# Properties

 Label 460.2.c.a.369.5 Level $460$ Weight $2$ Character 460.369 Analytic conductor $3.673$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$460 = 2^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 460.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.67311849298$$ Analytic rank: $$0$$ Dimension: $$12$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ Defining polynomial: $$x^{12} + 24x^{10} + 188x^{8} + 530x^{6} + 508x^{4} + 80x^{2} + 1$$ x^12 + 24*x^10 + 188*x^8 + 530*x^6 + 508*x^4 + 80*x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{23}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 369.5 Root $$3.08006i$$ of defining polynomial Character $$\chi$$ $$=$$ 460.369 Dual form 460.2.c.a.369.8

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-0.873449i q^{3} +(-1.89824 + 1.18182i) q^{5} -0.992530i q^{7} +2.23709 q^{9} +O(q^{10})$$ $$q-0.873449i q^{3} +(-1.89824 + 1.18182i) q^{5} -0.992530i q^{7} +2.23709 q^{9} +1.83236 q^{11} -3.28666i q^{13} +(1.03226 + 1.65801i) q^{15} -6.63631i q^{17} +5.64378 q^{19} -0.866924 q^{21} +1.00000i q^{23} +(2.20661 - 4.48675i) q^{25} -4.57433i q^{27} -2.01596 q^{29} -0.315080 q^{31} -1.60047i q^{33} +(1.17299 + 1.88406i) q^{35} -3.07470i q^{37} -2.87073 q^{39} -1.34964 q^{41} +5.97905i q^{43} +(-4.24652 + 2.64383i) q^{45} +0.306285i q^{47} +6.01489 q^{49} -5.79647 q^{51} +6.98500i q^{53} +(-3.47826 + 2.16552i) q^{55} -4.92955i q^{57} -9.49533 q^{59} +5.56160 q^{61} -2.22038i q^{63} +(3.88424 + 6.23887i) q^{65} +0.853521i q^{67} +0.873449 q^{69} +0.797419 q^{71} -7.67189i q^{73} +(-3.91894 - 1.92736i) q^{75} -1.81867i q^{77} +3.62884 q^{79} +2.71582 q^{81} +17.1966i q^{83} +(7.84291 + 12.5973i) q^{85} +1.76084i q^{87} +7.01565 q^{89} -3.26211 q^{91} +0.275207i q^{93} +(-10.7132 + 6.66992i) q^{95} -18.5807i q^{97} +4.09915 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 20 q^{9}+O(q^{10})$$ 12 * q - 20 * q^9 $$12 q - 20 q^{9} + 4 q^{11} + 2 q^{15} - 8 q^{19} + 8 q^{25} - 10 q^{29} + 18 q^{31} - 10 q^{35} + 16 q^{39} - 2 q^{41} + 2 q^{45} - 38 q^{49} - 24 q^{51} + 16 q^{55} + 22 q^{59} - 8 q^{61} + 38 q^{65} - 8 q^{69} - 34 q^{71} + 16 q^{75} - 20 q^{79} + 28 q^{81} + 6 q^{85} + 48 q^{89} - 8 q^{91} + 12 q^{95} + 32 q^{99}+O(q^{100})$$ 12 * q - 20 * q^9 + 4 * q^11 + 2 * q^15 - 8 * q^19 + 8 * q^25 - 10 * q^29 + 18 * q^31 - 10 * q^35 + 16 * q^39 - 2 * q^41 + 2 * q^45 - 38 * q^49 - 24 * q^51 + 16 * q^55 + 22 * q^59 - 8 * q^61 + 38 * q^65 - 8 * q^69 - 34 * q^71 + 16 * q^75 - 20 * q^79 + 28 * q^81 + 6 * q^85 + 48 * q^89 - 8 * q^91 + 12 * q^95 + 32 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$$.

 $$n$$ $$231$$ $$277$$ $$281$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.873449i 0.504286i −0.967690 0.252143i $$-0.918865\pi$$
0.967690 0.252143i $$-0.0811353\pi$$
$$4$$ 0 0
$$5$$ −1.89824 + 1.18182i −0.848917 + 0.528526i
$$6$$ 0 0
$$7$$ 0.992530i 0.375141i −0.982251 0.187570i $$-0.939939\pi$$
0.982251 0.187570i $$-0.0600613\pi$$
$$8$$ 0 0
$$9$$ 2.23709 0.745696
$$10$$ 0 0
$$11$$ 1.83236 0.552478 0.276239 0.961089i $$-0.410912\pi$$
0.276239 + 0.961089i $$0.410912\pi$$
$$12$$ 0 0
$$13$$ 3.28666i 0.911556i −0.890093 0.455778i $$-0.849361\pi$$
0.890093 0.455778i $$-0.150639\pi$$
$$14$$ 0 0
$$15$$ 1.03226 + 1.65801i 0.266528 + 0.428097i
$$16$$ 0 0
$$17$$ 6.63631i 1.60954i −0.593586 0.804770i $$-0.702288\pi$$
0.593586 0.804770i $$-0.297712\pi$$
$$18$$ 0 0
$$19$$ 5.64378 1.29477 0.647386 0.762163i $$-0.275862\pi$$
0.647386 + 0.762163i $$0.275862\pi$$
$$20$$ 0 0
$$21$$ −0.866924 −0.189178
$$22$$ 0 0
$$23$$ 1.00000i 0.208514i
$$24$$ 0 0
$$25$$ 2.20661 4.48675i 0.441321 0.897349i
$$26$$ 0 0
$$27$$ 4.57433i 0.880330i
$$28$$ 0 0
$$29$$ −2.01596 −0.374354 −0.187177 0.982326i $$-0.559934\pi$$
−0.187177 + 0.982326i $$0.559934\pi$$
$$30$$ 0 0
$$31$$ −0.315080 −0.0565901 −0.0282951 0.999600i $$-0.509008\pi$$
−0.0282951 + 0.999600i $$0.509008\pi$$
$$32$$ 0 0
$$33$$ 1.60047i 0.278607i
$$34$$ 0 0
$$35$$ 1.17299 + 1.88406i 0.198272 + 0.318464i
$$36$$ 0 0
$$37$$ 3.07470i 0.505478i −0.967534 0.252739i $$-0.918669\pi$$
0.967534 0.252739i $$-0.0813314\pi$$
$$38$$ 0 0
$$39$$ −2.87073 −0.459685
$$40$$ 0 0
$$41$$ −1.34964 −0.210779 −0.105389 0.994431i $$-0.533609\pi$$
−0.105389 + 0.994431i $$0.533609\pi$$
$$42$$ 0 0
$$43$$ 5.97905i 0.911797i 0.890032 + 0.455899i $$0.150682\pi$$
−0.890032 + 0.455899i $$0.849318\pi$$
$$44$$ 0 0
$$45$$ −4.24652 + 2.64383i −0.633034 + 0.394119i
$$46$$ 0 0
$$47$$ 0.306285i 0.0446762i 0.999750 + 0.0223381i $$0.00711103\pi$$
−0.999750 + 0.0223381i $$0.992889\pi$$
$$48$$ 0 0
$$49$$ 6.01489 0.859269
$$50$$ 0 0
$$51$$ −5.79647 −0.811669
$$52$$ 0 0
$$53$$ 6.98500i 0.959464i 0.877415 + 0.479732i $$0.159266\pi$$
−0.877415 + 0.479732i $$0.840734\pi$$
$$54$$ 0 0
$$55$$ −3.47826 + 2.16552i −0.469008 + 0.291999i
$$56$$ 0 0
$$57$$ 4.92955i 0.652935i
$$58$$ 0 0
$$59$$ −9.49533 −1.23619 −0.618094 0.786105i $$-0.712095\pi$$
−0.618094 + 0.786105i $$0.712095\pi$$
$$60$$ 0 0
$$61$$ 5.56160 0.712090 0.356045 0.934469i $$-0.384125\pi$$
0.356045 + 0.934469i $$0.384125\pi$$
$$62$$ 0 0
$$63$$ 2.22038i 0.279741i
$$64$$ 0 0
$$65$$ 3.88424 + 6.23887i 0.481781 + 0.773836i
$$66$$ 0 0
$$67$$ 0.853521i 0.104274i 0.998640 + 0.0521371i $$0.0166033\pi$$
−0.998640 + 0.0521371i $$0.983397\pi$$
$$68$$ 0 0
$$69$$ 0.873449 0.105151
$$70$$ 0 0
$$71$$ 0.797419 0.0946363 0.0473181 0.998880i $$-0.484933\pi$$
0.0473181 + 0.998880i $$0.484933\pi$$
$$72$$ 0 0
$$73$$ 7.67189i 0.897926i −0.893550 0.448963i $$-0.851793\pi$$
0.893550 0.448963i $$-0.148207\pi$$
$$74$$ 0 0
$$75$$ −3.91894 1.92736i −0.452521 0.222552i
$$76$$ 0 0
$$77$$ 1.81867i 0.207257i
$$78$$ 0 0
$$79$$ 3.62884 0.408276 0.204138 0.978942i $$-0.434561\pi$$
0.204138 + 0.978942i $$0.434561\pi$$
$$80$$ 0 0
$$81$$ 2.71582 0.301758
$$82$$ 0 0
$$83$$ 17.1966i 1.88757i 0.330560 + 0.943785i $$0.392762\pi$$
−0.330560 + 0.943785i $$0.607238\pi$$
$$84$$ 0 0
$$85$$ 7.84291 + 12.5973i 0.850683 + 1.36637i
$$86$$ 0 0
$$87$$ 1.76084i 0.188782i
$$88$$ 0 0
$$89$$ 7.01565 0.743658 0.371829 0.928301i $$-0.378731\pi$$
0.371829 + 0.928301i $$0.378731\pi$$
$$90$$ 0 0
$$91$$ −3.26211 −0.341962
$$92$$ 0 0
$$93$$ 0.275207i 0.0285376i
$$94$$ 0 0
$$95$$ −10.7132 + 6.66992i −1.09915 + 0.684320i
$$96$$ 0 0
$$97$$ 18.5807i 1.88659i −0.331958 0.943294i $$-0.607709\pi$$
0.331958 0.943294i $$-0.392291\pi$$
$$98$$ 0 0
$$99$$ 4.09915 0.411980
$$100$$ 0 0
$$101$$ −7.96538 −0.792585 −0.396293 0.918124i $$-0.629703\pi$$
−0.396293 + 0.918124i $$0.629703\pi$$
$$102$$ 0 0
$$103$$ 16.8268i 1.65799i 0.559253 + 0.828997i $$0.311088\pi$$
−0.559253 + 0.828997i $$0.688912\pi$$
$$104$$ 0 0
$$105$$ 1.64563 1.02455i 0.160597 0.0999856i
$$106$$ 0 0
$$107$$ 10.7429i 1.03855i 0.854606 + 0.519276i $$0.173798\pi$$
−0.854606 + 0.519276i $$0.826202\pi$$
$$108$$ 0 0
$$109$$ −8.34117 −0.798939 −0.399470 0.916746i $$-0.630806\pi$$
−0.399470 + 0.916746i $$0.630806\pi$$
$$110$$ 0 0
$$111$$ −2.68560 −0.254906
$$112$$ 0 0
$$113$$ 8.28008i 0.778925i 0.921042 + 0.389462i $$0.127339\pi$$
−0.921042 + 0.389462i $$0.872661\pi$$
$$114$$ 0 0
$$115$$ −1.18182 1.89824i −0.110205 0.177012i
$$116$$ 0 0
$$117$$ 7.35255i 0.679744i
$$118$$ 0 0
$$119$$ −6.58673 −0.603805
$$120$$ 0 0
$$121$$ −7.64245 −0.694768
$$122$$ 0 0
$$123$$ 1.17884i 0.106293i
$$124$$ 0 0
$$125$$ 1.11386 + 11.1247i 0.0996265 + 0.995025i
$$126$$ 0 0
$$127$$ 10.5531i 0.936437i −0.883613 0.468219i $$-0.844896\pi$$
0.883613 0.468219i $$-0.155104\pi$$
$$128$$ 0 0
$$129$$ 5.22240 0.459806
$$130$$ 0 0
$$131$$ 7.84966 0.685828 0.342914 0.939367i $$-0.388586\pi$$
0.342914 + 0.939367i $$0.388586\pi$$
$$132$$ 0 0
$$133$$ 5.60161i 0.485722i
$$134$$ 0 0
$$135$$ 5.40603 + 8.68316i 0.465277 + 0.747327i
$$136$$ 0 0
$$137$$ 9.27261i 0.792213i 0.918205 + 0.396106i $$0.129639\pi$$
−0.918205 + 0.396106i $$0.870361\pi$$
$$138$$ 0 0
$$139$$ −18.5293 −1.57163 −0.785816 0.618461i $$-0.787757\pi$$
−0.785816 + 0.618461i $$0.787757\pi$$
$$140$$ 0 0
$$141$$ 0.267524 0.0225296
$$142$$ 0 0
$$143$$ 6.02236i 0.503615i
$$144$$ 0 0
$$145$$ 3.82677 2.38250i 0.317796 0.197856i
$$146$$ 0 0
$$147$$ 5.25369i 0.433317i
$$148$$ 0 0
$$149$$ −23.6227 −1.93525 −0.967624 0.252395i $$-0.918782\pi$$
−0.967624 + 0.252395i $$0.918782\pi$$
$$150$$ 0 0
$$151$$ −19.2472 −1.56631 −0.783157 0.621825i $$-0.786392\pi$$
−0.783157 + 0.621825i $$0.786392\pi$$
$$152$$ 0 0
$$153$$ 14.8460i 1.20023i
$$154$$ 0 0
$$155$$ 0.598097 0.372368i 0.0480403 0.0299093i
$$156$$ 0 0
$$157$$ 6.61180i 0.527679i 0.964567 + 0.263840i $$0.0849890\pi$$
−0.964567 + 0.263840i $$0.915011\pi$$
$$158$$ 0 0
$$159$$ 6.10104 0.483844
$$160$$ 0 0
$$161$$ 0.992530 0.0782223
$$162$$ 0 0
$$163$$ 11.6157i 0.909809i 0.890540 + 0.454905i $$0.150327\pi$$
−0.890540 + 0.454905i $$0.849673\pi$$
$$164$$ 0 0
$$165$$ 1.89147 + 3.03808i 0.147251 + 0.236514i
$$166$$ 0 0
$$167$$ 18.4280i 1.42600i −0.701162 0.713002i $$-0.747335\pi$$
0.701162 0.713002i $$-0.252665\pi$$
$$168$$ 0 0
$$169$$ 2.19784 0.169065
$$170$$ 0 0
$$171$$ 12.6256 0.965505
$$172$$ 0 0
$$173$$ 5.51955i 0.419644i −0.977740 0.209822i $$-0.932712\pi$$
0.977740 0.209822i $$-0.0672884\pi$$
$$174$$ 0 0
$$175$$ −4.45323 2.19012i −0.336632 0.165558i
$$176$$ 0 0
$$177$$ 8.29369i 0.623392i
$$178$$ 0 0
$$179$$ 9.73640 0.727733 0.363866 0.931451i $$-0.381456\pi$$
0.363866 + 0.931451i $$0.381456\pi$$
$$180$$ 0 0
$$181$$ 21.8277 1.62244 0.811220 0.584741i $$-0.198804\pi$$
0.811220 + 0.584741i $$0.198804\pi$$
$$182$$ 0 0
$$183$$ 4.85777i 0.359097i
$$184$$ 0 0
$$185$$ 3.63374 + 5.83652i 0.267158 + 0.429109i
$$186$$ 0 0
$$187$$ 12.1601i 0.889235i
$$188$$ 0 0
$$189$$ −4.54016 −0.330248
$$190$$ 0 0
$$191$$ 16.4807 1.19250 0.596251 0.802798i $$-0.296656\pi$$
0.596251 + 0.802798i $$0.296656\pi$$
$$192$$ 0 0
$$193$$ 4.60541i 0.331504i −0.986167 0.165752i $$-0.946995\pi$$
0.986167 0.165752i $$-0.0530052\pi$$
$$194$$ 0 0
$$195$$ 5.44933 3.39269i 0.390235 0.242955i
$$196$$ 0 0
$$197$$ 0.157186i 0.0111990i −0.999984 0.00559951i $$-0.998218\pi$$
0.999984 0.00559951i $$-0.00178239\pi$$
$$198$$ 0 0
$$199$$ 1.94253 0.137702 0.0688511 0.997627i $$-0.478067\pi$$
0.0688511 + 0.997627i $$0.478067\pi$$
$$200$$ 0 0
$$201$$ 0.745507 0.0525840
$$202$$ 0 0
$$203$$ 2.00090i 0.140436i
$$204$$ 0 0
$$205$$ 2.56194 1.59503i 0.178934 0.111402i
$$206$$ 0 0
$$207$$ 2.23709i 0.155488i
$$208$$ 0 0
$$209$$ 10.3414 0.715332
$$210$$ 0 0
$$211$$ 23.5602 1.62195 0.810976 0.585079i $$-0.198937\pi$$
0.810976 + 0.585079i $$0.198937\pi$$
$$212$$ 0 0
$$213$$ 0.696505i 0.0477237i
$$214$$ 0 0
$$215$$ −7.06616 11.3497i −0.481908 0.774040i
$$216$$ 0 0
$$217$$ 0.312727i 0.0212293i
$$218$$ 0 0
$$219$$ −6.70100 −0.452812
$$220$$ 0 0
$$221$$ −21.8113 −1.46719
$$222$$ 0 0
$$223$$ 9.59356i 0.642432i 0.947006 + 0.321216i $$0.104092\pi$$
−0.947006 + 0.321216i $$0.895908\pi$$
$$224$$ 0 0
$$225$$ 4.93637 10.0372i 0.329091 0.669149i
$$226$$ 0 0
$$227$$ 9.90765i 0.657594i −0.944401 0.328797i $$-0.893357\pi$$
0.944401 0.328797i $$-0.106643\pi$$
$$228$$ 0 0
$$229$$ 4.90156 0.323904 0.161952 0.986799i $$-0.448221\pi$$
0.161952 + 0.986799i $$0.448221\pi$$
$$230$$ 0 0
$$231$$ −1.58852 −0.104517
$$232$$ 0 0
$$233$$ 15.3123i 1.00314i −0.865116 0.501571i $$-0.832755\pi$$
0.865116 0.501571i $$-0.167245\pi$$
$$234$$ 0 0
$$235$$ −0.361973 0.581401i −0.0236125 0.0379264i
$$236$$ 0 0
$$237$$ 3.16960i 0.205888i
$$238$$ 0 0
$$239$$ 3.88065 0.251018 0.125509 0.992092i $$-0.459944\pi$$
0.125509 + 0.992092i $$0.459944\pi$$
$$240$$ 0 0
$$241$$ 6.64578 0.428092 0.214046 0.976824i $$-0.431336\pi$$
0.214046 + 0.976824i $$0.431336\pi$$
$$242$$ 0 0
$$243$$ 16.0951i 1.03250i
$$244$$ 0 0
$$245$$ −11.4177 + 7.10851i −0.729449 + 0.454146i
$$246$$ 0 0
$$247$$ 18.5492i 1.18026i
$$248$$ 0 0
$$249$$ 15.0203 0.951875
$$250$$ 0 0
$$251$$ 5.82636 0.367756 0.183878 0.982949i $$-0.441135\pi$$
0.183878 + 0.982949i $$0.441135\pi$$
$$252$$ 0 0
$$253$$ 1.83236i 0.115200i
$$254$$ 0 0
$$255$$ 11.0031 6.85038i 0.689040 0.428988i
$$256$$ 0 0
$$257$$ 17.1979i 1.07278i 0.843971 + 0.536388i $$0.180212\pi$$
−0.843971 + 0.536388i $$0.819788\pi$$
$$258$$ 0 0
$$259$$ −3.05173 −0.189626
$$260$$ 0 0
$$261$$ −4.50988 −0.279154
$$262$$ 0 0
$$263$$ 19.5353i 1.20460i 0.798269 + 0.602301i $$0.205749\pi$$
−0.798269 + 0.602301i $$0.794251\pi$$
$$264$$ 0 0
$$265$$ −8.25501 13.2592i −0.507101 0.814506i
$$266$$ 0 0
$$267$$ 6.12781i 0.375016i
$$268$$ 0 0
$$269$$ 21.2275 1.29426 0.647132 0.762378i $$-0.275968\pi$$
0.647132 + 0.762378i $$0.275968\pi$$
$$270$$ 0 0
$$271$$ 9.19621 0.558630 0.279315 0.960200i $$-0.409893\pi$$
0.279315 + 0.960200i $$0.409893\pi$$
$$272$$ 0 0
$$273$$ 2.84929i 0.172447i
$$274$$ 0 0
$$275$$ 4.04330 8.22134i 0.243820 0.495765i
$$276$$ 0 0
$$277$$ 2.77325i 0.166628i −0.996523 0.0833141i $$-0.973450\pi$$
0.996523 0.0833141i $$-0.0265505\pi$$
$$278$$ 0 0
$$279$$ −0.704862 −0.0421990
$$280$$ 0 0
$$281$$ −32.7971 −1.95651 −0.978255 0.207407i $$-0.933497\pi$$
−0.978255 + 0.207407i $$0.933497\pi$$
$$282$$ 0 0
$$283$$ 23.6017i 1.40298i 0.712680 + 0.701489i $$0.247481\pi$$
−0.712680 + 0.701489i $$0.752519\pi$$
$$284$$ 0 0
$$285$$ 5.82584 + 9.35745i 0.345093 + 0.554288i
$$286$$ 0 0
$$287$$ 1.33956i 0.0790717i
$$288$$ 0 0
$$289$$ −27.0406 −1.59062
$$290$$ 0 0
$$291$$ −16.2293 −0.951380
$$292$$ 0 0
$$293$$ 1.83939i 0.107458i −0.998556 0.0537291i $$-0.982889\pi$$
0.998556 0.0537291i $$-0.0171107\pi$$
$$294$$ 0 0
$$295$$ 18.0244 11.2218i 1.04942 0.653356i
$$296$$ 0 0
$$297$$ 8.38182i 0.486363i
$$298$$ 0 0
$$299$$ 3.28666 0.190073
$$300$$ 0 0
$$301$$ 5.93439 0.342052
$$302$$ 0 0
$$303$$ 6.95735i 0.399690i
$$304$$ 0 0
$$305$$ −10.5572 + 6.57281i −0.604506 + 0.376358i
$$306$$ 0 0
$$307$$ 10.3956i 0.593310i −0.954985 0.296655i $$-0.904129\pi$$
0.954985 0.296655i $$-0.0958711\pi$$
$$308$$ 0 0
$$309$$ 14.6973 0.836103
$$310$$ 0 0
$$311$$ −12.2967 −0.697281 −0.348640 0.937257i $$-0.613357\pi$$
−0.348640 + 0.937257i $$0.613357\pi$$
$$312$$ 0 0
$$313$$ 17.2954i 0.977592i −0.872398 0.488796i $$-0.837436\pi$$
0.872398 0.488796i $$-0.162564\pi$$
$$314$$ 0 0
$$315$$ 2.62408 + 4.21480i 0.147850 + 0.237477i
$$316$$ 0 0
$$317$$ 33.6362i 1.88920i 0.328227 + 0.944599i $$0.393549\pi$$
−0.328227 + 0.944599i $$0.606451\pi$$
$$318$$ 0 0
$$319$$ −3.69397 −0.206822
$$320$$ 0 0
$$321$$ 9.38335 0.523728
$$322$$ 0 0
$$323$$ 37.4538i 2.08399i
$$324$$ 0 0
$$325$$ −14.7464 7.25237i −0.817984 0.402289i
$$326$$ 0 0
$$327$$ 7.28559i 0.402894i
$$328$$ 0 0
$$329$$ 0.303997 0.0167599
$$330$$ 0 0
$$331$$ −9.81704 −0.539593 −0.269797 0.962917i $$-0.586956\pi$$
−0.269797 + 0.962917i $$0.586956\pi$$
$$332$$ 0 0
$$333$$ 6.87838i 0.376933i
$$334$$ 0 0
$$335$$ −1.00871 1.62018i −0.0551115 0.0885201i
$$336$$ 0 0
$$337$$ 9.15644i 0.498783i −0.968403 0.249392i $$-0.919769\pi$$
0.968403 0.249392i $$-0.0802306\pi$$
$$338$$ 0 0
$$339$$ 7.23223 0.392801
$$340$$ 0 0
$$341$$ −0.577341 −0.0312648
$$342$$ 0 0
$$343$$ 12.9177i 0.697488i
$$344$$ 0 0
$$345$$ −1.65801 + 1.03226i −0.0892644 + 0.0555749i
$$346$$ 0 0
$$347$$ 32.5921i 1.74963i 0.484453 + 0.874817i $$0.339019\pi$$
−0.484453 + 0.874817i $$0.660981\pi$$
$$348$$ 0 0
$$349$$ 15.5701 0.833448 0.416724 0.909033i $$-0.363178\pi$$
0.416724 + 0.909033i $$0.363178\pi$$
$$350$$ 0 0
$$351$$ −15.0343 −0.802470
$$352$$ 0 0
$$353$$ 10.9313i 0.581816i −0.956751 0.290908i $$-0.906043\pi$$
0.956751 0.290908i $$-0.0939573\pi$$
$$354$$ 0 0
$$355$$ −1.51369 + 0.942405i −0.0803384 + 0.0500177i
$$356$$ 0 0
$$357$$ 5.75317i 0.304490i
$$358$$ 0 0
$$359$$ −0.405120 −0.0213814 −0.0106907 0.999943i $$-0.503403\pi$$
−0.0106907 + 0.999943i $$0.503403\pi$$
$$360$$ 0 0
$$361$$ 12.8522 0.676432
$$362$$ 0 0
$$363$$ 6.67529i 0.350362i
$$364$$ 0 0
$$365$$ 9.06678 + 14.5631i 0.474577 + 0.762265i
$$366$$ 0 0
$$367$$ 7.26443i 0.379200i 0.981861 + 0.189600i $$0.0607191\pi$$
−0.981861 + 0.189600i $$0.939281\pi$$
$$368$$ 0 0
$$369$$ −3.01927 −0.157177
$$370$$ 0 0
$$371$$ 6.93282 0.359934
$$372$$ 0 0
$$373$$ 3.36770i 0.174373i 0.996192 + 0.0871866i $$0.0277876\pi$$
−0.996192 + 0.0871866i $$0.972212\pi$$
$$374$$ 0 0
$$375$$ 9.71687 0.972898i 0.501777 0.0502402i
$$376$$ 0 0
$$377$$ 6.62578i 0.341245i
$$378$$ 0 0
$$379$$ 4.54534 0.233478 0.116739 0.993163i $$-0.462756\pi$$
0.116739 + 0.993163i $$0.462756\pi$$
$$380$$ 0 0
$$381$$ −9.21760 −0.472232
$$382$$ 0 0
$$383$$ 12.0978i 0.618167i 0.951035 + 0.309084i $$0.100022\pi$$
−0.951035 + 0.309084i $$0.899978\pi$$
$$384$$ 0 0
$$385$$ 2.14934 + 3.45227i 0.109541 + 0.175944i
$$386$$ 0 0
$$387$$ 13.3757i 0.679923i
$$388$$ 0 0
$$389$$ −22.8934 −1.16074 −0.580371 0.814352i $$-0.697092\pi$$
−0.580371 + 0.814352i $$0.697092\pi$$
$$390$$ 0 0
$$391$$ 6.63631 0.335612
$$392$$ 0 0
$$393$$ 6.85627i 0.345853i
$$394$$ 0 0
$$395$$ −6.88839 + 4.28863i −0.346593 + 0.215784i
$$396$$ 0 0
$$397$$ 23.9748i 1.20326i 0.798774 + 0.601631i $$0.205482\pi$$
−0.798774 + 0.601631i $$0.794518\pi$$
$$398$$ 0 0
$$399$$ −4.89272 −0.244943
$$400$$ 0 0
$$401$$ 26.8722 1.34193 0.670967 0.741487i $$-0.265879\pi$$
0.670967 + 0.741487i $$0.265879\pi$$
$$402$$ 0 0
$$403$$ 1.03556i 0.0515851i
$$404$$ 0 0
$$405$$ −5.15527 + 3.20961i −0.256167 + 0.159487i
$$406$$ 0 0
$$407$$ 5.63397i 0.279266i
$$408$$ 0 0
$$409$$ −15.7840 −0.780467 −0.390233 0.920716i $$-0.627606\pi$$
−0.390233 + 0.920716i $$0.627606\pi$$
$$410$$ 0 0
$$411$$ 8.09915 0.399502
$$412$$ 0 0
$$413$$ 9.42440i 0.463744i
$$414$$ 0 0
$$415$$ −20.3232 32.6432i −0.997629 1.60239i
$$416$$ 0 0
$$417$$ 16.1844i 0.792552i
$$418$$ 0 0
$$419$$ −19.6999 −0.962402 −0.481201 0.876610i $$-0.659799\pi$$
−0.481201 + 0.876610i $$0.659799\pi$$
$$420$$ 0 0
$$421$$ −15.6913 −0.764748 −0.382374 0.924008i $$-0.624893\pi$$
−0.382374 + 0.924008i $$0.624893\pi$$
$$422$$ 0 0
$$423$$ 0.685185i 0.0333149i
$$424$$ 0 0
$$425$$ −29.7754 14.6437i −1.44432 0.710325i
$$426$$ 0 0
$$427$$ 5.52005i 0.267134i
$$428$$ 0 0
$$429$$ −5.26022 −0.253966
$$430$$ 0 0
$$431$$ −1.33660 −0.0643819 −0.0321909 0.999482i $$-0.510248\pi$$
−0.0321909 + 0.999482i $$0.510248\pi$$
$$432$$ 0 0
$$433$$ 4.26379i 0.204905i 0.994738 + 0.102452i $$0.0326689\pi$$
−0.994738 + 0.102452i $$0.967331\pi$$
$$434$$ 0 0
$$435$$ −2.08099 3.34249i −0.0997759 0.160260i
$$436$$ 0 0
$$437$$ 5.64378i 0.269978i
$$438$$ 0 0
$$439$$ 32.6899 1.56020 0.780101 0.625653i $$-0.215167\pi$$
0.780101 + 0.625653i $$0.215167\pi$$
$$440$$ 0 0
$$441$$ 13.4558 0.640753
$$442$$ 0 0
$$443$$ 16.8373i 0.799964i −0.916523 0.399982i $$-0.869016\pi$$
0.916523 0.399982i $$-0.130984\pi$$
$$444$$ 0 0
$$445$$ −13.3174 + 8.29123i −0.631304 + 0.393042i
$$446$$ 0 0
$$447$$ 20.6332i 0.975919i
$$448$$ 0 0
$$449$$ −12.8502 −0.606440 −0.303220 0.952921i $$-0.598062\pi$$
−0.303220 + 0.952921i $$0.598062\pi$$
$$450$$ 0 0
$$451$$ −2.47303 −0.116451
$$452$$ 0 0
$$453$$ 16.8114i 0.789870i
$$454$$ 0 0
$$455$$ 6.19226 3.85522i 0.290298 0.180736i
$$456$$ 0 0
$$457$$ 40.1900i 1.88001i 0.341161 + 0.940005i $$0.389180\pi$$
−0.341161 + 0.940005i $$0.610820\pi$$
$$458$$ 0 0
$$459$$ −30.3566 −1.41693
$$460$$ 0 0
$$461$$ −34.7208 −1.61711 −0.808554 0.588422i $$-0.799750\pi$$
−0.808554 + 0.588422i $$0.799750\pi$$
$$462$$ 0 0
$$463$$ 26.7292i 1.24221i 0.783727 + 0.621106i $$0.213316\pi$$
−0.783727 + 0.621106i $$0.786684\pi$$
$$464$$ 0 0
$$465$$ −0.325245 0.522408i −0.0150829 0.0242261i
$$466$$ 0 0
$$467$$ 17.6579i 0.817112i 0.912733 + 0.408556i $$0.133968\pi$$
−0.912733 + 0.408556i $$0.866032\pi$$
$$468$$ 0 0
$$469$$ 0.847144 0.0391175
$$470$$ 0 0
$$471$$ 5.77507 0.266101
$$472$$ 0 0
$$473$$ 10.9558i 0.503748i
$$474$$ 0 0
$$475$$ 12.4536 25.3222i 0.571410 1.16186i
$$476$$ 0 0
$$477$$ 15.6261i 0.715468i
$$478$$ 0 0
$$479$$ 37.8085 1.72752 0.863758 0.503907i $$-0.168104\pi$$
0.863758 + 0.503907i $$0.168104\pi$$
$$480$$ 0 0
$$481$$ −10.1055 −0.460772
$$482$$ 0 0
$$483$$ 0.866924i 0.0394464i
$$484$$ 0 0
$$485$$ 21.9591 + 35.2706i 0.997110 + 1.60156i
$$486$$ 0 0
$$487$$ 27.9951i 1.26858i 0.773096 + 0.634289i $$0.218707\pi$$
−0.773096 + 0.634289i $$0.781293\pi$$
$$488$$ 0 0
$$489$$ 10.1457 0.458804
$$490$$ 0 0
$$491$$ 10.1212 0.456762 0.228381 0.973572i $$-0.426657\pi$$
0.228381 + 0.973572i $$0.426657\pi$$
$$492$$ 0 0
$$493$$ 13.3785i 0.602538i
$$494$$ 0 0
$$495$$ −7.78116 + 4.84446i −0.349737 + 0.217742i
$$496$$ 0 0
$$497$$ 0.791462i 0.0355019i
$$498$$ 0 0
$$499$$ 37.0240 1.65742 0.828712 0.559676i $$-0.189074\pi$$
0.828712 + 0.559676i $$0.189074\pi$$
$$500$$ 0 0
$$501$$ −16.0960 −0.719114
$$502$$ 0 0
$$503$$ 22.5700i 1.00635i −0.864185 0.503174i $$-0.832166\pi$$
0.864185 0.503174i $$-0.167834\pi$$
$$504$$ 0 0
$$505$$ 15.1202 9.41364i 0.672839 0.418902i
$$506$$ 0 0
$$507$$ 1.91970i 0.0852571i
$$508$$ 0 0
$$509$$ −29.3212 −1.29964 −0.649819 0.760089i $$-0.725155\pi$$
−0.649819 + 0.760089i $$0.725155\pi$$
$$510$$ 0 0
$$511$$ −7.61457 −0.336849
$$512$$ 0 0
$$513$$ 25.8165i 1.13983i
$$514$$ 0 0
$$515$$ −19.8862 31.9413i −0.876292 1.40750i
$$516$$ 0 0
$$517$$ 0.561224i 0.0246826i
$$518$$ 0 0
$$519$$ −4.82105 −0.211620
$$520$$ 0 0
$$521$$ 13.9057 0.609220 0.304610 0.952477i $$-0.401474\pi$$
0.304610 + 0.952477i $$0.401474\pi$$
$$522$$ 0 0
$$523$$ 36.6591i 1.60299i 0.598001 + 0.801496i $$0.295962\pi$$
−0.598001 + 0.801496i $$0.704038\pi$$
$$524$$ 0 0
$$525$$ −1.91296 + 3.88967i −0.0834884 + 0.169759i
$$526$$ 0 0
$$527$$ 2.09097i 0.0910841i
$$528$$ 0 0
$$529$$ −1.00000 −0.0434783
$$530$$ 0 0
$$531$$ −21.2419 −0.921819
$$532$$ 0 0
$$533$$ 4.43582i 0.192137i
$$534$$ 0 0
$$535$$ −12.6961 20.3925i −0.548902 0.881645i
$$536$$ 0 0
$$537$$ 8.50425i 0.366986i
$$538$$ 0 0
$$539$$ 11.0214 0.474727
$$540$$ 0 0
$$541$$ 15.8082 0.679647 0.339823 0.940489i $$-0.389633\pi$$
0.339823 + 0.940489i $$0.389633\pi$$
$$542$$ 0 0
$$543$$ 19.0654i 0.818174i
$$544$$ 0 0
$$545$$ 15.8335 9.85776i 0.678233 0.422260i
$$546$$ 0 0
$$547$$ 25.6129i 1.09513i −0.836764 0.547563i $$-0.815556\pi$$
0.836764 0.547563i $$-0.184444\pi$$
$$548$$ 0 0
$$549$$ 12.4418 0.531003
$$550$$ 0 0
$$551$$ −11.3776 −0.484703
$$552$$ 0 0
$$553$$ 3.60173i 0.153161i
$$554$$ 0 0
$$555$$ 5.09790 3.17389i 0.216394 0.134724i
$$556$$ 0 0
$$557$$ 21.9292i 0.929172i −0.885528 0.464586i $$-0.846203\pi$$
0.885528 0.464586i $$-0.153797\pi$$
$$558$$ 0 0
$$559$$ 19.6511 0.831154
$$560$$ 0 0
$$561$$ −10.6212 −0.448429
$$562$$ 0 0
$$563$$ 34.2718i 1.44439i −0.691692 0.722193i $$-0.743134\pi$$
0.691692 0.722193i $$-0.256866\pi$$
$$564$$ 0 0
$$565$$ −9.78556 15.7176i −0.411682 0.661243i
$$566$$ 0 0
$$567$$ 2.69553i 0.113202i
$$568$$ 0 0
$$569$$ −4.05998 −0.170203 −0.0851015 0.996372i $$-0.527121\pi$$
−0.0851015 + 0.996372i $$0.527121\pi$$
$$570$$ 0 0
$$571$$ −21.7533 −0.910347 −0.455174 0.890403i $$-0.650423\pi$$
−0.455174 + 0.890403i $$0.650423\pi$$
$$572$$ 0 0
$$573$$ 14.3951i 0.601362i
$$574$$ 0 0
$$575$$ 4.48675 + 2.20661i 0.187110 + 0.0920219i
$$576$$ 0 0
$$577$$ 23.6094i 0.982872i 0.870914 + 0.491436i $$0.163528\pi$$
−0.870914 + 0.491436i $$0.836472\pi$$
$$578$$ 0 0
$$579$$ −4.02259 −0.167173
$$580$$ 0 0
$$581$$ 17.0681 0.708105
$$582$$ 0 0
$$583$$ 12.7991i 0.530083i
$$584$$ 0 0
$$585$$ 8.68939 + 13.9569i 0.359262 + 0.577046i
$$586$$ 0 0
$$587$$ 13.2321i 0.546146i −0.961993 0.273073i $$-0.911960\pi$$
0.961993 0.273073i $$-0.0880400\pi$$
$$588$$ 0 0
$$589$$ −1.77824 −0.0732713
$$590$$ 0 0
$$591$$ −0.137294 −0.00564750
$$592$$ 0 0
$$593$$ 8.85971i 0.363825i −0.983315 0.181912i $$-0.941771\pi$$
0.983315 0.181912i $$-0.0582287\pi$$
$$594$$ 0 0
$$595$$ 12.5032 7.78432i 0.512580 0.319126i
$$596$$ 0 0
$$597$$ 1.69670i 0.0694412i
$$598$$ 0 0
$$599$$ −8.01552 −0.327505 −0.163753 0.986501i $$-0.552360\pi$$
−0.163753 + 0.986501i $$0.552360\pi$$
$$600$$ 0 0
$$601$$ 24.3621 0.993752 0.496876 0.867821i $$-0.334480\pi$$
0.496876 + 0.867821i $$0.334480\pi$$
$$602$$ 0 0
$$603$$ 1.90940i 0.0777568i
$$604$$ 0 0
$$605$$ 14.5072 9.03199i 0.589801 0.367203i
$$606$$ 0 0
$$607$$ 36.5642i 1.48409i 0.670348 + 0.742047i $$0.266145\pi$$
−0.670348 + 0.742047i $$0.733855\pi$$
$$608$$ 0 0
$$609$$ 1.74768 0.0708197
$$610$$ 0 0
$$611$$ 1.00665 0.0407249
$$612$$ 0 0
$$613$$ 9.21498i 0.372190i 0.982532 + 0.186095i $$0.0595832\pi$$
−0.982532 + 0.186095i $$0.940417\pi$$
$$614$$ 0 0
$$615$$ −1.39318 2.23773i −0.0561784 0.0902338i
$$616$$ 0 0
$$617$$ 36.4154i 1.46603i 0.680213 + 0.733015i $$0.261887\pi$$
−0.680213 + 0.733015i $$0.738113\pi$$
$$618$$ 0 0
$$619$$ −34.3781 −1.38177 −0.690886 0.722963i $$-0.742780\pi$$
−0.690886 + 0.722963i $$0.742780\pi$$
$$620$$ 0 0
$$621$$ 4.57433 0.183561
$$622$$ 0 0
$$623$$ 6.96324i 0.278976i
$$624$$ 0 0
$$625$$ −15.2618 19.8010i −0.610471 0.792039i
$$626$$ 0 0
$$627$$ 9.03272i 0.360732i
$$628$$ 0 0
$$629$$ −20.4047 −0.813588
$$630$$ 0 0
$$631$$ 42.3309 1.68517 0.842584 0.538565i $$-0.181033\pi$$
0.842584 + 0.538565i $$0.181033\pi$$
$$632$$ 0 0
$$633$$ 20.5786i 0.817928i
$$634$$ 0 0
$$635$$ 12.4719 + 20.0323i 0.494931 + 0.794958i
$$636$$ 0 0
$$637$$ 19.7689i 0.783272i
$$638$$ 0 0
$$639$$ 1.78390 0.0705699
$$640$$ 0 0
$$641$$ 43.2608 1.70870 0.854349 0.519699i $$-0.173956\pi$$
0.854349 + 0.519699i $$0.173956\pi$$
$$642$$ 0 0
$$643$$ 2.36283i 0.0931809i −0.998914 0.0465905i $$-0.985164\pi$$
0.998914 0.0465905i $$-0.0148356\pi$$
$$644$$ 0 0
$$645$$ −9.91335 + 6.17193i −0.390338 + 0.243019i
$$646$$ 0 0
$$647$$ 21.9473i 0.862837i −0.902152 0.431418i $$-0.858013\pi$$
0.902152 0.431418i $$-0.141987\pi$$
$$648$$ 0 0
$$649$$ −17.3989 −0.682966
$$650$$ 0 0
$$651$$ 0.273151 0.0107056
$$652$$ 0 0
$$653$$ 34.7170i 1.35858i −0.733869 0.679291i $$-0.762287\pi$$
0.733869 0.679291i $$-0.237713\pi$$
$$654$$ 0 0
$$655$$ −14.9005 + 9.27687i −0.582211 + 0.362477i
$$656$$ 0 0
$$657$$ 17.1627i 0.669580i
$$658$$ 0 0
$$659$$ 23.1858 0.903192 0.451596 0.892223i $$-0.350855\pi$$
0.451596 + 0.892223i $$0.350855\pi$$
$$660$$ 0 0
$$661$$ −39.6148 −1.54084 −0.770418 0.637539i $$-0.779953\pi$$
−0.770418 + 0.637539i $$0.779953\pi$$
$$662$$ 0 0
$$663$$ 19.0511i 0.739882i
$$664$$ 0 0
$$665$$ 6.62010 + 10.6332i 0.256716 + 0.412338i
$$666$$ 0 0
$$667$$ 2.01596i 0.0780583i
$$668$$ 0 0
$$669$$ 8.37949 0.323970
$$670$$ 0 0
$$671$$ 10.1909 0.393414
$$672$$ 0 0
$$673$$ 30.3084i 1.16830i −0.811645 0.584152i $$-0.801427\pi$$
0.811645 0.584152i $$-0.198573\pi$$
$$674$$ 0 0
$$675$$ −20.5238 10.0937i −0.789963 0.388508i
$$676$$ 0 0
$$677$$ 9.26419i 0.356052i −0.984026 0.178026i $$-0.943029\pi$$
0.984026 0.178026i $$-0.0569711\pi$$
$$678$$ 0 0
$$679$$ −18.4419 −0.707736
$$680$$ 0 0
$$681$$ −8.65382 −0.331615
$$682$$ 0 0
$$683$$ 22.9835i 0.879439i 0.898135 + 0.439720i $$0.144922\pi$$
−0.898135 + 0.439720i $$0.855078\pi$$
$$684$$ 0 0
$$685$$ −10.9585 17.6016i −0.418705 0.672523i
$$686$$ 0 0
$$687$$ 4.28126i 0.163340i
$$688$$ 0 0
$$689$$ 22.9574 0.874606
$$690$$ 0 0
$$691$$ −27.2916 −1.03822 −0.519111 0.854707i $$-0.673737\pi$$
−0.519111 + 0.854707i $$0.673737\pi$$
$$692$$ 0 0
$$693$$ 4.06853i 0.154551i
$$694$$ 0 0
$$695$$ 35.1729 21.8982i 1.33419 0.830648i
$$696$$ 0 0
$$697$$ 8.95664i 0.339257i
$$698$$ 0 0
$$699$$ −13.3745 −0.505871
$$700$$ 0 0
$$701$$ 24.1308 0.911407 0.455704 0.890132i $$-0.349388\pi$$
0.455704 + 0.890132i $$0.349388\pi$$
$$702$$ 0 0
$$703$$ 17.3529i 0.654479i
$$704$$ 0 0
$$705$$ −0.507824 + 0.316165i −0.0191258 + 0.0119075i
$$706$$ 0 0
$$707$$ 7.90588i 0.297331i
$$708$$ 0 0
$$709$$ 15.0156 0.563922 0.281961 0.959426i $$-0.409015\pi$$
0.281961 + 0.959426i $$0.409015\pi$$
$$710$$ 0 0
$$711$$ 8.11802 0.304450
$$712$$ 0 0
$$713$$ 0.315080i 0.0117999i
$$714$$ 0 0
$$715$$ 7.11733 + 11.4319i 0.266173 + 0.427527i
$$716$$ 0 0
$$717$$ 3.38955i 0.126585i
$$718$$ 0 0
$$719$$ −29.4211 −1.09722 −0.548611 0.836078i $$-0.684843\pi$$
−0.548611 + 0.836078i $$0.684843\pi$$
$$720$$ 0 0
$$721$$ 16.7011 0.621981
$$722$$ 0 0
$$723$$ 5.80475i 0.215881i
$$724$$ 0 0
$$725$$ −4.44843 + 9.04510i −0.165211 + 0.335926i
$$726$$ 0 0
$$727$$ 47.8025i 1.77290i −0.462829 0.886448i $$-0.653166\pi$$
0.462829 0.886448i $$-0.346834\pi$$
$$728$$ 0 0
$$729$$ −5.91080 −0.218918
$$730$$ 0 0
$$731$$ 39.6788 1.46757
$$732$$ 0 0
$$733$$ 44.0763i 1.62800i 0.580867 + 0.813998i $$0.302714\pi$$
−0.580867 + 0.813998i $$0.697286\pi$$
$$734$$ 0 0
$$735$$ 6.20892 + 9.97276i 0.229019 + 0.367851i
$$736$$ 0 0
$$737$$ 1.56396i 0.0576091i
$$738$$ 0 0
$$739$$ −3.75235 −0.138032 −0.0690162 0.997616i $$-0.521986\pi$$
−0.0690162 + 0.997616i $$0.521986\pi$$
$$740$$ 0 0
$$741$$ −16.2018 −0.595187
$$742$$ 0 0
$$743$$ 19.6859i 0.722205i −0.932526 0.361103i $$-0.882400\pi$$
0.932526 0.361103i $$-0.117600\pi$$
$$744$$ 0 0
$$745$$ 44.8415 27.9178i 1.64287 1.02283i
$$746$$ 0 0
$$747$$ 38.4703i 1.40755i
$$748$$ 0 0
$$749$$ 10.6626 0.389604
$$750$$ 0 0
$$751$$ −26.3594 −0.961868 −0.480934 0.876757i $$-0.659702\pi$$
−0.480934 + 0.876757i $$0.659702\pi$$
$$752$$ 0 0
$$753$$ 5.08902i 0.185454i
$$754$$ 0 0
$$755$$ 36.5357 22.7467i 1.32967 0.827837i
$$756$$ 0 0
$$757$$ 11.9270i 0.433493i −0.976228 0.216747i $$-0.930455\pi$$
0.976228 0.216747i $$-0.0695446\pi$$
$$758$$ 0 0
$$759$$ 1.60047 0.0580935
$$760$$ 0 0
$$761$$ 1.03123 0.0373821 0.0186911 0.999825i $$-0.494050\pi$$
0.0186911 + 0.999825i $$0.494050\pi$$
$$762$$ 0 0
$$763$$ 8.27886i 0.299715i
$$764$$ 0 0
$$765$$ 17.5453 + 28.1812i 0.634351 + 1.01889i
$$766$$ 0 0
$$767$$ 31.2080i 1.12685i
$$768$$ 0 0
$$769$$ 3.37170 0.121587 0.0607933 0.998150i $$-0.480637\pi$$
0.0607933 + 0.998150i $$0.480637\pi$$
$$770$$ 0 0
$$771$$ 15.0215 0.540986
$$772$$ 0 0
$$773$$ 33.0031i 1.18704i −0.804819 0.593520i $$-0.797738\pi$$
0.804819 0.593520i $$-0.202262\pi$$
$$774$$ 0 0
$$775$$ −0.695259 + 1.41369i −0.0249744 + 0.0507811i
$$776$$ 0 0
$$777$$ 2.66553i 0.0956255i
$$778$$ 0 0
$$779$$ −7.61708 −0.272910
$$780$$ 0 0
$$781$$ 1.46116 0.0522844
$$782$$ 0 0
$$783$$ 9.22166i 0.329555i
$$784$$ 0 0
$$785$$ −7.81395 12.5508i −0.278892 0.447956i
$$786$$ 0 0
$$787$$ 7.29525i 0.260048i 0.991511 + 0.130024i $$0.0415054\pi$$
−0.991511 + 0.130024i $$0.958495\pi$$
$$788$$ 0 0
$$789$$ 17.0631 0.607463
$$790$$ 0 0
$$791$$ 8.21823 0.292206
$$792$$ 0 0
$$793$$ 18.2791i 0.649110i
$$794$$ 0 0
$$795$$ −11.5812 + 7.21033i −0.410744 + 0.255724i
$$796$$ 0 0
$$797$$ 32.1730i 1.13963i −0.821775 0.569813i $$-0.807016\pi$$
0.821775 0.569813i $$-0.192984\pi$$
$$798$$ 0 0
$$799$$ 2.03260 0.0719082
$$800$$ 0 0