 36.0000i 1.80907 + 1.80907i
$$397$$ 13.4164 13.4164i 0.673350 0.673350i −0.285137 0.958487i $$-0.592039\pi$$
0.958487 + 0.285137i $$0.0920390\pi$$
$$398$$ 44.7214i 2.24168i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −20.0000 −0.998752 −0.499376 0.866385i $$-0.666437\pi$$
−0.499376 + 0.866385i $$0.666437\pi$$
$$402$$ 0 0
$$403$$ 35.7771 1.78218
$$404$$ −3.00000 3.00000i −0.149256 0.149256i
$$405$$ 0 0
$$406$$ −15.0000 35.0000i −0.744438 1.73702i
$$407$$ −17.8885 + 17.8885i −0.886702 + 0.886702i
$$408$$ 0 0
$$409$$ −3.00000 + 3.00000i −0.148340 + 0.148340i −0.777376 0.629036i $$-0.783450\pi$$
0.629036 + 0.777376i $$0.283450\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −20.1246 20.1246i −0.991468 0.991468i
$$413$$ 0 0
$$414$$ 15.0000 + 15.0000i 0.737210 + 0.737210i
$$415$$ 0 0
$$416$$ −30.0000 + 30.0000i −1.47087 + 1.47087i
$$417$$ 0 0
$$418$$ −35.7771 −1.74991
$$419$$ 24.0000 1.17248 0.586238 0.810139i $$-0.300608\pi$$
0.586238 + 0.810139i $$0.300608\pi$$
$$420$$ 0 0
$$421$$ 9.00000 9.00000i 0.438633 0.438633i −0.452919 0.891552i $$-0.649617\pi$$
0.891552 + 0.452919i $$0.149617\pi$$
$$422$$ −35.7771 + 35.7771i −1.74160 + 1.74160i
$$423$$ 13.4164i 0.652328i
$$424$$ −20.0000 20.0000i −0.971286 0.971286i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −40.2492 −1.94780
$$428$$ 20.1246 20.1246i 0.972760 0.972760i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ 0 0
$$433$$ 22.3607 1.07459 0.537293 0.843396i $$-0.319447\pi$$
0.537293 + 0.843396i $$0.319447\pi$$
$$434$$ 40.0000 1.92006
$$435$$ 0 0
$$436$$ 30.0000 1.43674
$$437$$ −8.94427 −0.427863
$$438$$ 0 0
$$439$$ −16.0000 −0.763638 −0.381819 0.924237i $$-0.624702\pi$$
−0.381819 + 0.924237i $$0.624702\pi$$
$$440$$ 0 0
$$441$$ 9.00000i 0.428571i
$$442$$ 44.7214 44.7214i 2.12718 2.12718i
$$443$$ −31.3050 −1.48734 −0.743672 0.668545i $$-0.766917\pi$$
−0.743672 + 0.668545i $$0.766917\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −25.0000 25.0000i −1.18378 1.18378i
$$447$$ 0 0
$$448$$ −29.0689 + 29.0689i −1.37338 + 1.37338i
$$449$$ −13.0000 + 13.0000i −0.613508 + 0.613508i −0.943858 0.330350i $$-0.892833\pi$$
0.330350 + 0.943858i $$0.392833\pi$$
$$450$$ 0 0
$$451$$ 8.00000 0.376705
$$452$$ 13.4164 0.631055
$$453$$ 0 0
$$454$$ 15.0000 15.0000i 0.703985 0.703985i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −17.8885 17.8885i −0.836791 0.836791i 0.151644 0.988435i $$-0.451543\pi$$
−0.988435 + 0.151644i $$0.951543\pi$$
$$458$$ −6.70820 6.70820i −0.313454 0.313454i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −9.00000 + 9.00000i −0.419172 + 0.419172i −0.884918 0.465746i $$-0.845786\pi$$
0.465746 + 0.884918i $$0.345786\pi$$
$$462$$ 0 0
$$463$$ 2.23607 2.23607i 0.103919 0.103919i −0.653236 0.757155i $$-0.726589\pi$$
0.757155 + 0.653236i $$0.226589\pi$$
$$464$$ 2.00000 5.00000i 0.0928477 0.232119i
$$465$$ 0 0
$$466$$ 20.0000 + 20.0000i 0.926482 + 0.926482i
$$467$$ 13.4164 0.620837 0.310419 0.950600i $$-0.399531\pi$$
0.310419 + 0.950600i $$0.399531\pi$$
$$468$$ −40.2492 + 40.2492i −1.86052 + 1.86052i
$$469$$ 10.0000 0.461757
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −17.8885 + 17.8885i −0.822516 + 0.822516i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 30.0000 30.0000i 1.37505 1.37505i
$$477$$ 26.8328 + 26.8328i 1.22859 + 1.22859i
$$478$$ 0 0
$$479$$ 18.0000 + 18.0000i 0.822441 + 0.822441i 0.986458 0.164017i $$-0.0524451\pi$$
−0.164017 + 0.986458i $$0.552445\pi$$
$$480$$ 0 0
$$481$$ −20.0000 20.0000i −0.911922 0.911922i
$$482$$ 17.8885i 0.814801i
$$483$$ 0 0
$$484$$ 63.0000i 2.86364i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −20.1246 + 20.1246i −0.911933 + 0.911933i −0.996424 0.0844910i $$-0.973074\pi$$
0.0844910 + 0.996424i $$0.473074\pi$$
$$488$$ 20.1246 + 20.1246i 0.910998 + 0.910998i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −6.00000 + 6.00000i −0.270776 + 0.270776i −0.829413 0.558636i $$-0.811325\pi$$
0.558636 + 0.829413i $$0.311325\pi$$
$$492$$ 0 0
$$493$$ −8.94427 + 22.3607i −0.402830 + 1.00707i
$$494$$ 40.0000i 1.79969i
$$495$$ 0 0
$$496$$ 4.00000 + 4.00000i 0.179605 + 0.179605i
$$497$$ 26.8328 + 26.8328i 1.20362 + 1.20362i
$$498$$ 0 0
$$499$$ −20.0000 −0.895323 −0.447661 0.894203i $$-0.647743\pi$$
−0.447661 + 0.894203i $$0.647743\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −8.94427 8.94427i −0.399202 0.399202i
$$503$$ 22.3607 0.997013 0.498507 0.866886i $$-0.333882\pi$$
0.498507 + 0.866886i $$0.333882\pi$$
$$504$$ −15.0000 + 15.0000i −0.668153 + 0.668153i
$$505$$ 0 0
$$506$$ 40.0000i 1.77822i
$$507$$ 0 0
$$508$$ 13.4164 0.595257
$$509$$ 24.0000i 1.06378i 0.846813 + 0.531891i $$0.178518\pi$$
−0.846813 + 0.531891i $$0.821482\pi$$
$$510$$ 0 0
$$511$$ 10.0000 10.0000i 0.442374 0.442374i
$$512$$ −11.1803 −0.494106
$$513$$ 0 0
$$514$$ 10.0000 10.0000i 0.441081 0.441081i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 17.8885 17.8885i 0.786737 0.786737i
$$518$$ −22.3607 22.3607i −0.982472 0.982472i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 10.0000i 0.438108i −0.975713 0.219054i $$-0.929703\pi$$
0.975713 0.219054i $$-0.0702971\pi$$
$$522$$ 13.4164 33.5410i 0.587220 1.46805i
$$523$$ −15.6525 15.6525i −0.684435 0.684435i 0.276561 0.960996i $$-0.410805\pi$$
−0.960996 + 0.276561i $$0.910805\pi$$
$$524$$ 42.0000 42.0000i 1.83478 1.83478i
$$525$$ 0 0
$$526$$ 20.0000i 0.872041i
$$527$$ −17.8885 17.8885i −0.779237 0.779237i
$$528$$ 0 0
$$529$$ 13.0000i 0.565217i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 26.8328i 1.16335i
$$533$$ 8.94427i 0.387419i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −5.00000 5.00000i −0.215967 0.215967i
$$537$$ 0 0
$$538$$ −15.6525 15.6525i −0.674826 0.674826i
$$539$$ 12.0000 12.0000i 0.516877 0.516877i
$$540$$ 0 0
$$541$$ −9.00000 9.00000i −0.386940 0.386940i 0.486654 0.873595i $$-0.338217\pi$$
−0.873595 + 0.486654i $$0.838217\pi$$
$$542$$ −31.3050 + 31.3050i −1.34466 + 1.34466i
$$543$$ 0 0
$$544$$ 30.0000 1.28624
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 15.6525 15.6525i 0.669252 0.669252i −0.288291 0.957543i $$-0.593087\pi$$
0.957543 + 0.288291i $$0.0930871\pi$$
$$548$$ −40.2492 −1.71936
$$549$$ −27.0000 27.0000i −1.15233 1.15233i
$$550$$ 0 0
$$551$$ 6.00000 + 14.0000i 0.255609 + 0.596420i
$$552$$ 0 0
$$553$$ 8.94427i 0.380349i
$$554$$ 20.0000 20.0000i 0.849719 0.849719i
$$555$$ 0 0
$$556$$ 12.0000i 0.508913i
$$557$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$558$$ 26.8328 + 26.8328i 1.13592 + 1.13592i
$$559$$ −20.0000 20.0000i −0.845910 0.845910i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 26.8328 1.13187
$$563$$ −35.7771 −1.50782 −0.753912 0.656975i $$-0.771836\pi$$
−0.753912 + 0.656975i $$0.771836\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −25.0000 + 25.0000i −1.05083 + 1.05083i
$$567$$ 20.1246 20.1246i 0.845154 0.845154i
$$568$$ 26.8328i 1.12588i
$$569$$ 7.00000 + 7.00000i 0.293455 + 0.293455i 0.838444 0.544988i $$-0.183466\pi$$
−0.544988 + 0.838444i $$0.683466\pi$$
$$570$$ 0 0
$$571$$ −12.0000 −0.502184 −0.251092 0.967963i $$-0.580790\pi$$
−0.251092 + 0.967963i $$0.580790\pi$$
$$572$$ −107.331 −4.48775
$$573$$ 0 0
$$574$$ 10.0000i 0.417392i
$$575$$ 0 0
$$576$$ −39.0000 −1.62500
$$577$$ 40.2492i 1.67560i 0.545979 + 0.837799i $$0.316158\pi$$
−0.545979 + 0.837799i $$0.683842\pi$$
$$578$$ −6.70820 −0.279024
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 30.0000 1.24461
$$582$$ 0 0
$$583$$ 71.5542i 2.96347i
$$584$$ −10.0000 −0.413803
$$585$$ 0 0
$$586$$ 10.0000i 0.413096i
$$587$$ 20.1246 20.1246i 0.830632 0.830632i −0.156972 0.987603i $$-0.550173\pi$$
0.987603 + 0.156972i $$0.0501731\pi$$
$$588$$ 0 0
$$589$$ −16.0000 −0.659269
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 4.47214i 0.183804i
$$593$$ −8.94427 + 8.94427i −0.367297 + 0.367297i −0.866491 0.499193i $$-0.833630\pi$$
0.499193 + 0.866491i $$0.333630\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −60.0000 −2.45770
$$597$$ 0 0
$$598$$ −44.7214 −1.82879
$$599$$ −22.0000 + 22.0000i −0.898896 + 0.898896i −0.995339 0.0964429i $$-0.969253\pi$$
0.0964429 + 0.995339i $$0.469253\pi$$
$$600$$ 0 0
$$601$$ −21.0000 21.0000i −0.856608 0.856608i 0.134329 0.990937i $$-0.457112\pi$$
−0.990937 + 0.134329i $$0.957112\pi$$
$$602$$ −22.3607 22.3607i −0.911353 0.911353i
$$603$$ 6.70820 + 6.70820i 0.273179 + 0.273179i
$$604$$ 36.0000i 1.46482i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 13.4164i 0.544555i −0.962219 0.272278i $$-0.912223\pi$$
0.962219 0.272278i $$-0.0877769\pi$$
$$608$$ 13.4164 13.4164i 0.544107 0.544107i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 20.0000 + 20.0000i 0.809113 + 0.809113i
$$612$$ 40.2492 1.62698
$$613$$ 8.94427 8.94427i 0.361256 0.361256i −0.503019 0.864275i $$-0.667778\pi$$
0.864275 + 0.503019i $$0.167778\pi$$
$$614$$ 70.0000 2.82497
$$615$$ 0 0
$$616$$ −40.0000 −1.61165
$$617$$ 40.2492i 1.62037i −0.586172 0.810186i $$-0.699366\pi$$
0.586172 0.810186i $$-0.300634\pi$$
$$618$$ 0 0
$$619$$ 12.0000 + 12.0000i 0.482321 + 0.482321i 0.905872 0.423551i $$-0.139217\pi$$
−0.423551 + 0.905872i $$0.639217\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 8.94427 + 8.94427i 0.358633 + 0.358633i
$$623$$ 31.3050i 1.25421i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 50.0000 + 50.0000i 1.99840 + 1.99840i
$$627$$ 0 0
$$628$$ 40.2492i 1.60612i
$$629$$ 20.0000i 0.797452i
$$630$$ 0 0
$$631$$ 40.0000i 1.59237i 0.605050 + 0.796187i $$0.293153\pi$$
−0.605050 + 0.796187i $$0.706847\pi$$
$$632$$ −4.47214 + 4.47214i −0.177892 + 0.177892i
$$633$$ 0 0
$$634$$ 70.0000i 2.78006i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 13.4164 + 13.4164i 0.531577 + 0.531577i
$$638$$ 62.6099 26.8328i 2.47875 1.06232i
$$639$$ 36.0000i 1.42414i
$$640$$ 0 0
$$641$$ 1.00000 + 1.00000i 0.0394976 + 0.0394976i 0.726580 0.687082i $$-0.241109\pi$$
−0.687082 + 0.726580i $$0.741109\pi$$
$$642$$ 0 0
$$643$$ −29.0689 + 29.0689i −1.14636 + 1.14636i −0.159103 + 0.987262i $$0.550860\pi$$
−0.987262 + 0.159103i $$0.949140\pi$$
$$644$$ −30.0000 −1.18217
$$645$$ 0 0
$$646$$ −20.0000 + 20.0000i −0.786889 + 0.786889i
$$647$$ 6.70820 + 6.70820i 0.263727 + 0.263727i 0.826566 0.562839i $$-0.190291\pi$$
−0.562839 + 0.826566i $$0.690291\pi$$
$$648$$ −20.1246 −0.790569
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −31.3050 −1.22506 −0.612529 0.790448i $$-0.709848\pi$$
−0.612529 + 0.790448i $$0.709848\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −1.00000 + 1.00000i −0.0390434 + 0.0390434i
$$657$$ 13.4164 0.523424
$$658$$ 22.3607 + 22.3607i 0.871710 + 0.871710i
$$659$$ −2.00000 + 2.00000i −0.0779089 + 0.0779089i −0.744987 0.667078i $$-0.767545\pi$$
0.667078 + 0.744987i $$0.267545\pi$$
$$660$$ 0 0
$$661$$ −40.0000 −1.55582 −0.777910 0.628376i $$-0.783720\pi$$
−0.777910 + 0.628376i $$0.783720\pi$$
$$662$$ 13.4164 13.4164i 0.521443 0.521443i
$$663$$ 0 0
$$664$$ −15.0000 15.0000i −0.582113 0.582113i
$$665$$ 0 0
$$666$$ 30.0000i 1.16248i
$$667$$ 15.6525 6.70820i 0.606066 0.259743i
$$668$$ −20.1246 20.1246i −0.778645 0.778645i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 72.0000i 2.77953i
$$672$$ 0 0
$$673$$ 4.47214 4.47214i 0.172388 0.172388i −0.615640 0.788028i $$-0.711102\pi$$
0.788028 + 0.615640i $$0.211102\pi$$
$$674$$ 30.0000i 1.15556i
$$675$$ 0 0
$$676$$ 81.0000i 3.11538i
$$677$$ 4.47214i 0.171878i −0.996300 0.0859391i $$-0.972611\pi$$
0.996300 0.0859391i $$-0.0273890\pi$$
$$678$$ 0 0
$$679$$ −10.0000 10.0000i −0.383765 0.383765i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 71.5542i 2.73995i
$$683$$ −33.5410 33.5410i −1.28341 1.28341i −0.938714 0.344698i $$-0.887981\pi$$
−0.344698 0.938714i $$-0.612019\pi$$
$$684$$ 18.0000 18.0000i 0.688247 0.688247i
$$685$$ 0 0
$$686$$ −20.0000 20.0000i −0.763604 0.763604i
$$687$$ 0 0
$$688$$ 4.47214i 0.170499i
$$689$$ −80.0000 −3.04776
$$690$$ 0 0
$$691$$ −20.0000 −0.760836 −0.380418 0.924815i $$-0.624220\pi$$
−0.380418 + 0.924815i $$0.624220\pi$$
$$692$$ −40.2492 + 40.2492i −1.53005 + 1.53005i
$$693$$ 53.6656 2.03859
$$694$$ 35.0000 + 35.0000i 1.32858 + 1.32858i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 4.47214 4.47214i 0.169394 0.169394i
$$698$$ 67.0820i 2.53909i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 18.0000i 0.679851i −0.940452 0.339925i $$-0.889598\pi$$
0.940452 0.339925i $$-0.110402\pi$$
$$702$$ 0 0
$$703$$ 8.94427 + 8.94427i 0.337340 + 0.337340i
$$704$$ −52.0000 52.0000i −1.95982 1.95982i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −4.47214 −0.168192
$$708$$ 0 0
$$709$$ −10.0000 −0.375558 −0.187779 0.982211i $$-0.560129\pi$$
−0.187779 + 0.982211i $$0.560129\pi$$
$$710$$ 0 0
$$711$$ 6.00000 6.00000i 0.225018 0.225018i
$$712$$ −15.6525 + 15.6525i −0.586601 + 0.586601i
$$713$$ 17.8885i 0.669931i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 26.8328 26.8328i 1.00139 1.00139i
$$719$$ 20.0000i 0.745874i −0.927857 0.372937i $$-0.878351\pi$$
0.927857 0.372937i $$-0.121649\pi$$
$$720$$ 0 0
$$721$$ −30.0000 −1.11726
$$722$$ 24.5967i 0.915396i
$$723$$ 0 0
$$724$$ −60.0000 −2.22988
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 44.7214 1.65862 0.829312 0.558786i $$-0.188733\pi$$
0.829312 + 0.558786i $$0.188733\pi$$
$$728$$ 44.7214i 1.65748i
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 20.0000i 0.739727i
$$732$$ 0 0
$$733$$ 4.47214 0.165182 0.0825911 0.996584i $$-0.473680\pi$$
0.0825911 + 0.996584i $$0.473680\pi$$
$$734$$ −60.0000 −2.21464
$$735$$ 0 0
$$736$$ −15.0000 15.0000i −0.552907 0.552907i
$$737$$ 17.8885i 0.658933i
$$738$$ −6.70820 + 6.70820i −0.246932 + 0.246932i
$$739$$ 18.0000 18.0000i 0.662141 0.662141i −0.293744 0.955884i $$-0.594901\pi$$
0.955884 + 0.293744i $$0.0949012\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −89.4427 −3.28355
$$743$$ 22.3607 0.820334 0.410167 0.912010i $$-0.365470\pi$$
0.410167 + 0.912010i $$0.365470\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 30.0000 + 30.0000i 1.09838 + 1.09838i
$$747$$ 20.1246 + 20.1246i 0.736321 + 0.736321i
$$748$$ 53.6656 + 53.6656i 1.96221 + 1.96221i
$$749$$ 30.0000i 1.09618i
$$750$$ 0 0
$$751$$ 24.0000 24.0000i 0.875772 0.875772i −0.117322 0.993094i $$-0.537431\pi$$
0.993094 + 0.117322i $$0.0374308\pi$$
$$752$$ 4.47214i 0.163082i
$$753$$ 0 0
$$754$$ 30.0000 + 70.0000i 1.09254 + 2.54925i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −40.2492 −1.46288 −0.731441 0.681904i $$-0.761152\pi$$
−0.731441 + 0.681904i $$0.761152\pi$$
$$758$$ 26.8328 26.8328i 0.974612 0.974612i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 10.0000 0.362500 0.181250 0.983437i $$-0.441986\pi$$
0.181250 + 0.983437i $$0.441986\pi$$
$$762$$ 0 0
$$763$$ 22.3607 22.3607i 0.809511 0.809511i
$$764$$ 18.0000 + 18.0000i 0.651217 + 0.651217i
$$765$$ 0 0
$$766$$ −25.0000 + 25.0000i −0.903287 + 0.903287i
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −27.0000 27.0000i −0.973645 0.973645i 0.0260166 0.999662i $$-0.491718\pi$$
−0.999662 + 0.0260166i $$0.991718\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 13.4164i 0.482867i
$$773$$ 13.4164i 0.482555i 0.970456 + 0.241277i $$0.0775663\pi$$
−0.970456 + 0.241277i $$0.922434\pi$$
$$774$$ 30.0000i 1.07833i
$$775$$ 0 0
$$776$$ 10.0000i 0.358979i
$$777$$ 0 0
$$778$$ 15.6525 + 15.6525i 0.561168 + 0.561168i
$$779$$ 4.00000i 0.143315i
$$780$$ 0 0
$$781$$ −48.0000 + 48.0000i −1.71758 + 1.71758i
$$782$$ 22.3607 + 22.3607i 0.799616 + 0.799616i
$$783$$ 0 0
$$784$$ 3.00000i 0.107143i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 33.5410 + 33.5410i 1.19561 + 1.19561i